International Fans – Loyal to the Player or Loyal to the Team?

So, I have a bit of a dilemma. This blog is, obviously, primarily statistical in nature. However, my ideas for statistical analysis tend to be a bit few and far between – too much so to really carry a real blog.

So, I’m introducing a category called “Little White Lies”, which are regular blog entries, minus the heavy statistical slant. Don’t worry, this blog will still be grounded in statistics, but it’ll be nice to not have to run a database full of numbers for each post.

Introducing this idea is a post on a growing trend I’ve noticed in the NBA. Traditionally, fans are theoretically fans of teams. They debate their team, they discuss their team, and they cheer for players on their own team. There are exceptions of course, but in general, you’re a fan of a team.

With the growing influx of international players, there’s been a notable trend that bucks this traditional framework. Fans from that player’s home nation overwhelmingly favor the team that their player plays on. This isn’t a groundbreaking idea – survey China for their favorite NBA team and every single person will cite the Rockets or Nets (naturally I don’t have a poll to back this up or else that note at the top wouldn’t be necessary).

Now, there’s nothing wrong with this at this level. Fans want their player to succeed, and success in the NBA is typically defined by the ultimate team accomplishment: a championship. And this idea most cetainly exists in the United States as well. Atlanta Falcons rookie quarterback Matt Ryan recently played in Philadelphia, his hometown, and had a strong show of support from the Philadelphia fans. Local fans tend to cheer for local players, even if the player is not playing for a local team.

The international audience adheres to this concept, but hyper-charges it. We’re not talking about Carlos Boozer’s 30,000-citizen hometown. We’re not even talking about Allen Iverson’s home of Hampton, Virgnia and its 150,000 citizens. We’re talking about entire countries – China’s 1.3 billion people are an obvious example, but don’t forget other countries, like Argentina’s 40 million. These are entire countries lining up behind single players.

The country label carries a greater inherent strength to it as well. It’s the country that appears in place of your college, the flag you wrap around your waist, and the country you play for in the offseason. In many cases, it’s even the origin of your name. I can’t say for certain, but I don’t anticipate many NBA fans outside Virginia (or maybe even in Virgnia) knew that Allen Iverson hailed from there. But I’d be hard-pressed to find a semi-interested NBA fan that doesn’t know that Manu Ginobili comes Argentina, or even any American that doesn’t know that Yao Ming comes from China.

The connection is similar to American towns’ allegiance to their players, but blown incredibly out of proportion. These are entire countries of tens of millions people, uniting behind a player who is indelibly stamped with the name of their home country. Every player carries come contingent of fans that supports their player over anything else – their family, their hometown, their friends. But international players carry entire nations’ worth.

What am I getting at? I have no problem with nations cheering for individual players. It’d be ridiculous to expect China to continue to care about the Bucks right now after they traded Yi. The problem, however, comes in those instances where the interests of a particular player conflict with the interests of the team they plan on.

My example of what I mean comes from my tendency to frequent Spurs-related forums. There is a huge proportion of Spurs fans from Argentina that only care about the team because of Manu Ginobili (and to a lesser extend, Fabricio Oberto – but Manu is clearly the focus). I’ve spoken with Argentinean fans that hate – yes, hate – Gregg Popovich for not starting Manu. Most analysts state-side, while perhaps not completely agreeing with his decision to bring Manu off the bench, can at least see the value in it. But there’s a contigency of Argentinean fans that consider it a personal affront to Manu to bring him off the bench.

This is where the conflict lies and true colors show. As far as his personal fame, success and legacy, it would probably be better for Manu to start. He’d easily be one of the league’s leading scorers and would likely be a shoe-in for the All-Star team. However, that may not be what’s best for the Spurs franchise.

The problem goes further than that. When the team isn’t successful, there is a tendency among international fans of their hometown player to lay the blame everywhere else but on their own player. The front ofice, the coach, the other players – but their home player is infallible.

I’m treading on light territory here, so let me pause and say that I am not implying for the slightest second that all international fans fall into this category – that is most certainly not the case. But there is a large, vocal contigent of fans behind every international player that, when you get down to it, is more a fan of their player than of the team they play for.

If the relationship isn’t clear yet, let’s consider an analogy: marriage, putting two entire families together on account of a single pairing. The pairing of a team’s fans and a new international player’s fans is similar. They deal amicably and they rejoice at the couple’s happiness. But if things go south in the couple, the particular circumstances become irrelevant – each family sides with their member.

Fortunately, in most circumstances, the fans have little or no impact on the actual team. But that’s the crucial note: in most circumstances. There do come circumstances, rare as they are, where fan desires actually impact the decisions made. Think Yi Jianlian and the Bucks – it was pressure from the Chinese government, itself essentially a really powerful fan, that caused the Bucks to cave and promise Yi playing time as a rookie. And if we venture outside the NBA for a moment, recently it was fan pressure that caused the Cleveland Browns to switch quarterbacks.  Fan pressure does occassionally influence the decisions by the franchise. It shouldn’t be that way, but at the end of the day, the NBA’s a business and ticket sales, merchandise and TV contracts rule.

My prediction is there’s going to come a day when somehow, some way, international fans of a particular player are going to affect a team’s decision-making in a significant way, and there’s going to be consequences. It’s going to change the way NBA teams do business with international players. Teams are going to become more and more skeptical of the worth in dealing with a player’s international baggage in exchange for their play. Or, teams are going to see the marketing value associated with international players and make concessions for the sake of profit. Either way, it’s not a good result.

So all I can say is that international fans, take a long look at what you’re supporting. Ask yourself, if my player was traded would I still care about his current team? If the answer is no, that’s perfectly fine – but please, for the sake of the league, stay out of the coach’s, front office’s, and others players’ business. Yes, they’re doing what’s best for the franchise, not what’s best for your player – that’s what team sports are. If you persist in allegiance to your player above and beyond the team’s best interest, all you’ll end up doing is hurting the player, the team and the league in general.

November 24th, 2008, posted by joyner

Kobe Bryant’s “High-Volume Shooting”: Wrap-Up

Alright, let’s wrap this puppy up. It’s been way too long. This post will summarize everything we’ve done, so if you don’t want to read the pages and pages I’ve written, you won’t miss the conclusions: just the reasoning.

Why were we doing this all again? Oh yeah, because a few months ago, Christopher Reina made the claim that the Lakers are a better team when Kobe isn’t a “High Volume Shooter”. His reasoning was simple: the Lakers were 26-18 when Kobe took 20 or more, but 31-7 when he took 19 or less. Pretty straight-forward, right?

The fellas at Ball Don’t Lie subsequently slammed the analysis for a variety of reasons – mostly, not considering the game situation, and for drawing such an arbitrary cut-off. Their analysis, however, wasn’t backed by any numbers, so it was really a matter of one blog’s opinion against another.

So, what we’ve been trying to do is put better numbers behind both of those blogs’ conclusions. And once we did, it became pretty clear that Ball Don’t Lie is right, while Christopher Reina was wrong (sorry, Chris).

First of all, it’s true that Kobe averages more shots in losses than wins – four more shots per loss than per win. It’s also true, however, that Kobe averages more minutes in losses then wins – by about 4 minutes. With his shooting rate (a bit under 22 shots/game overall), that difference automatically accounts for about 2 shots per game, meaning that – balanced for minutes – Kobe averages closer to 21 shots per game in losses. That pretty much immediately throws out the 20-shot cut-off used by Reina. But, that’s still more shots per game in losses then wins.

Then we considered the fact that blowouts are special instances in which Kobe’s statistics are drastically off. 18 times during the season, the Lakers blew out their opponents by more than 12 points while Kobe played below-average minutes. Only one time were the Lakers blown out in similar fashion with Kobe playing below-average minutes. Averaging without those games, we discover the same thing we discovered above: that Kobe only averages 2 shots less per win than per loss.

But why 2 shots more per loss? Well, we then proceeded to go way too in-depth into individual games to discover when Kobe’s shot attempts increased, and we discovered something interesting. Kobe’s shot attempts and the Lakers’ corresponding winning percentage fell quite plainly into three categories. When Kobe takes less than 17 shots, the Lakers were 9-1. When Kobe took 18 to 28 shots, the Lakers were 28-19. When Kobe took 29 or more, the Lakers were 2-4. Note that these aren’t arbitrary cut-offs like the 20-shot cut-off, but rather they’re cut-offs where the change in the Lakers’ fortunes is most evident. And note that these divisions are not including that special case, blowouts where Kobe plays below-average minutes.

With those categories in mind, there are only two options: either (a) Kobe’s increasing shot attempts are causing the Lakers’ fortunes to change, or (b) some third variable is causing both Kobe’s shot attempts to increase and the Lakers’ fortunes to change. If (b) is true, there should be characteristics that group together all the games in each category.

And, upon examining the games quite closely, such characteristics do emerge. In the games where Kobe takes 17 or less shots, the Lakers are nearly never even challenged. They get an early lead and never relinquish it. Several of these games are blowouts where Kobe still plays his average number of minutes, but the important thing is that the Lakers are really never challenged.

In the games where Kobe takes 18 to 28 shots, the Lakers are almost always challenged. Sometimes they jump out to an early lead but have their opponent come back. Sometimes they fall behind early and comeback. Sometimes the game is close before the Lakers (or, rarely, the opponents) pull away. And sometimes the game is just close throughout. But the point is, all these games are united by one fact: the Lakers are challenged.

And within those games, we discover something very interesting. There are definite particular instances when Kobe’s shot attempts increase. More often than not, it’s in the second half, sparking either a comeback or a run to seal the game. But in a general sense, it’s when the Lakers are most challenged and most at risk for letting the game slip away. In these instances, Kobe becomes more aggressive and shoots more – and often succeeds in shooting the Lakers back into the game.

And in that final category, where Kobe shoots 29 shots or more and the Lakers are 2-4, we observe an extremely clear pattern: Kobe is the only offensive weapon. Gasol played in none of these games, and Bynum played in only one. And, like in the previous categories, these are all games where the Lakers were at risk of losing.

So, we’ve noticed a pattern, an answer to the (b) from a few paragraphs up. The “third variable” is how much the Lakers are challenged. In games where they aren’t challenged, they overwhelmingly win – an obvious conclusion, since they aren’t challenged. In games where they are challenged, they don’t win as often. This isn’t a revolutionary concept: they’re more likely to lose games where their competitor actually competes and plays well. That’s quite simple. And in games where they’re challenged and don’t have two of their top three offensive weapons, they lose even more often. Again, not a revolutionary concept.

This third variable is also what causes Kobe’s shot attempts to increase. As the best player on his team, the primary offensive weapon, and the ultimate competitor, he will tend to see more shots when his team is threatened. In games where they aren’t, there isn’t the need for him to be as aggressive. In games where they are, his aggressiveness and shot attempts increase. And in games where they’re threatened and there are no other options, his shot attempts increase even more.

The problem with the initial study conducted by Reina was misplaced causation: he suggested that Kobe’s high-volume shooting caused the Lakers’ fortunes to drop, but in reality it was the risk of the Lakers’ fortunes dropping that caused Kobe’s shooting volume to increase. Had Kobe restricted himself to the same shot counts in those games where the Lakers were challenged, it is reasonable to assume the Lakers would have lost more because oftentimes, it was Kobe’s shooting that sparked Lakers comebacks. His higher-volume shooting didn’t cause the Lakers’ fortunes to drop – it caused the Lakers’ already-dropping fortunes to not drop as far.

LITTLE WHITE TAKEAWAYS

The Lakers are not better off when Kobe doesn’t shoot as much, despite him averaging fewer shots in wins than losses. Instead, The Lakers depend on Kobe to lift them over their opponents in competitive games. Therefore, Kobe’s shot attempts increase in competitive games compared to non-competitive games. Naturally, the Lakers also are more likely to lose competitive games than non-competitive games.

The proof for this can be observed in a variety of ways. First of all, in most of the games where Kobe’s shot attempts are elevated, the Lakers are challenged at some point; on the other hand, in most of the games where his attempts are not elevated, the Lakers are never challenged.

What’s more, the actual increase in his shot attempts is observed typically in the second half, and typically sparks either a Lakers comeback (if the opponent leads) or a Lakers run to seal a win (if the game was close). Because these increases are typically observed in the second half, it is completely unreasonable to say that the increased attempts caused the Lakers’ misfortunes in the first place.

In short, the Lakers are more likely to lose competitive games, and Kobe shoots more in competitive games to try to prevent that. The competitiveness of the game causes both the Lakers’ lower winning percentage and Kobe’s increased shot count. Kobe’s shot count does not cause the Lakers’ lower winning percentage in those games.

October 22nd, 2008, posted by joyner

Kobe Bryant’s “High-Volume Shooting”: Part 6

Apologies for the delay – I started graduate school this past month, and I’ve had precious little time to write. But things are started to calm down, so hopefully we’ll be able to wrap up these two studies (Kobe Bryant’s “High-Volume Shooting” and the Box Score Analysis) before the season started in a couple weeks, and then we’ll try to introduce a weekly or bi-weekly feature.

But for now, it’s time to wrap this up. We’ve discussed how Kobe Bryant doesn’t play as much traditionally in Lakers’ blowouts, thus lowering his shot attempts. We’ve discussed how, even in blowouts where Kobe plays just as much, his shot total is lower. And we’ve discussed how, time and time again, Kobe’s shot attempts go up when his team is threatened: either in the event of an opposing team’s comeback, or when the Lakers trail and are running out of time to start a comeback, or in the waning seconds of a close game.

But now let us consider one more type of game: games where Kobe took drastically more shots than his season average. Six times during the season, Kobe took 30 or more shots in a single game – 30 twice and 32, 33, 37 and 44 once each. In these games, the Lakers were 2-4 – winning in Kobe’s 30- and 44-shot games and losing in the others. So, what prompted Kobe to take so many shots in these games?

Analyzing these games in the detail we’ve used previously is a bit silly considering that Kobe’s shot attempts are pretty high throughout the game, so instead let’s look at the overall storyline of each game and try to figure out subjectively what prompted his high shot total.

  • March 23rd: Golden State 115, Lakers 111: Kobe goes 13/30 from the field, 3/9 from 3 and 7/7 from the line for 36 points, along with 14 rebounds and 8 assists. In this game, the Lakers play with a very short rotation (8 players play, no Bynum and no Gasol), and only half of those 8 players actually play well (6/19 for Odom though he does bring in 22 rebounds, 3/8 for Radmanovic, 0/5 for Vujacic, 3/10 for Farmar). The Lakers fall behind in the second quarter and trail by as much as 26 before mounting a furious and almost-successful comeback. 18 of Kobe’s 30 FGAs come during this attempted comeback – his first-half shot total (when the Lakers fell behind) matched his season average.
  • March 24th: Lakers 123, Golden State 119: Second verse, same as the first. The Lakers play the same team the next day, fall behind around halftime (though not by as much, maximum of 13 points), and comeback. Same short rotation, and still no Gasol or Bynum. And this time, they win in overtime. And, almost identically to the game the day before, Kobe’s shot total while the Lakers fall behind is only slightly above his season average (12 shots for the first half), while his shot total is higher while the Lakers come back and win (18 shots).
  • October 30th: Houston 95, Lakers 93: First game of the season, and still follows the same framework of these first two. Lakers fall behind (in the 3rd and early 4th this time, by a maximum of 13) and come back later. At first glance it doesn’t appear that his shot attempts go up significantly during the late comeback (9 shots in the comeback which spans the last 10 minutes, 32 for the game, so only a moderate increase), but if one counts the times Kobe is fouled in the act of shooting as shot attempts (which, in my opinion, they really should), that total shoots up to 15, while his total for the game (when counting the entire game this way) shoots up to 45 – meaning a third of his shots take place during a fifth of the game, when the Lakers come back. (in retrospect, I should’ve calculated ‘true FGA’ for every game we’ve analyzed, but we’ve considered it already when relevant)
  • March 16th: Houston 104, Lakers 92: Two against the Warriors, now two against the Rockets. This game was the final win in Houston’s remarkable 22-game winning streak. You might also know that it falls within that same date range as those earlier Warriors games, which means that Gasol and Bynum were on the sidelines. Like the other three games, this game saw the Lakers fall behind (max of 15) and then come back, although in this instance the Rockets did pull away at the end. In this particular case, his shots actually fell evenly across the two halves (17 in the first, 16 in the second). However, 13 of those first-half shots came while the Lakers were still within 4 points – it wasn’t until Kobe’s shots dropped off in the first half that the Rockets pulled away.
  • March 28th: Memphis 114, Lakers 111: You probably saw this coming – yet another game in that group of games where the Lakers were without Gasol and Bynum. The rest of the Lakers should’ve sat the came out too: of the 10 players who played, only two shot at or above 45%: Bryant and Mbenga, who was 2/3. The rest of the team combined to shoot a dismal 20 for 64 for 31%. Bryant’s 19/37 shooting elevated the team’s number substantially. Kobe’s shot distribution was fairly even for the game: 12 shots in the 1st, 10 in the 2nd, 9 in the 3rd and 6 in the 4th. The drop-off in the 4th quarter can be attributed mostly to Memphis finally realizing that Kobe was the only one who showed up to play and devoting even more defensive attention to him, as the 4th quarter is littered with shots that would’ve been Kobe assists if his teammates had actually hit the shots.
  • January 14th: Lakers 123, Seattle 121: Lakers fans know this game as the game after Bynum went down with his season-ending injury – so, like the previous games, this was one of the Lakers’ games with no Bynum or Gasol. Vujacic and Radmanovic sat out as well, although the rest of the Lakers (excepting Odom’s 3/15 performance and Walton’s 1/6 debacle) played quite well, with Brown, Fisher, Ariza, Farmar, Turiaf and Crittenton – yes, Crittenton – each shooting at or above a 50% clip (although none attempted more than 6 shots). Despite their play, the Lakers still fell behind by 10 early in the 4th quarter. As for Kobe, he shot at a high clip throughout the game, (11 FGA in the 1st, 7 in the 2nd, 12 in the 3rd), but as usual, a disproportionately high number of his shots (12 over 10 minutes) came during the Lakers’ comeback in the final 5 minutes of regulation and overtime. That’s 27% of his shots being contained in 18% of the game.
  • So, we uncovered a nice little pattern amongst these games. First of all, five of the six games (excepting Houston on October 30th) are played without Gasol or Bynum, while none of the games feature Gasol at all (two before the trade, four during his late-season ankle injury). Five of the six (excepting Memphis) games also saw the Lakers behind by double-digits in the second half, a very rare occurrence for the season, though commonplace amongst this sampling of games. And, five of the six games (excepting Memphis) also saw Kobe’s shot attempts increase during the Lakers’ comebacks.

    That’s a pretty clear correlation: Kobe’s six highest FGA games come when Gasol and Bynum don’t play, and when the Lakers are threatened.

    LITTLE WHITE TAKEAWAYS


    For the six games where Kobe takes drastically more shots than his season average (30 shots or more while he averages 21.44 in non-blowouts), there are three very clear criteria that each take place in at least five of the six games: first, the Lakers are playing without Gasol or Bynum; second, the Lakers fall behind by double digits at some point during the second half; and third, the Lakers come back – in every single game – to make it competitive, while Kobe’s shot attempts increase during the comeback.

    It’s a very match between these criteria and the games. The lack of the Lakers’ other offensive weapons will obviously lead Kobe to shoot more, and that the Lakers are threatened at some point has been shown in our study to lead to an increase in Kobe’s shot attempts. And, as we’ve seen, when Kobe’s shot attempts go up, the Lakers come back.

    Considering how large this analysis has been, I’ll be posting a wrap-up summary post in the next couple days to re-state our conclusions. And it won’t be another month and a half this time, I swear.

October 15th, 2008, posted by joyner

Kobe Bryant’s “High-Volume Shooting”: Part 5

Here we are again, hopefully finishing up analyzing this batch of games this time. You know the drill, so let’s get right to it.

By the way, we’re trying out a new spam filter over here – if you post a comment that doesn’t show up within a day or two, shoot me an e-mail.

Lakers lead, then their opponent comes back

The second most common type of Laker game (12 occurrences) this season (within the 18 to 28 shot range for Kobe) saw the Lakers pull away to a lead, then their opponent come back. Typically after that (9 times) the game remained close, while twice the Lakers pulled away and once the opponent pulled away.

  • January 6th: Lakers 112, Pacers 96; Lakers pull away three times, Pacers come back twice
    • Critical Points: 1st Quarter, Lakers 21-9 run; 2nd Quarter, Pacers 21-4 run; 3rd Quarter, Lakers 27-12 run; 4th Quarter, Pacers 13-2 run; 4th Quarter, Lakers 20-8 run
    • Kobe During Critical Points: 2/3 for 6 points, 2 rebounds, 1 assist, 1 steal; 0/3 for 2 points; 4/6 for 12 points, 1 assist; 0/0 for 0 points; 2/4 for 4 points, 1 steal, 3 assists
    • Kobe’s Other Shots: 0/3 in 1st, 0/2 in 2nd, 0/0 in 3rd, 0/0 in 4th
    • Summary: This is an odd game to analyze because the majority of the game was a run for either team – the entire first quarter (though we didn’t consider the Pacers’ opening 9-0 run), the vast majority (10 of 12 minutes) of the second quarter, the entire third quarter, and the entire fourth quarter (first half of it for the Pacers, second half for the Lakers). So while some of the shot attempts above seem high (like Kobe’s 0/3 during the Pacers’ 2nd quarter run), you have to remember that’s over nearly the entire quarter, and is substantially below his season average. Overall, we again see Kobe’s output increase during Laker runs: 8/13 during Laker runs, 0/3 during Pacer runs, and 0/5 otherwise.
  • January 23rd: Lakers 91, Spurs 103; Lakers pull away in 1st half, Spurs come back and pull away in 3rd
    • Critical Points: 2nd Quarter, Lakers 16-7 run; 3rd Quarter, Spurs 14-0 run; 3rd Quarter, Lakers 10-2 run; 3rd Quarter, 18-5 Spurs run
    • Kobe During Critical Points: 1/2 for 2 points, 2 assists; 0/5 for 0 points; 3/4 for 7 points, 1 assist, 2 rebounds; 1/1 for 2 points
    • Kobe’s Other Shots: 4/6 in 1st, 2/4 in 2nd, 0/0 in 3rd, 2/6 in 4th
    • Summary: You always have to be wary in generalizing the results from Spurs’ games – I know I’m biased, but the Spurs really are one of the greatest defensive teams around. This game is also unique in that unlike the general trend of the Lakers’ season, in this game, Kobe was the only one who really showed up. Only 8 Lakers scored, only 4 in double figures and only Kobe above 20. That said, this game still carries some of the indicators we’ve been looking for, most notably in the Lakers’ quick mini-burst in the 3rd quarter. Here we see the idea of Kobe coming alive to stop an opponent’s run. It’s arguable that he was trying to fend off the Spurs throughout their 3rd quarter comeback, but regardless it’s apparent that when Kobe started hitting his shorts, the Lakers got back in the game. In this particular instance, the Lakers’ fortunes were tied directly to Kobe, and thus he put them on his shoulders and tried to deliver the win. Against a team like the Spurs, he couldn’t do it alone.I’d like to pause here for a moment and point out how this relates to the very original study we’re referring to. The original idea was that when Kobe shoots too much, his team loses – so he shouldn’t shoot so much. This game is the perfect example of why that isn’t true. When Kobe shoots too much, it’s because his team isn’t getting the job done. In this particular game, his teammates hardly did anything – and as such, Kobe was forced to take more shots. Kobe taking more shots is indicative of him needing to take more shots. It’s not causing his team’s misfortunes, the Lakers are simply more likely to lose in situations where Kobe is forced to shoot more (meaning his team is being threatened). Kobe shoots less in games where the Lakers are never threatened, and if the Lakers are never threatened, they’re far less likely (obviously) to lose.

      In my opinion, the thesis has been proven and there’s no real reason to go ahead. But for the sake of argument, let’s run through a couple more games of different types just to make sure it holds true. In case you’re not aware, when I write, I don’t go back and change anything – this writing is as if you’re sitting on my shoulder watching me discover it as I go along.

  • March 18th: Lakers 102, Mavericks 100; Lakers build a huge lead, Mavs mount an incredible comeback
    • Critical Points: Lakers 52-30 run (Lakers’ lead built too steadily from the end of the 1st to the middle of the 3rd to identify smaller runs); Mavericks 23-3 run (3rd and 4th quarters); 4th Quarter, Mavericks 22-12 run
    • Kobe During Critical Points: 6/12 for 15 points, 7 assists; 1/2 for 2 points; 1/3 for 3 points
    • Kobe’s Other Shots: 4/5 in 1st, 0/0 in 2nd, 0/0 in 3rd, 0/0 in 4th
    • Summary: Crazy game, Mavericks come back from 25 down to lose by only 2. Kobe actually sat on the bench during the early part of their comeback run, coming back in to try to fend them off. It appears it wasn’t needed though; his teammates took care of it for him, though it would’ve been nice to see Kobe take a few more shots near the end. That’d further confirm our thesis, but its absence would have to be systematic to threaten it – and so far this is the first instance of it we’ve seen.
Other miscellaneous games

While those two categories make up the majority of the games we’re analyzing, it’s important to touch on the other categories too. The Lakers did have games where they found themselves initially down and had to come back, and they did have games where the opponent just outright pulled away.

  • March 4th: Lakers 117, Kings 105; Kings lead throughout, Lakers come back in the fourth
    • Critical Points: 2nd Quarter, Kings 11-0 run; 4th Quarter, Lakers 27-7 run
    • Kobe During Critical Points: 0/3 for 0 points; 3/4 for 17 points (11/12 FT)
    • Kobe’s Other Shots: 1/4 in 1st, 3/3 in 2nd, 4/10 in 3rd, 0/2 in 4th
    • Summary: I was hoping a game like this would come up (remember, I’m choosing these games randomly within the representative categories to ensure statistical validity – although the rules apply oddly in this case considering it’s trends we’re subjectively observing, not straight-up numbers). This game exemplifies an idea I believed, but had not yet observed: is it really Kobe’s shot attempts that go up when his team is challenged, or is it his overall aggressiveness, and the increase in shot attempts is the most numerically observable indicator of this? Here we see it’s really his overall aggressiveness, getting to the line 12 times in the final quarter, keying the Lakers’ pivotal run. The 3rd quarter is notable as well; while we don’t see the Lakers making a run, we do see both teams performing well offensively (57 combined points in the quarter). The downside to using ‘runs’ to analyze a player’s offensive productivity is that if the opposition equals his offensive productivity, then no run occurs despite the player’s heightened performance. Here we see Kobe keying a run, but Sacramento’s offense matches him stride for stride – but note that if Kobe hadn’t increased his output, it likely would’ve been a Sacramento run. The time of the game is notable here: our idea that Kobe increases his offensive output when his team is threatened naturally needs a definition of ‘threaten’, and in this case it needs to note that he responds better in the second half than in the first. Thus, an opponent’s equal performance in the first half and second half will result in different responses from Kobe Bryant.

      Overall, once again, the trend holds true for this game. Kobe is needed, so Kobe attempts to deliver (and succeeds, in this case).

  • April 8th: Lakers 103, Blazers 112; Blazers pull away in 2nd
    • Critical Points: 2nd Quarter, Blazers 19-7 run
    • Kobe During Critical Points: 1/6 for 2 points
    • Kobe’s Other Shots: 2/5 in 1st, 2/7 in 2nd, 4/7 in 3rd, 4/8 in 4th
    • Summary: And we’ll close with one of those games every team has. Sometimes even when you do everything right, the ball just doesn’t bounce your way. During a key stretch in the 2nd quarter, Kobe went cold, allowing the Blazers to build a lead that they were able to carry throughout. Throughout the second half, Kobe responds – as we know by now that he will – increasing his offensive output to try to counter the threat, but as in the 3rd quarter of the above Kings game, all the offense in the world can’t help you if the other team’s hitting their shots too. Kobe went for 24 points in the 2nd half and had assists on 10 more, (giving him a role in 34 of the Lakers’ 56 second-half points, a staggering proportion). It wasn’t enough in this case, but the trend, once again, holds true.

It’s pretty rare for a trend to be this explicit. Kobe’s shot attempts reliably go up when his team is threatened, to the point where you can almost pick the point in the game where he goes off without every looking at the box score. For those still a bit confused as to why this study is valid, remember we’re choosing the ‘runs’ based solely on the game progression, without every looking at the individual players’ contributions. So, when we see a single player’s contributions rising whenever there’s a run, we know there must be a correlation between the two.

Only one part left in this study, and then a great big wrap-up post. Next time we’ll look at those 6 games where Kobe attempts 29 or more shots – more than 9 above his season average. Since there are only 6, and since in order to attempt 29 shots he essentially has to be shooting the entire game, we’ll likely look at the characteristics of the games that lead to him shooting more. Then we’ll wrap up this study, then we’ll revisit the Box Score Analysis and look at individual teams’ performances in different quarters, and then maybe we’ll get around to looking at some of the things y’all have requested a look at.

August 27th, 2008, posted by joyner

Kobe Bryant’s “High-Volume Shooting”: Part 4

Like I said last time, in this we’re going to choose some representative games from the “Kobe took 18 to 28 shots” group of games. In these games, the Lakers were 28-19 – a winning percentage of .595, down from .900 in the “under 17 shots” category.

To analyze some ‘representative’ games, first we want to see what patterns are frequent in these 47 games that saw Kobe take between 18 and 28 shots. This is a pretty broad range, but it’s not arbitrary: nearly all the winning percentages connected to a certain number of shots in this range (that is, the Lakers’ winning percentage when Kobe takes that many shots) fall in the .5 to .75 range; the only exceptions are 18 shots (winning percentage .333), 21 shots (.400) and 28 (1.000). This is distinct from the other two ranges of shots, but there’s no distinction within this range.

So, what do we observe within this range? 5 distinct trends, with subtrends (which could pretty much encompass any game, really) – the number in parentheses represents how often that particular type of game happened, in games where Kobe took between 18 and 28 shots:

  • The Lakers trail, then come back (6).
    • The Lakers then pull away (2).
    • The opponent then pulls away (1).
    • The game remains close until the end (3).
  • The Lakers lead, then their opponent comes back (12).
    • The Lakers then pull away (2).
    • The opponent then pulls away (1).
    • The game remains close (9).
  • The game stays close, then the Lakers pull away (no opponent comeback) (13).
    • The Lakers pull away in the 1st quarter and hold that lead (3).
    • The Lakers pull away in the 2nd quarter and hold that lead (1).
    • The Lakers pull away in the 3rd quarter and hold that lead (4).
    • The Lakers pull away in the 4th quarter and hold that lead (5).
  • The game stays close, then the opponent pulls away (no Laker comeback) (8).
    • The opponent pulls away in the 1st quarter and holds that lead (2).
    • The opponent pulls away in the 2nd quarter and holds that lead (2).
    • The opponent pulls away in the 3rd quarter and holds that lead (3).
    • The opponent pulls away in the 4th quarter and holds that lead (1).
  • The game is back-and-forth throughout (8).
    • The game is close throughout (neither team takes a substantial lead) (4).
    • Each team takes a substantial lead at some point, losing it – the game is close at the end (4).

Now, there’s a lot of interesting stuff here. So rather than go in-depth on a small sample of games (like the last portion as the analysis), we’re going to ask two questions about several of the games: (a) where is Kobe during the ‘critical points’ of the games (when the either team pulls away or comes back), and (b) when do most of his shot attempts come? If our hypotheses from earlier in the analysis hold up, we should find that Kobe’s shot attempts increase at these specific, critical times. You may have noticed we’re still not including blowout victories where Kobe plays below-average numbers of minutes, but remember we’re also only looking at games where Kobe attempted between 18 and 28 shots – thus the excluded games wouldn’t be included in this group anyway (given that Kobe nearly never attempts more than 18 shots in a blowout below-average-playtime game).

At first it’s a bit difficult to see what we’re looking for in the below analysis, so in general, we’re choosing the Lakers’ ‘critical points’ in the game (before ever looking at who was involved in the run) and then seeing if Kobe’s shot attempts increased over that time period compared to the rest of the game. Because Kobe’s shot behavior doesn’t impact what we’re choosing as runs, observing increased shot activity from him should indicate that his increase in shot attempts are correlated to Lakers’ runs. There’s more than this, but this is the core of what we’re looking for.

Game stays close, then the Lakers pull away

Let’s start with the most common type of game from the Lakers’ season. 13 times during the 07-08 season, the Lakers found themselves in a fairly close game, only to eventually pull away and win. 4 times this happened in the first half (three times in the first quarter, once in the second), 9 times it happened in the second half (four times in the third quarter, five in the fourth). These games:

  • December 16th: Lakers 113, Clippers 92; Lakers pull away in the first quarter
    • Critical Points: 1st Quarter, Lakers 23-5 run
    • Kobe During Critical Points: 5/8 for 11 points, 5 rebounds, 1 steal, 1 turnover
    • Kobe’s Other Shots: 0/1 in 1st, 2/3 in 2nd, 1/4 in 3rd, 3/4 in 4th
    • Summary: As expected, Kobe’s shots are up during the run, low otherwise
  • December 23rd: Lakers 95, Knicks 90; Lakers pull away throughout, then are threatened late
    • Critical Points: 1st Quarter, Lakers 16-11 run; 2nd Quarter, Lakers 25-12 run; 3rd Quarter, Lakers 15-8 run; 4th Quarter, Lakers 6-4 run (follows a 13-2 Knicks run to pull within 5)
    • Kobe During Critical Points: 3/5 for 10 points; 2/6 for 5 points, 5 rebounds, 4 assists, 1 steal; 2/3 for 6 points; 2/4 for 4 points
    • Kobe’s Other Shots: 1/4 in 1st, 0/0 in 2nd, 0/2 in 3rd, 3/3 in 4th
    • Summary: Interestingly, a run ensues when Kobe’s shooting but isn’t hitting his shots (2nd quarter). The final run is more notable than 4 points makes it seem: it took place over only 2 minutes and sealed the victory for the Lakers.
  • November 10: Lakers 107, Wolves 93; Lakers pull away in the third quarter
    • Critical Points: 3rd Quarter, Lakers 12-3 run; 4th Quarter, 11-3 run (following 11-6 Wolves run to pull within 6)
    • Kobe During Critical Points: 1/1 for 2 points, 3 assists; 1/1 for 7 points
    • Kobe’s Other Shots: 5/8 in 1st, 0/2 in 2nd, 1/2 in 3rd, 1/4 in 4th
    • Summary: An interesting game; instead of Kobe’s shot attempts being high during runs, they’re highest during the first quarter, which remains fairly close. It’s notable, though, that the rest of the Lakers were 5/10 in the 1st with 5 turnovers – Kobe performance here may have kept them in the game. This is also an interesting example of Kobe possibly sparking a run without his FGAs increasing: despite taking only 1 shot in both runs, he was responsible for 8 of the first run’s 12 points and 7 of the second run’s 11 points.
  • December 14: Lakers 102, Spurs 97; Lakers pull away in the fourth quarter
    • Critical Points: 4th Quarter, Lakers 20-8 run
    • Kobe During Critical Points: 3/4 for 7 points, 1 assist
    • Kobe’s Other Shots: 4/8 in 1st, 1/3 in 2nd, 2/8 in 3rd, 0/0 in 4th
    • Summary: Another game outside the mold of the first two, Kobe’s 3rd quarter performance begs analysis. In the 3rd quarter, the Spurs outscored the Lakers by 10 to go from an 8-point deficit to a 2-point lead entering the 4th quarter. In our hypothesis, this represents a time when Kobe would theoretically respond – his increased shot attempts during this time indicate that this hypothesis should apply to this situation as well. Either from the Spurs’ superior defense or lady luck forgetting about Kobe for a night, in this particular instance the shots didn’t fall – but success isn’t what we’re interested in here, only effort. When the Lakers were threatened, it appears that Kobe again tried to carry them out of it; only this time, he didn’t succeed the first time, only the second (accounting for 10 of the 20 points in the final run).

In the next entry we’ll finish analyzing these games and see if the trend observed here holds true. So far, however, it certainly appears that our hypothesis that Kobe’s shot attempts increase at critical points in the game has held true through these first four games.

August 13th, 2008, posted by joyner

Kobe Bryant’s “High-Volume Shooting”: Part 3

You know the drill – detailed case study of individual games in which Kobe Bryant’s shots fell within a certain range. Today, three games: the Lakers’ 106-88 victory over the Heat on February 28th, the Lakers’ 95-98 loss to the Hawks on February 6th, and the Lakers’ 102-108 victory over the Mavericks on April 4th.

February 28th: Lakers 106, Heat 88

A rather run-of-the-mill game in the Lakers’ excellent season, this 18-point win saw Kobe attempt only 14 shots despite playing 41 minutes – and yet, the Lakers still won by 18. How’d that happen? And so you don’t have to run to the box score and check: this game occurred after the trades that brought Gasol to LA and Marion to Miami.

First Quarter
The Lakers jumped out to a quick 18 point lead in the first quarter, leading 18-4 at the halfway point and 22-6 with 3 minutes remaining. Preceding that lead, however, both teams were relatively inept through the 3 minutes – the Lakers led 6-2 on 3/7 shooting before taking off.

Over the next 5 minutes, the Lakers outscored the Heat 16-4. Kobe Bryant led the run with 6 points, but without controlling the ball: he attempted only two shots (both dunks) and made a pair of free throws. During the run, Walton went 2/2 on jumpers and Gasol threw in two dunks of his own (while missing a layup). Odom also made his only shot, while Fisher missed his only attempt (a three). Overall, however, the run is easily attributable to a balanced team effort.

Following that run, the Heat countered with a 13-4 run of their own. Kobe Bryant forced one bad shot (a fadeaway jumper), but overall – like last game’s run – the Heat’s run resulted from forced turnovers and strong shooting. Of the Lakers’ possessions following their 16-4 run, 3 ended in turnovers, 3 ended in missed shots and 2 ended in made shots – not exceptional, but not a horrible ratio.

Second Quarter
In case you haven’t noticed, we’re basically looking at when the Lakers go on a run, when their opponent goes on a run, which players lead those runs, and the circumstances that result in runs. In this second quarter, there are three such zones: a 21-10 run to put the Lakers up by 18, a 2-12 run to bring the Heat back within 8, and a 4-0 run to give the Lakers a 12-point lead going into halftime.

In that decisive 21-10 run, we again see a collective team effort by the Lakers – but we also see the kind of play that sends coaches like Phil Jackson and Gregg Popovich into a frenzy. The Lakers, despite building their lead up by 11, shoot only 7/17. Bryant misses two jumpers (and makes a dunk) while Turiaf missed 3 of 4 and Gasol misses both his. Instead, carrying the Lakers through the run is Farmar, shooting 2/4 and making both his three-point attempts. Vujacic also scores 4 points on 2/3 shooting, while Walton makes his only attempt (a layup). Farmar and Bryant also contribute from the line, combining for 5 FTs. But overall, the Lakers’ run is keyed more by the Heat’s shooting woes (missing their first 7 FGs and shooting 3/13 overall), turnovers (2), fouls (4) and poor rebounding (4 Lakers offensive rebounds) leading to more Lakers possessions.

The ensuing 2-12 Heat run, like previous Lakers’ dry spells, should be attributed not to poor shooting (Lakers attempt only 2 shots during this run, missing both while Kobe makes 2 FTs), but to a lack of shot attempts: the Lakers had only 5 possessions during this span, with 2 ending in missed shots and 2 in turnovers. The Heat, in turn, made the most of their 6 possessions, ending 5 with made shots.

Ending the quarter, Kobe Bryant single-handedly put the Lakers back up by 4 with two FTs and a FG. During this time, the Heat went cold, turning the ball over once and missing two shots.

Third Quarter
Let’s expedite this process. Third quarter runs: 6-11 Heat run (Heat trail by 7) and a 14-6 Laker run (Lakers lead by 15).

What happened at the beginning? The Lakers went cold: Fisher shoots 1/3, Bryant 0/1 and Walton 1/2 while no one else attempts a FG (Walton and Gasol each go 1/2 from the line as well). Of their first 11 possessions, 4 end in made shots (or made FTs, including 1/2 splits), 4 end in missed shots and 3 end in turnovers. Meanwhile, the Heat score 11 points – but, we don’t really care how they did that, now do we?

The Laker run that followed? It’s the end of the 2nd all over again: shooting was decent (6/13 with a FT and a three), balanced effort: 5 different players contributed to those 14 points. Towards the end, both teams went cold (neither team scores for 3 minutes), during which Kobe forces a few bad shots.

Fourth Quarter
The fourth quarter didn’t feature any truly discrete runs – the Lakers’ lead varies between 10 and 17, never less and never greater. The Heat pull within 10 late on a quick 7-point run (2 missed shots and a TO by the Lakers), but the Lakers respond quickly, holding the Heat to only 2 points over the final 3 minutes while putting up 11. In this final run, we see another team effort: 4 players contributing to that 11 points (4 for Turiaf, 3 for Odom and Vujacic, 2 for Davis).

Summary
The immediately obvious takeaway is simple: team effort, Lakers win. In this game, we see the Lakers get out to a quick start on a team effort, suggesting that Kobe never needs to take over with a flurry of shot attempts. But we also see another notable aspect: the Lakers were never challenged in this game. The closest the Heat came was within 8 points late in the second and 12 points late in the fourth.

This suggests some support for the idea that Kobe’s high-volume shooting is caused by the situation (which also causes the lower win percentage): when the Lakers are challenged, Kobe’s shot attempts rise as he tries to lift them out of it; and, obviously, the Lakers are less likely to lose games when they are actually challenged. But, this is speculation for the end of the analysis: I only mention it here so that later I can simply say ‘this further supports that idea I babbled about up there’.

April 4th: Lakers 112, Mavericks 108

This late-season victory represents an interesting issue with regards to our emerging hypothesis. In the two previous games we’ve analyzed, the Lakers were never truly challenged, forwarding the idea that his shot attempts go up when the Lakers are threatened and need Kobe to lift them past it. However, in this game we see the Lakers escape with a close 4-point win (after trailing by 4 with a minute to go), yet Kobe only takes 14 shots – 5 shots below his season average. So, what happened?

First Quarter
Runs: None. No, really, this was one of the most evenly-matched first quarters I’ve ever seen. The teams were tied at 31 after one quarter, with several lead changes and no lead larger than 4 points. The closest thing to a run for either team was a 7-0 run by the Mavericks to erase the Lakers’ early 8-4 lead.

Kobe got started early, nailing his first two shots (both 3′s) to put the Lakers up 6-2 only 30 seconds into the game. After that hot start, however, Kobe goes trigger-shy, accounting for only two assists, a rebound, a foul and two FTs the rest of the quarter (don’t get me wrong, 8 points in a quarter is good for Kobe, but this was on only 2 FG attempts). Doing the work for the Lakers instead are Odom and Gasol, accounting for 9 and 10 points, respectively – almost exclusively on dunks, layups and put-backs. Radmanovic and Fisher account for the Lakers’ other 4 points.

Second Quarter
Runs: 0-17 to put the Mavs up by 15. That pretty much sums up the quarter. After Farmar’s 2 to open the second, the Lakers go 6 full minutes without scoring another bucket. As is our custom, when another team goes on a run we don’t look at why they scored so much – we look at why the Lakers didn’t. And unlike the past two games we analyzed (where the Lakers went cold due to turnovers more than missed shots), here the Lakers just forgot where the basket was – as a team, they shot 0/7 with one TO. But as we’ve seen in the past two games, they play as a team – in this case, they suck as a team, with Farmar and Radmanovic each accounting for two misses while Bryant, Gasol and Walton each accounted for one (with the turnover attributed to Pau).

Let’s pause for a moment and consider what we don’t see here. For the first time, we see the Lakers actually challenged – the Mavericks’ 15 lead is by far the largest deficit we’ve seen for the Lakers so far. But what we don’t see is Kobe Bryant single-handedly trying to lift them out of it – he takes only one shot in the first half of the quarter. Why not? There’s no telling at this point – my first instinct is to say that he recognizes that it’s only the second quarter, and there’s plenty of time for his teammates to lift them out of it. Personally, I believe that Kobe recognizes that a team effort is more likely to bring home a win than a strong individual effort by him, and perhaps the early deficit here motivates him to give his teammates the chance. We’ll know if this is a viable possibility if we see a continued reluctance to take over in the first half compared to the second.

The second half of the quarter matched the first quarter – the teams were even, with the Lakers trailing by between 10 and 15 points the entire time. During this time, we see Kobe continue to differ – he takes two shots, one a slam dunk and one a missed last-minute layup. Instead, accounting for the Lakers’ 21 points during this time are Odom (8), Fisher (5), Gasol (4) and Radmanovic (2). That puts Kobe at 3/5 at halftime with the Lakers trailing by 11.

Third Quarter
Runs: 12-6 Laker run (Lakers trail by 5), 3-10 Mavs run (Lakers trail by 12). This quarter is easily divisible into three portions: a modest Lakers run, a modest Mavs run, and an even run, ending with the Lakers trailing by 2 – an overall net gain of 3 points for the quarter.

In the Lakers’ early run, we see what we might have expected: Kobe tries to take over. And succeeds, to a certain degree. In the Lakers 12-6 run to cut the lead to 5, Kobe shoots 3/4 for 6 of the Lakers’ 12 points over that period (also scoring are Odom (4) and Gasol (2)).

Following that, in the modest Mavs run, the Lakers’ woes come from possessions ending in turnovers (1), missed shots (2) and FT splits (1). More notably, however, is that Kobe appears to back off, commanding the ball at the end of only one of these possessions (the FT split). Needless to say, without watching the actual game it’s difficult to absolutely say that Kobe does, indeed, back off – but typically, looking at the player who results in a possession’s end (via turnover, shot or foul drawn) is an effective way of determining who’s in control.

Then, through the even ending of the quarter (or 11-7 Lakers run, if you’d like to call it that), Bryant shoots 1/2 (a 3-pointer) while Gasol and Vujacic each account for 4 points.

So, what does this tell us? Kobe fans will say he does just enough to keep the Lakers in the game, while still differing to his teammates somewhat to keep them in it. Kobe haters will say that he didn’t do enough (although if he’d tried to do more and failed, they’d criticize that too). I feel like this is a good moment to remind everyone that, as a die-hard lifelong Spurs fan, accusing me of being a Kobe fan is pretty silly. In a world with no Kobe, the Spurs could have won four more championships (’01, ’02, ’04, ’08) – the keyword being ‘could’.

Fourth Quarter
The fourth quarter, like the first, has no true runs – instead, the Lakers steadily climb back, pulling within 5 early in the quarter and hovering between 2 and 5 down until 3 minutes to go, pulling within 1 and then tying before taking the lead in the final minute.

And where was Bryant in all this? Only one FG attempt (a missed layup) and 5 free throws. His free throws did come at key moments though – the first on a Technical to bring the Lakers back within 4 as the Mavs threatened to pull away, the second two to pull the Lakers within 1, and the final 2 to seal the game, putting the Lakers up by 3 with 14 seconds to play. But notably, Kobe didn’t try to take over the game – instead, the fourth quarter was dominated by Odom’s 10 points, Farmar’s 7 and Vujacic’s 5. From start to finish, though, the Lakers’ supporting cast proved able to shoulder the load, slowly chipping away at the lead.

Summary
The Lakers win against a top-tier NBA team while Kobe takes only 14 shots (only 12 of which I can actually find in CBS SportsLine’s play-by-play, oddly enough) – how did it happen? Same thing we’ve seen before: balanced team effort, and frankly, an incredibly above-average games by a teammate. In Game 1 it was Fisher’s 28 points, just shy of his career high. In Game 2, it was Farmar’s 24, a career-high. Here in Game 3, it’s Odom’s 31. All three games saw a Kobe Bryant teammate score at least 17 more points than their season average, allowing Kobe to lay back and let the game flow more. The question remains, was it Kobe Bryant’s unselfish play that allowed his teammates to play so well, or did their excellent play allow him to be unselfish? At this stage it’s difficult to say (given that we haven’t established the standard for comparison yet), but what’s certain is that we don’t see these players putting up these numbers on a semi-regular basis (showing they aren’t streaky shooters, able to get hot and score in bunches on a specific given night given the chance, like Jannero Pargo). Instead, they all had career games, which every player has at some point in a season. Credit Kobe with allowing such games to happen (given that he could easily dominate beyond allowing any other player being able to contribute at all), but in my opinion it’s unfair to say they would happen more often if Kobe hung back more. These kinds of games happen to every role player, but we don’t see them happening more often on other teams.

February 6th: Lakers 95, Hawks 98

Here’s where things should get interesting, theoretically. I typically don’t come back and re-write introductions once I’ve actually gotten through the statistics – I write as I research, so you’re walking through this the same way I do. It’d probably be better to research everything, form my conclusions, then write my analysis, but that wouldn’t be nearly as fun, now would it?

In this game, Kobe Bryant takes only 16 shots in 37 minutes – no small number, granted, but 3 below his season average, and 7 below his season average not including blowout wins (and that one blowout loss). But unlike every other non-blowout game that saw Kobe take less than 17 shots, the Lakers lost this one. To the lowly Hawks, no less (hey, I live a mile from Phillips Arena, I get to call the Hawks lowly). So, what happened?

First Quarter
Runs: 2-7 Atlanta run (Atlanta up 5), 17-6 Laker run (Lakers up 6), 10-14 Atlanta “run” (Lakers lead by 2). Overall, a fairly even quarter; the early Atlanta run resulted from Lakers’ shooting woes as they went 1/5 to open (with Odom, Radmanovic and Gasol each missing one and Bryant hitting 1 for 2).

The subsequent Lakers run was mostly Gasol’s handiwork, scoring 9 on 3 FGs (one 3-pointer, 2/2 from the line); also contributing were Radmanovic (5) and Odom (3), while Fisher was the only Laker to miss a shot during this 4-minute stretch. On top of that, the Lakers committed only one turnover, while Kobe Bryant’s only appearances came in the form of three assists and a rebound.

Through the rest of the quarter, the Hawks narrowed their deficit slightly as the Lakers came back down to earth: well, actually, it’d be more accurate to say that both teams sank notably – or, to be more positive, put on a strong showcase of defensive ability. The Lakers closed the quarter shooting 4/9 while scoring on only 4 of 11 possessions (Gasol, Farmar and Turiaf each missing a shot while Radmanovic went 2/2 and Kobe went 2/4), but the Hawks didn’t perform much better and only narrowed the lead to two entering the second quarter. 6 of Kobe’s inevitable 16 shots came in the first, suggesting that his shot attempts dropped off as the game went on (or at least for some portion of the game), which – if our past analysis has any predictive power – should suggest the Lakers built a lead at some point. But we also know that the Hawks end up winning. How does that work?

Second Quarter
Runs: 8-4 Laker run (Lakers lead by 6), 3-10 Hawks run (Hawks lead by 1), 13-4 Laker run (Lakers lead by 8). Both teams were pretty flat coming out, combining for only 12 points in the first 6 minutes as the Lakers shot 4/9 (Farmar 2/3, Odom 1/1, Gasol 1/4, Vujacic 0/1) with one turnover. As with late in the first, the Hawks still were even worse, letting the Lakers build their lead up to 6.

The following Hawks 10-3 run came over only 2 minutes (yes, the teams scored more in these 2 minutes than the first 6), and was largely due to the Hawks’ fast-paced basketball. The Lakers shot a modest 1/4 (1/3 Vujacic, 0/1 Gasol), while the Hawks scored on 5 consecutive possessions (including two offensive rebounds).

That last run put the Hawks up by 1 point, but the Lakers immediately responded with a 13-4 run. Give that run to Fisher – 3/3 from beyond the arc for 9 points, while Turiaf and Kobe each add 2 FTs (Kobe also missed a FG). Kobe’s sole FG attempt in the second quarter brought his total to 7 – partially expected, given that the Lakers built up a lead (as we mentioned at the end of the first quarter), although Kobe’s continued absence when the Hawks momentarily took the lead might be considered surprising. Fisher answered immediately, however (two 3′s within 40 seconds of the Hawks’ taking the lead), possibly belaying the need for Kobe to take charge.

Third Quarter
The Lakers entered the third quarter up by 8, and not to be a spoiler, they ended it the same way. This entry’s getting long and, let’s face it, the Lakers’ supporting cast by name doesn’t matter to the conclusion of this study.

The Lakers built their lead up to 9 through the beginning of the quarter, only to see the Hawks rally and cut the lead to 2 – only to see the Lakers rally back and lead by 8 at the end again (maybe – again, the CBS SportsLine play-by-play doesn’t always match up exactly with the box score). And Bryant? 0-fer-4 in the quarter, with all his shots coming while the Lakers built up their lead to 9. No sign of him as the Hawks clawed back, or as the Lakers rallied again.

Fourth Quarter
Theoretically, Kobe should have 5 shots remaining to be taken (6 in the first, 1 in the second, 4 in the third). Hopefully CBS Sportsline will cooperate this game.

The Lakers maintained their lead through the first half of the quarter, building it up to 9 and never leading by less than 4. That changed, however, when the Lakers hit 88 – the Hawks then rallied to tie the game. It stayed close through the last 3 minutes, with the teams exchanging leads until finally the Hawks sealed the win with 2 FTs from Joe Johnson with 3 seconds to go.

And Bryant? We got exactly what we’ve predicted. As the Hawks started to rally, Kobe tried to step up – he didn’t shoot in the fourth quarter until halfway through, taking shots when the Hawks began their run, as they were about to tie the game, after they tied the game (twice), and near the end. It’s also notable that in the last minute, the teams combined for 10 FTA and only one FGA (a Vujacic layup), suggesting that Bryant could not have done much more. The game was close, and a late turnover gave the Hawks the last trip to the free throw line, which was the difference in this game.

Summary
This game is interesting because it represents, to a large extent, what we might expect to see in the next group of games: Kobe’s shot attempts going up when the Lakers are challenged. This game represents an intersection of the two groups: like what we hypothesize may happen in the next group, Kobe’s shots go up when the Lakers are challenged; but like the previous games in this group, the Lakers were in control for the majority of the game, allowing Kobe to differ more. This is actually essentially the same reasoning that allowed us to leave out blow-out victories: because of the Lakers’ strong performance anyway, Kobe is able to contribute less without hurting the team’s chances. In blow-outs, this goes far enough to allow Kobe to actually sit on the bench, but in these in-between games he (theoretically) stays out on the floor in case the other team makes a run. This game is a good example: although the Lakers hold a modest lead halfway through the fourth, Kobe stays out because the game isn’t quite in-the-bag. And when the Hawks make their run, Kobe tries to answer – this time, his shots don’t fall. It happens.

So what does this predict for an overall thesis? It’s still pretty early to say, but my prediction is that we’ll see Kobe’s shot attempts increase when the Lakers are challenged, like we saw here. Hopefully I’ll be able to find some games where the Lakers hold big leads, then give them up to test this idea more conclusively.

Since this is the last game in this group, let’s also revisit our initial question: we know that Kobe shoots more in losses than in wins. Does Kobe’s high-volume shooting lead to his teammates’ performing poorly, or does his teammates’ poor shooting lead to Kobe taking more shots? Either one could cause Kobe to shoot more in losses – it’s a problem of causality.

But what we’ve found so far is that this may have been an entirely wrong way to approach the problem: there aren’t any games (at least in this group) where Kobe came out shooting, only to see his teammates falter as the game went on; and there aren’t any games where his teammates came out cold, and Kobe responded by taking more shots. Instead, we see Kobe take shots when he needs to, and differ to his teammates the rest of the time. This leads to a very, very obvious, yet still incredibly important, fact: the Lakers are more likely to lose games in which they’re actually challenged. I know, revolutionary, right? But it makes sense that if (a) Kobe shoots more when his team is challenged and (b) the Lakers are a winning, dominant team, then on average, he’ll shoot more in losses than in wins. The ‘dominant team’ part of that conclusion is necessary because it shows there are more Lakers’ wins where Kobe takes fewer shots than usual than Lakers’ losses (I can explain this more thoroughly if need be).

Now, this doesn’t completely clear out our original comparison (namely, does Kobe coming out shooting cause his teammates to fail to get into a rhythm, or do his teammates’ early shortcomings cause Kobe to need to shoot more?) – this comparison might still correlate to when the Lakers are challenged. But it might not – we’ll keep an eye out.

The more important proposition at this point is whether or not Kobe’s shot attempts habitually rise when the Lakers are challenged by their opponent. If so, we have our evidence. If not, we’re back to the drawing board. It’s also important to note that a single game won’t prove or disprove this – considering how many games there are in the next group (47), we’re going to choose around 7 games. Not randomly, though – I’ll cursorily look over at least half those games and choose some that are representative. If the Lakers regularly jump out to an early lead and give it up, we’ll include a couple of those. If the Lakers regularly leave it close and pull away late, we’ll include more of those. And if there’s no trend, we’ll look at a bunch of different general trends.

I also want to make sure it’s clear that there are no conclusions yet – all we have from this portion of the study is a standard of comparison. We’ve observed certain characteristics of these games: when the Lakers are in control, Kobe’s shot attempts are low – that’s the main takeaway from this portion. There’s also early evidence that when the Lakers are at risk of either losing (towards the end of the Hawks game) or falling behind too far to catch up (third quarter of the Mavericks game), Kobe starts shooting to try to shoot the Lakers back into it. Our conclusion will be proven if we see that the Lakers are challenged more often in our next group of games than in this previous one, and if Kobe’s shot attempts continue to go up when the team is challenged.

I’ll also be (mercifully) differing to the more brief analysis used in the last game of this analysis, so the next stage won’t be a novel.

LITTLE WHITE TAKEAWAYS

No actual real conclusions in this portion; in this part of the study (continued from the last part), we looked in-depth at the games in which Kobe Bryant shot 16 or fewer shots – 5 fewer than his season average (not including blowouts). What we found is that in these games, one major trend emerges: in games where Kobe doesn’t shoot as much, the Lakers aren’t really challenged. In these games, the Lakers are in control the majority of the game – most notably, the entire Denver and Miami games. When they’re challenged – by either an opponent’s late comeback (Atlanta), or an opponent threatening to pull away (Dallas) – Kobe’s shot attempts go up.

But the important aspect of this hypothesis is that the challenge precedes (and, thereby, causes) the shot attempt increase. In the next installment, we’ll look at a collection of games where Kobe attempts around his season average (18 to 28 shots). If we see this trend continue – that is, that Kobe takes more shots under particular circumstances – we’ll have conclusive evidence for why Kobe takes (on average) more shots in losses than in wins.

July 19th, 2008, posted by joyner

Kobe Bryant’s “High-Volume Shooting”: Part 2

Apologies for the delay – it took me forever to find a site that offered archived play-by-plays of NBA regular season games. In other words, it took me two weeks to consider checking the site that I actually use for play-by-play of my Spurs games when I’m following them from Atlanta. In related news, the play-by-plays used in the following part of the analysis is courtesy CBSSportsline.com.

As mentioned in the last post (two weeks ago), the idea that the Lakers’ fortunes fall as Kobe Bryant’s shot attempts increase is overblown; however, the discrepancy is still present. Kobe averaged 23.75 shot attempts in losses while he shot only 21.44 shots in wins (when blowout games in which Kobe plays fewer minutes than usual are thrown out); and the Lakers were 9-1 with Kobe shooting less than 17 shots, 28-19 when he took 18 to 28 shots, and 2-4 when he took 29 or more.

It might seem odd that the intervals are different, but the reasoning behind the division is sound: the Lakers win around 100% of their games when Kobe takes anywhere from 7 to 17 shots; but, they win essentially 67% of their games for every shot amount from 18 to 28. Then, above 29, they win around 33% of their games. The divisions are interesting: they aren’t just the cumulative sum over the range, but they are – to a large extent – accurate for every number of shot attempts within their range. I’m mentioning this mainly because one of the criticisms of the original study was that it utilized an odd cut-off point – but the cut-off points used here are sound.

So, anyway, for the next portion of this analysis, we want to answer a simple question: does Kobe’s “over-shooting” cause his teammates to be out of rhythm and thus drag the team’s fortunes down, or does his teammates’ off nights cause Kobe Bryant to need to shoot more to keep his team afloat? Statistically this is pretty difficult to analyze numerically, so instead we’re going to opt for some “case studies”. Essentially, we’re going to choose some games from each of those groups and figure out what exactly happened.

First, let’s examine games where Kobe shot less than 17 shots – in these games, the Lakers went 9-1. Why? Let’s take a closer look:

January 21st: Lakers 116, Nuggets 99

Here’s an interesting game: in this mid-season blowout, we see Kobe Bryant shoot only 7 shots – his lowest shot total in any game all season long – while still playing 38 minutes. What’s more, the Lakers dominated the Nuggets, winning by 17 points, and they were already playing without Andrew Bynum, and what’s most notable, this came before the arrival of Pau Gasol.

So what the heck happened? A cursory glance would likely pin the entire ordeal on Carmelo Anthony leaving in the 2nd quarter with a sprained ankle; but the Lakers held a 10-point lead after one quarter, defeating that idea. So let’s move on to the supporting cast.

Naturally, for the Lakers to win while Kobe shoots only 7 FGs, one of two things has to happen: either his supporting cast has to show up, or he has to set an NBA record for FTAs in a game. Considering he shot only 8 in this game, the former must be true; and indeed it is. Jordan Farmar hits 8 out of 15 for 19 points, Odom and Brown both pull in 11 rebounds, and most notably Derek Fisher puts in his career second-best with 28 points on only 16 shots.

But that’s not what we’re asking – it’s obvious that if the Lakers win while Kobe shoots only 7 shots, his teammates played out of their minds (which, incidentally, they really didn’t – outside Kobe, Fisher and Farmar, only two other Lakers shot 50% – Crittenton at 1-2 and Turiaf at 4-8). But which came first, Kobe backing off or his teammates’ hot performances?

First Quarter
After one quarter, the Lakers led by 10 points, scoring 39 – most of that came during an insane run in which the Lakers scored 18 points in 4 minutes. Kobe Bryant in the first quarter? Outside an offensive rebound and a turnover in the opening minute, he doesn’t even show up until the final four minutes of the quarter. He takes no shots in the quarter, but has 3 rebounds, 2 assists and a foul.

Now, in games where Kobe takes very few shots, we’re looking for one of two things: either his teammates come out hot (allowing Kobe to take fewer shots) or Kobe comes out selfless (allowing his teammates to get into a rhythm). In this case, it’s difficult to pinpoint which we see. The Lakers open up cold, down 12-4 early. During this time, Kobe does nothing, suggesting the latter – however, beginning at the 9-minute mark, his teammates wake up. From the 12-4 deficit to the final four minutes (where the Lakers went on their 18-point run), the Lakers climb back to within 1. During this time, Fisher shoots 4/6, Brown 2/4 (both dunks), Odom 1/2 (and two FTs), and Turiaf 0/1. Not shabby and certainly load-carrying.

So did Kobe’s early selflessness allow his teammates to get hot, or did their performance early-on allow him to lay back? It’s hard to say in this game: his teammates aren’t on their A-game right from the get-go, but it doesn’t take long at all for them to get into their rhythm. So which is it? I’m leaning towards the teammates-hot side, but it’s pretty close in this case.

Either way, the intended effect of his teammates getting into a rhythm early takes place: the 18-point burst in the final 4 minutes is led by Odom’s 7 points.

Second Quarter
The second quarter saw each team go for 29 points, leaving the Lakers with a 10-point halftime lead. Carrying the load for the Lakers in the second are Turiaf (carried over from 5 points to close the first) with 4 points, Farmar with 7 and Bryant with 6. The second also saw a balanced attack, with 7 Lakers scoring while 9 attempt FGs. In short, in the second quarter Kobe’s supporting cast continued shouldering the load, with Bryant chipping in.

Third Quarter
The third quarter presents an interesting point of analysis – after entering the third quarter with a 10-point lead, the Lakers find themselves down by two 8 minutes later, then up by 9 after another 4 minutes. What caused the Lakers’ slump, and who keyed their reawakening?

The early-quarter slump can be blamed on turnovers more than shooting woes: the Lakers commit 6 turnovers (2 on Kobe) in 8 minutes. That’s not to say the Lakers’ shooting is fine, though: the Lakers shoot only 3/11 from the field, 2/4 from the line and 2/6 from three. Kobe doesn’t try to take over (takes only one shot, missing it), nor are his teammates able to bring anything (only Fisher, Vujacic and Brown hit shots, and only one apiece).

And the Lakers’ resurgence in the final four minutes? Look no further than Fisher – 3/3 from downtown, while Farmar and Turiaf account for 5 more points.

Fourth Quarter
The fourth quarter extension of the Lakers’ lead from 9 to 17 can be attributed mostly to defense (Lakers holding Denver to 17 points) as the Lakers’ offense sputtered (6/20 from the field with one 3) only to be saved from the line (12 points). Like the early third, everyone on the Lakers not named Kobe Bryant went cold, and while Kobe shot well, he didn’t shoot much (2/3 from the field, 3/4 from the line for the quarter).

Summary
So, what do we see here? In the first quarter, starting about 3 minutes in, the Lakers’ supporting cast handily carries the Lakers to a 10-point lead, led by Derek Fisher. While Kobe Bryant doesn’t do much about the Lakers’ woes very early, it doesn’t take long for his teammates to awaken and pull their weight. It’s hard to say if this lies on the “Kobe allowed them to get into a rhythm” side or on the “they were already in a rhythm, so Kobe was able to lay back” side, but given how early Derek Fisher’s shooting began (3 minutes in), it likely leans more on the latter side.

In the fourth quarter, the Lakers saw their lead dissipate as the entire team – Kobe included – slumped. With 4 minutes to go, however, Derek Fisher took over, carrying the Lakers back to a 9-point lead. Is this an instance of Kobe allowing someone else to get into a rhythm, or did Fisher’s rhythm allow Kobe to relax? Again, this is hard to say given that the Lakers barely gave up their lead before Fisher brought it back, but this likely leans on the side of Kobe allowing his teammates to work – in the third, Kobe attempts only one shot.

So, this game shows some conflicting evidence, but overall the notable part is that in the instances where Kobe would likely take over (early in the game or with a dwindling lead), another player (Fisher, mostly) was already stepping up and carrying the team, theoretically allowing Kobe to hang back.

That concludes our far-too-in-depth analysis of the first game of this: the subsequent ones will be about half as long, this is mostly to set up the type of logic we’ll be using. An important note about case studies like this is that they really aren’t generalizable at all on their own: it’s entirely possible – even likely – that these results are completely different from other games. That’s why we’ll be doing several of these – probably at least 4 from each group, randomly selected to hopefully catch if there’s any variance.

Since this is only the first analysis, I’m leaving off the takeaways because, well, there aren’t any. I wouldn’t be posting this analysis on its own if it hadn’t been two weeks since the last one, but I figure I’ll let y’all know I’m still alive and not one of those bloggers that writes a ton the first two weeks before quitting.

Next time we’ll have three more game analyses from the “Kobe shot less than 17 shots” category. And depending on how much I can limit myself from getting overly detailed, hopefully that won’t take very long.

July 6th, 2008, posted by joyner

Kobe Bryant’s “High-Volume Shooting”: Part 1

So, until I figure out what the current problem on my Box Score Analysis data sheet is (don’t worry though, it’s a problem that only affects the next stage of the analysis), the team-by-team analysis is on hold.

But the good news is, that lets us jump into our analysis of the claims made by Christopher Reina and thoroughly criticized by the fellas at Ball Don’t Lie.

To summarize, Christopher Reina pointed out that the Lakers this regular season were 26-18 when Kobe shot more than 20 shots, and 31-7 when he shot 19 shots or less. Ball Don’t Lie, in turn, calls that study way too short-sighted, limited and confounded to be considered a viable conclusion.

The truth is, the study is certainly not conclusive enough to make the statement ‘the Lakers are better when Kobe doesn’t shoot as much’. That’d just be ridiculous. Not only is the criteria used here too limited (as Ball Don’t Lie points out, the very nature of a ‘cut-off’ point between completely opposite categories is insufficient), attributing causality based on it is ludicrous.

Here, we want to make it not-so-ludicrous. We want to answer two questions:

Is it true that the Lakers are more likely to win when Kobe’s shot attempts are lower?

If so, does Kobe’s “high-volume shooting” cause the Lakers to under-perform, or does another variable cause both the Lakers’ under-performance and Kobe’s high-volume shooting?

So to start out, we want to answer that first question better than the original study did. We’ll consider two different ways to do this: Overall Averages and Overall Correlation.

Overall Averages

I’m really not sure why the original study opted for using a cut-off point to judge whether Bryant’s shooting matched up with the Lakers’ win/loss record when there’s a much more logical (and equally simple) way to do it – but hey, to each his own.

Let’s consider something a bit more informative: Kobe Bryant’s averages in wins and losses.

FGA in Wins: 19.32
FGA in Losses: 23.56

Well, that decides it, right? Kobe averages over 4 more shots in losses than in wins. So it has to be true, right?

Not quite. Why not? We’ll get to that a bit later. This just shows how misleading a very cursory glance at the stats can be.

But as long as we’re here, let’s look at other differences between Kobe’s stats in wins and losses – just for curiosity sake, right?

  • Kobe averaged .9 more assists in wins than in losses – which, depending on your point of view, means either he actually gives his teammates opportunities in wins, or they actually hit on the opportunities he gives them in wins.
  • Kobe averaged 1.1 more 3-point attempts in losses, but made about the same number regardless of the game’s outcome.
  • Kobe shoots 1.7 more free throws in losses than in wins.
  • And, though it’s pretty irrelevant, Kobe plays 4 more minutes/game in losses than in wins.

Hopefully you picked up on the sarcasm on the ‘irrelevant’ part of that last bullet. You mean the more minutes Kobe plays, the more shots he takes? Extraordinary!

Let’s not get too excited though (or depressed, if you’re hoping I show Kobe really does over-shoot in losses) – that difference only accounts for about half of that four-shot discrepancy.

So why does Kobe average less minutes/game in wins? Consider that same ‘special case’ we considered in the last analysis: blowouts. 18 times this year, the Lakers blew out (>12 point win) their opposition as Kobe played less than his average number of minutes. Those are games when it’s only natural for Kobe to shoot less – not because it actually affects the team’s performance, but because he doesn’t play as much.

Throwing out those blowouts from consideration (it’d be more statistically sound to look at Kobe’s stats through three quarters of each game, but I haven’t found a database that has that easily parseable), we arrive at some different statistics: 41 minutes/game in both wins and losses, 21.44 FGA in wins, 23.56 FGA in losses.

But, it would only be fair to throw out those blowout wins if we also threw out blowout losses when Kobe also played less than his average number of minutes. But, that happened only once – Lakers vs. Utah, November 30th. Throwing this game out barely impacts the stats (+.19 FGA in losses, bringing the difference to 2.31).

Not considering blowout games, Kobe averages 21.44 FGA in wins and 23.75 in losses. That’s a huge difference from the 19.32 and 23.56 we considered initially. Right away we blow away that silly 20-shot cut-off used in the original study, since the only time Kobe shoots less than 20 shots (on average) is when the Lakers are in a blowout win.

But that 2.31 difference in FGA is still notable – not nearly as notable, but notable. So, considering what we know now, let’s revisit the method used by the original study of cut-off points at different shot attempts – but, let’s do so far more thoroughly.

Overall Correlation

Unfortunately, this data isn’t exactly conducive to a real correlation analysis – the sample sizes for each number of shots are far too small to really establish a correlation between FGA and win percentage.

So instead, let’s go back to the original approach (the cut-off point), but instead of arbitrarily choosing one (or worse, choosing one specifically to prove a certain point), let’s look at every number of FGA and how the more/less correlates to wins/losses – and, like above, we aren’t considering blowout wins/losses, given how they confound his statistics.

Doing so reveals an interesting division, far more informative than the original 19-or-less/20-or-more split. The Lakers were 9 and 1 when Kobe shot 17 or less shots. Above that, they were 28-19 with him taking 18 to 28 shots; and finally, 2 and 4 with him taking 29 or more. Note these divisions aren’t arbitrary, they’re chosen from what appear to be the critical points where the Lakers’ fortunes change – naturally there is likely a more smooth progression, but the small sample size does not allow us to establish one.

These observations, unlike the earlier portion of the analysis, do not debunk the idea that Kobe’s increased shot attempts correlate to the Lakers’ winning percentage dropping – rather, they seem to suggest it. The Lakers are best-off when Kobe takes relatively few shots (winning percentage of 90% when he takes 17 or less, 100% for 15 or less), substantially less-well-off when he takes a medium number of shots, and downright bad when he takes a large number of shots.

LITTLE WHITE TAKEAWAYS

This study is trying to find if there’s any truth to the idea that Kobe Bryant handicaps the Lakers sometimes by taking too many shots. In order to analyze this idea, we want to examine two questions: is there actually a connection between Kobe’s shot attempts and the Lakers’ winning percentage, and does Kobe’s overshooting cause the losses or does something else cause both his overshooting and the Lakers’ losing?

This first portion addresses that first question. One study revealed that the Lakers were substantially more likely to win when Kobe shot less than 20 shots than when he shot more than 20; but this study had several issues, so we wanted to more thoroughly analyze it.

What we found is notable: while it is true that the Lakers were more likely to win when Kobe shot less, it wasn’t nearly as severe as the original study suggested. The initial study suggested that the Lakers were 38% better when Kobe took 20 shots or less, but it would be more accurate to say the Lakers are 11% better under those conditions. A cursory glance at the statistics would show that Kobe averaged four more shot attempts per game in losses than wins, but it would be more accurate to say that he only averages two more shot attempts in losses.

The reason for this discrepancy is that the Lakers had 18 blowout wins and 1 blowout loss in which Kobe played less than his average number of minutes, suggesting that his playtime was altered by the nature of the game. It’s obviously more likely for Kobe to take less shots in games where he plays less minutes, so these games should not be considered on the same level.

So, in short, there’s some truth to the idea that Kobe shoots more in losses, but it certainly isn’t as severe a problem as the statistics would immediately suggest – in fact, it’s only a minor alteration when blowouts aren’t considered.

In order to more fully address these questions, though, it would be better to instead utilize a shots-per-minute statistic than to simply throw out games under certain conditions. I’ll look into this to see if it represents any major alterations to the conclusions reached here – if it does, I’ll write about that, but I don’t anticipate that it will.

Given that there’s still a discrepancy between Kobe’s shots in wins and losses (though it is less notable than originally anticipated), it would still be useful to see where the causality lies: does Kobe over-shooting cause his team to under-perform, or does something else – for example, teammates under-performing – cause both Kobe’s extra shooting and the Lakers’ eventual loss?

This is difficult to analyze numerically, so instead, we’ll likely resort to a few case studies of the games in question. But, that’s a job for next time.

-DJ

June 24th, 2008, posted by joyner

Box Score Analysis: Wins by Differential, Part 2

First order of business: congratulations, Boston Celtics, on your 17th title. Consolations to the Lakers as well. And a preliminary prediction of a Spurs championship next year if Manu stays healthy – it’s an odd year, after all.

In case you can’t tell, I’m a huge fan of differentials. It’s fairly well-documented that the best predictor of playoff success over the past several years hasn’t been regular season record, but regular season differential.

Want proof? Just look at this year. In 2008, almost every team was eliminated by a team with a higher differential. Celtics over Pistons (#1 and #2), Lakers over Jazz (#3 and #4), Pistons over Magic (#2 and #5), Jazz over Rockets (#4 and #9), Hornets over Mavs (#6 and #10), and the list goes on. The only exceptions were the Spurs over the Suns and Hornets (and as we all know, the Spurs don’t really care about the regular season) and the Cavs over the Raptors. Differential matters.

Want more proof? Highest differential in 2005 and 2007 were both the Spurs, despite not owning the NBA’s best record in either season. In fact, half of the last 10 NBA champions have won the point differential crown, with only the 2002 and 2004 Lakers winning the title without ranking at least top-5.

So, all this considered, it’s a pretty powerful statistic. It correlates ridiculously well with total regular season wins, but it’s an even better predictor of playoff success, considering how rarely (via Ball Don’t Lie) regular season victories predict championships.

It’s also an extremely versatile statistic. You don’t have to consider things like pace of the game, the team’s focus (offensive or defensive), efficiency ratings or anything else. It’s very straight-forward, and everything else that’s significant in the game comes through in the differential.

That’s why I’m utilizing (ok, abusing) it so much in this on-going analysis; it’s one of the more powerful statistics, and we’re reaffirming that here. We’ve already uncovered a few quite notable discoveries, but the ones in this entry are better than all the rest. I think in this entry, we’re actually going to bridge the gap between ‘interesting to statistics nerds’ (like myself) and ‘interesting to the casual NBA fan’.

Today we’ll be answering the question, is it more important for a team to play well in the first half or second, and is there a particular quarter that it’s more important for a team to perform well in?

Before we continue, let me define real quick what I’m referring to when I say one differential was ‘more beneficial’ than the other. Essentially, if a positive differential (for the home team, meaning they outscored the away team) during quarter (or half) A led to more wins than the same differential over quarter B, then quarter A is defined as ‘more beneficial’ (meaning performing better in that quarter more closely led to more wins). If, on the other hand, a negative differential during quarter A led to more wins than the same differential in quarter B, quarter A is considered less beneficial because being outscored during that portion of the game was less likely to result in a loss.

This approach isn’t without fault, though, and I’d be a propagandist (woah, that’s actually a word?) instead of a statistician if I didn’t mention them. This study assumes that winning a quarter is good, and losing a quarter is bad. The last portion of the study didn’t entirely support this, showing that it could be that losing a quarter by two or less is still good – but, this would only confound a tiny percent of our data. That’s the only obvious confound I can identify; if anyone reading notices something I’ve overlooked, e-mail me – I’m not defending this idea simply because I believe it, but because the statistics appear to back it up.

Fortunately, most other typical confounds don’t really apply here: usually a study like this would need to ensure the four quarters were played out under equal conditions, but this study does not seek to attribute causation: we’re not trying to find out why a particular quarter is more important, only if a particular quarter is more important. So with that, on to the results:

Difference Between Halves

Is it more important to perform well in the first half, or the second half? There are several ways to approach this, but one of the best would be to look at identical performances in the first and second half (here, identical differentials) and find if the same differential leads to more wins in one half than the other. And, in this case, it does – well, sort of.

For this portion of the study, I actually calculated the statistical significance for the difference between win percentages between the first and second halves for every possible differential. OpenOffice.org Calc is my friend.

What we find is that there are 39 differentials which occurred at some point in the season in each half. For 21 of these differentials, it was better to win the second half by that score than the first (for example, winning the second half by 8 led to an 86% winning percentage, whereas winning the first half by 8 led to only a 64% winning percentage). For the other 18, it was better to win the first half; so right here we see no strong evidence that the second half is more important.

But, this goes to another level when taking statistical significance into account. Of those 39 differentials, the difference in winning percentage between the first and second halves is only statistically significant (at the 90% confidence level) for 14 of them – meaning that only 14 of the differences are actually indicative of a relevant discrepancy. And of those 14, 11 come when the second half yields more wins.

This is about the strongest statistical evidence I’ve yet come across that strong second half performance results in more wins than identical first half performance. When the statistics show that a certain differential is more beneficial when achieved in a certain half, it shows that the second half is the more beneficial one 11 out of the 14 times. I can’t really re-state that in any other way; the stats strongly suggest that the second half is more important. I’m sure the Lakers will agree, having seen both sides of just how much the second half matters (Game 1 vs. the Spurs, Game 4 vs. the Celtics).

The study does raise several questions though. One oddity is that all 14 statistically-significant differences don’t lead to the same half winning. Why do three appear to benefit the first half, but the other eleven appear to benefit the second half? Is there a pattern to which lie on which side?

Let’s find out: the differentials that are more beneficial in the second half are -20, -17, -16, -14, -9, -3, 1, 7, 8, 9 and 18. The differentials that are more beneficial in the first half are -13, 10 and 19. Now, those results are rather unusual – the beneficial first-half differentials all lie right next to a differential that’s more beneficial encountered in the second half. For example, every home team (all 20) carrying a 19-point advantage into halftime won, whereas only eight out of eleven home teams pulling in a 19-point advantage in the second half won. On the flip side, every home team that achieved an 18-point advantage in the second half won, whereas only eleven out of fourteen won after doing the same in the first half. The same sorts of trends (though not as drastic) can be observed for 9 vs. 10-point differentials and -13 vs. -14-point differentials.

That’s a very strange observation indeed, and requires some explanation. There are two high-level possibilities:

  • There are certain differentials that are more beneficial when encountered in the first half, and certain ones that are more beneficial in the second half.
  • There is an overall trend to which half is it better to encounter every differential in, and the differentials pointing towards the first half being more beneficial are a result of sampling error.

The first of those options would be more plausible if there was a pattern to which differentials were more beneficial when – for example, if large differentials were better when encountered in the second half and narrow ones better in the first half. But the results don’t suggest that – the beneficial first-half differentials are right next to the beneficial second-half differentials.

So, that leaves us with the second option. The second option seems a bit like a cop-out – just throw out the results that we don’t like? And I admit, it is – statistically it’s a pretty slim chance that three of the fourteen would come up just by chance (somewhere around a 2% chance). But it’s an even slimmer chance that the difference would be as high as it is (11 vs. 3), and there remains no logical explanation for why such close differentials would yield completely opposite results.

Fortunately, we can drop this here – why? Because like I mentioned in the last post, we can re-hash this analysis when we multiply our sample size. With a sample size of 12,300, every difference will be statistically relevant – so if these results persist into that study, we can conclude that somehow, for some inexplicable reason, an 18-point differential is better in the second half, but a 19-point one is better in the first.

Difference between Quarters

Like the halves study, this was done by finding the statistical difference between every pair of quarters – all six pairs. And since we already set up the framework for how we’re doing these analyses, let’s jump right into the results – all ‘statistically significant’ stats are at least at the 90% confidence level.

Rather than get unnecessarily wordy, here’s the format for the stats: (Quarter): (number of differentials with advantage); (Quarter): (number of differentials with advantage); (Quarter) SS: (number of statistically significant advantages); (Quarter) SS: (number of statistically significant advantages) – followed by a brief summary of what I’m taking away from it. Like above, below we’re assuming that one of the quarters is absolutely better (over all differentials) than the other – this is not a conclusively proven assumption, nor can it be at this stage, but there’s no evidence (logical or statistical) to the contrary.

1st Quarter vs. 2nd Quarter: 1st: 19; 2nd: 15; 1st SS: 3; 2nd SS: 2
No real conclusive evidence that the first quarter is more important than the second, though this is fairly conclusive that the second quarter is not more important than the first.

1st Quarter vs. 3rd Quarter: 1st: 19; 3th: 17; 1st SS: 2; 3th SS: 8
Now, this is interesting. The 1st quarter holds a slight advantage over the third in terms of the winning percentage resulting from different differentials; but, only 2 of the 19 first-quarter-favoring differentials is statistically significant. On the other hand, almost half of the third-quarter-favoring differentials are statistically significant. This suggests a notable lean towards the third quarter, but not a completely conclusive one.

1st Quarter vs. 4th Quarter: 1st: 16; 4th: 19; 1st SS: 2; 4th SS: 4
Like the 1st vs. 2nd data, this data is too close to suggest that the fourth quarter is conclusively more important than the first; however, like in the second, this is evidence that the first quarter almost certainly is not more important than the fourth.

2nd Quarter vs. 3rd Quarter: 2nd: 13; 3rd: 21; 2nd SS: 3; 3rd SS: 4
The wide discrepancy in non-statistically significant differentials is not as notable as the closeness of the statistically significant differentials, but it’s still statistically significant that the non-statistically significant differentials are so far apart (once again, statistics analyzing statistics – and don’t you dare try to read that sentence 3 times fast). So what does that mean in non-statistics-ese? Basically, there’s evidence that the third might be a bit more critical than the 2nd, but more notably the second certainly isn’t more critical than the third.

2nd Quarter vs. 4th Quarter: 2nd: 16; 4th: 18; 2nd SS: 2; 4th SS: 7
Fourth is more important than second, basically – the large discrepancy in statistically-significant differentials shows that.

3rd Quarter vs. 4th Quarter: 3rd: 18; 4th: 19; 3rd SS: 8; 4th SS: 9
And the third and fourth are about as equal as they can be from the data available – either could actually be better than the other, or they could be functionally the same.

Now, pardon me, but I’m going to be a nerd for a moment and break these into nonsensical looking equations to try to come up with a Unified Theory of Quarter Differentials.

So, we have 1st >= 2nd, 3rd > 1st, 4th >= 1st, 3rd > 2nd, 4th > 2nd, 3rd = 4th.

Well, right away that’s good news (well, ‘good’ if you want this study to have a conclusion): there are no blatant contradictions there. That’s actually better news than it may appear – if there truly was no pattern to which quarter was better than which (and all the observed results were simply random), there would almost certainly be a contradiction.

The conclusion is not, however, what I had anticipated. Judging from earlier data, I was fairly sure that the third quarter would prove to be conclusively most important. However, according to this data, it isn’t: the unified formula suggested by the data is 4th = 3rd > 1st >= 2nd – that is, the third and fourth quarters are definitely more important than the first and second, but are themselves even, and the first and second may also be even.

Now, these statistics allow a certain degree of interpretation – for example, how do you resolve 4th >= 1st, 1st >= 2nd but 4th >2nd? The nature of this discrepancy – that is, two comparisons suggesting a logical order but not a logical degree, is not an uncommon characteristic of this type of analysis’s random error. There is likely a resolution (or, alternatively, there is no pattern and these results are, in fact, by chance), but unfortunately the only way to establish that resolution is to increase the sample size – that, again, is a task for later in the summer.

I could milk this some more, but let’s cut this portion off here – we have one more thing to touch on before we turn the page on this portion of the analysis.

Overall Differences

Before ending this portion of the analysis, let’s look at one last approach. This approach is not as specific or thorough as the above ideas, which actually grants an advantage: while the following approach would not be able to pick up on subtle differences between different quarters and halves, it can be assumed that any notable difference in the following approach is indicative of a true difference.

This approach is simple: what was the overall winning percentage of teams that “won” each quarter and half? A simple compilation of the gargantuan dataset we already had revealed these results (note, the numbers do not add to 1230 due to tied quarters that hypothetically favor neither team):

  • 1st Quarter Winners: 756 wins, 405 losses, 65.1%
  • 2nd Quarter Winners: 745 wins, 429 losses, 63.4%
  • 3rd Quarter Winners: 786 wins, 387 losses, 67.0%
  • 4th Quarter Winners: 766 wins, 396 losses, 65.9%
  • 1st Half Winners: 855 wins, 323 losses, 72.5%
  • 2nd Half Winners: 889 wins, 304 losses, 74.5%

And lastly comes that epic question of statistical significance. Which of these differences are statistically significant? I’ll spare the math and just jump to the conclusion; factoring everything in, these statistics show a statistically significant advantage in the comparisons of 1st > 2nd, 3rd > 1st, 3rd > 2nd, and 4th > 2nd (it’s notable that though all are significant at nearly the 90% level, the 3rd > 2nd and 4th > 2nd are the most significant). Additionally, the data suggests that 4th > 1st and 3rd > 4th, though not at nearly certain confidence levels (66% and 72%, respectively).

So, considering only these conclusions, we would come up with this demented equation: 3rd >= 4th > 1st > 2nd. Don’t get too excited by the absence of a contradiction with our earlier formula – while usually a conclusion is nearly-certainly proven when two separate approaches lead to the same result, these two approaches aren’t entirely different – they’re based on the same data, so it’s natural for them to be closely related.

What’s notable, though, is that there is a larger degree of certainty of the relationships when using this method. Whereas the earlier method failed to make a determination between the 3rd and 4th quarter, this one suggests a possible benefit for the 3rd quarter (and certainly shows no benefit for the 4th quarter – equality is still possible, however). To a greater degree, this approach marks a more certain definition for the comparison of the 1st and 2nd – namely, that the 1st is, indeed, more important.

So which do we accept? That’s a surprisingly subjective question for a statistical issue. Statistically, we could take either of the two studies, or a combination of the two – but they do show slightly different things (‘Little White Statistics’), so the question becomes where we attribute the random error. This effect can be minimized by expanding the study size, but in the meantime it’s a matter of judgment – I, personally, feel random error will affect the first method more due to its more segmented nature – the sample sizes for each individual comparison are smaller (giving random error a larger impact), and there are many, many more samples to be affected. Therefore, I believe the conclusion of this latter portion to be more accurate.

Statistically, the proper way to say this would be something along the lines of “we can be 90% confident of the latter conclusion (3rd >= 4th > 1st > 2nd) and 95% confident of the former conclusion (3rd = 4th > 1st >= 2nd)”. Looking carefully, we see that the latter conclusion is really a specific case of the former conclusion (noting that ’3rd = 4th’ means that we can’t make a judgment, not that we’re judging them to be equal) – or, in other words, both the former and latter conclusion can be correct, but the latter can’t be correct without the former. One of those ‘all squares are rectangles but not all rectangles are squares’ types of situations.

So, I’m accepting the latter for the time being, but we’ll definitely revisit this portion of the study when we analyze the past 10 years – at a sample size of 12,300, nearly everything is statistically significant, allowing us to more definitively define these trends.

But wait! What about a comparison of the halves? Comparing the halves allows us to say with 86% confidence that the second half is more important (under the definition we’ve repeated several times) – but, it’s a commonly accepted notion that at least a 90% confidence level is required (many places a 95% confidence level) to make a conclusion, so alas, we have no conclusion. If the same ratio holds up when looking at the last 10 years, we’ll have an incredibly statistically significant conclusion, so we’ll see then. But verily this vichyssoise of verbiage veers most verbose, so let me move on to the Little White Takeaways.

LITTLE WHITE TAKEAWAYS


In this installment, we looked at whether or not certain quarters (or halves) were more beneficial to perform well in – or, in other words, which quarters correlated best with a team’s success – or, in even simpler terms, which quarters are most important. And in our analysis, we arrived at the following conclusions:

  • The 2nd half is likely to be more important than the 1st half, but the statistical evidence is not yet definitive (though it’s about as close as it can be without being considered definitive).
  • There is a “pecking order” of which quarter is most important to perform well in. Generally, this order is of the form 3rd ? 4th > 1st >= 2nd (or, the 1st is better than or as good as the 2nd, and the 3rd and 4th are indistinguishable both better than then 1st and 2nd).
  • Specifically, that same order can be narrowed down a bit, down to 3rd >= 4th > 1st > 2nd (or, the 1st is better than the 2nd, the 3rd and 4th are better than the 1st, and the 3rd may be better than the 4th). This doesn’t contradict the above idea, it’s just a special case of it – we can be very confident that the above is true, and slightly less confident that this one is true.
  • All these conclusions will become much more set-in-stone when we perform this analysis on every box score over the past 10 years (rather than just this season). Some of you may wonder about the rule changes over the past 10 years affecting the results – but the good news is that the differential statistic should not be affected with regards to wins. There’s no reason to believe that the rule changes resulted in a certain quarter becoming more important (although never fear, just in case we’ll run some basic tests to see if somehow they did).
  • So what’s next? Well, there’s three items of business on tap for the near-future. First, there are still many angles of this analysis to consider – most notably, do certain teams perform better in certain quarters, and do the elite teams perform better in a particular quarter? Second of all, like I said in the first post, we want to conduct that analysis on Kobe Bryant and test if his team’s success really does go down as his shot volume increases, as well as whether that’s due to his choices or other causes (teammates’ off-nights forcing him to shoot more). And thirdly, I’d like to run a few of these tests we’ve been doing the past few days on just NBA playoff or NBA finals games, to see if the statistics change.

    So what comes first? Probably the first (on teams and differentials), but after that we’re likely headed for a break from this study for a few weeks so we can focus on Kobe Bryant. Yes, I know it would’ve been smarter to analyze Kobe during the Finals when all eyes were on him. I’m a blogger, not a businessman.

June 18th, 2008, posted by joyner

Box Score Analysis: Wins by Differential, Part 1

Good afternoon, sports fans – I’m going to start out by saying that the whole ‘entry every two days’ thing isn’t going to continue all summer, so if you’re getting tired of reading a novel every couple days, never fear, this rate of posting will only continue through shortly after the season ends. I’ll probably settle into a once- or twice-a-week schedule over the summer, depending on how long my ideas for analysis hold out.

Speaking of which, does anyone know the plural for ‘analysis’? Analysises? Analyses? Analysi?

Today we’re going to look at one of the two things I previewed in the last Box Score Analysis entry – how quarter differentials correlate to wins. Essentially, we’re asking the question “how often did a team winning by X points after the first quarter go on to win the game?” for every possible value of X (and for every quarter and half).

In this case, I’ll be splitting the analysis in half. Unknown to me when I set out on this part of this research, there are a lot of conclusions, some far more important than others. Putting them all in one entry would dilute the impact of the more meaningful ones, so in this entry we’ll be covering the less impactful (though still interesting) ones. Next entry we’ll cover the real heavy-hitters. So today we want to see if there’s a certain time when the probability of winning drastically increases – for example, how much more likely to win is a team leading by 7 at halftime compared to a team leading by 5? Is it significant at all?

Unlike the last entry, I’m going to spend a good bit less time covering the statistical reasoning behind the conclusions and more time covering the conclusions themselves. If you want to see the proof behind the numbers, by all means let me know and I’d be glad to send it to you; or, you can run the numbers yourself: I’m posting the data sheet that’s being used to derive all this information right here.

Statistical Significance Overview

But let me start by going back to that pesky ‘statistical significance’ idea (which, if you understand already, jump ahead three paragraphs). Again, the upcoming ‘Stats Primer for a Sports Fan’ will detail what statistical significance is, but basically if something doesn’t have it, it’s not proven. A stat is ‘statistically significant’, by definition, if it is very unlikely to have simply happened by chance. For example, if a player is listed as a 60% free-throw shooter and misses three times out of three free-throw attempts, that’s not statistically significant enough to make us doubt that he’s really a 60% shooter (because statistically there was a 1-in-20 chance he’d miss all three). But, if a player is listed as a 95% free-throw shooter and misses three straight, that’s pretty significant because it’s unlikely that a shooter who was really that good would miss three out of three (statistically, it’s about a 1-in-10,000 chance). (Important note: we’re saying this as if we only observed the shooter taking three free-throws. The best free-throw shooter in the world will miss three straight at some point in his career – but what are the odds that the specific time we say ‘hey, take three free-throws’ and observe only those three that he misses all three?)

Statistical significance is thrown around a lot because it’s a pretty general term, but here we’re going to mainly use it when talking about comparing two statistics. For example, Peja Stojakovic shot 92.9% from the free-throw line this year, and Dirk Nowitzki shot 87.9%. Is that difference statistically significant? If so, we can say that there’s statistical proof that Stojakovic was a better free-throw shooter than Nowitzki this year; but if not, we can’t conclusively assert that (incidentally, it’s not statistically significant, although the difference between Chauncey Billups shooting 91.8% and Dirk is significant even though Chauncey shot worse than Stojakovic. See why we call it ‘Little White Statistics’?).

And a final note: when we refer to ‘confidence’ in terms of statistical significance, it means something pretty simple: basically, we can that confident that the observed results come from an actual difference, rather than just a random sampling error. So basically, when we say “we can conclude this at 95% confidence”, it means we’re 95% sure what we’re concluding is true.

Study Background

Alright, enough fluff. The reason I bring up statistical significance is because this analysis really depends on it to make any kind of conclusions. But before we get to the takeaways, a brief background:

This portion of the study was completed by taking all the box scores from the 2007-2008 NBA regular season, computing the quarter/half differentials for each quarter (with respect to the home team, so a negative differential means the away team outscored the home team), and then looking at how many wins and losses each quarter/half differential led to. Then, we did our correlation voo-doo magic to see what increase in win percentage each point added to the differential gave. And finally, we looked to see if any of that crap was statistically significant. And if you really want to see the numbers, I can show them to you – but I’d recommend taking my word on it. If I was making stuff up, I’d make up far more conclusions than this.

And with that, on to the results, subdivided into topics for your reading convenience:

The Halftime Differential

Let’s lead off with something bizarre. In the 2007-08 season, what halftime differential from leading-by-5 to trailing-by-5 was most likely to lead to a home team victory? Leading-by-5? No – within that range, the home team won most often (over that margin) when they were trailing by three points at halftime. This season, the home team trailing at halftime by 3 points won a bizarre 75.7% of their games (28 out of 37), compared to about 65% from margins +1 to +5, and around 55% from -1 to -2. That’s statistically significant at 95% confidence compared to differentials -2 through 1, but not statistically significant compared to 2 and higher.

Similarly bizarre, in games that were tied at halftime, the home team actually lost more often than they won – the home team won only 46% of games that were tied at halftime (24 out of 52). That’s not statistically significant compared to most negative differentials, but it is compared to that -3 halftime differential (at an excessively high confidence level, too).

So is the home team really more likely to win when they’re down by 3 at halftime than if they’re tied? I’m taking this conclusion with a grain of salt. 95% confidence is a high level, but statistically that means that for every 20 conclusions you make at 95% confidence, one will likely be wrong. I have a feeling this might be that one – but fortunately, this topic is very easy for further research (which I’ll mention later). And yes, in case you’re keeping score at home, we just used statistics to analyze statistics. To be specific, we statistically proved that statistics aren’t always reliable. But is that a reliable conclusion? And with that, this blog disappeared in a puff of logic.

But by that same token, we’re not talking 95% confidence in this statistic. According to the numbers, we can (apparently, note I’m still as skeptical as you) assume a 3-point halftime deficit leads to more home team wins (than a halftime tie) with a remarkable 99.7% confidence. So either I completely screwed up the math somewhere, or we’re on to something (if anyone’s skeptical enough to check my math, we have a proportion of .757 with 37 samples and a proportion of .462 with 52 samples). But I’m still skeptical, so this will definitely be one of the items touched on when we re-do certain parts of this analysis for all the games over the past ten years (oops, gave away the ending).

I should also note I’m not implying any causation here – I’m certainly not saying it’s wise for a home team to drop down 3 points before halftime. What we’re looking at here are measures that predict what would happen anyway. We aren’t saying that trailing by three at halftime leads to a win – what we’re saying is that the conditions that lead to a 3-point halftime deficit also lead to a victory by the end of the game.

Through-Three Differential

The team leading at the end of three quarters was always more likely to win this season, regardless of whether they were home or away, and regardless of the differential. Away teams leading by as little as one point after three quarters won 61.5% of the time, while the home team leading by as little as one point won 54.7% of the time. The difference in the winner is certainly statistically significant (at 94% confidence).

Also interesting (and touched on more in the next analysis) is that once you get to a meager 4-point lead going into the fourth quarter, your victory percentage is sky-high – 75% for the home team, 71% for the away at a 4-point differential, and the percentages only get higher from there.

Critical Points

There’s absolutely no way to phrase this section title that completely prevents any possible puns.

At the beginning, we said we wanted to see if there’s a certain differential in each quarter/half that signifies greatly increased odds of a win. And, as it turns out, one does appear. Analyzing statistical significance here is difficult (because we’d have to compare every pair of differentials’ winning percentages over a large range, for each of the seven time periods), but just some random sampling (yes, now we’re randomly sampling our statistics) for statistical significance revealed these are likely significant at the 90% confidence level, at the least.

  • 1st Quarter: Home: 2; Away: 6
  • 2nd Quarter: Home: 4; Away: 6
  • 3rd Quarter: Home: 5; Away: 5
  • 4th Quarter: Home: 3; Away: 7
  • First Half: Home: -3; Away: 5
  • Second Half: Home: 1; Away: 4
  • Through-3: Home: 2; Away: 1

There’s some pretty interesting stuff in there, believe it or not. In most cases, those point differentials correspond to a point at which teams become around 20% more likely to win the game, and sustain that increased win percentage over higher differentials. There’s a couple notable items in this:

  • First of all, it’s pretty notable how much less the home team needs to do to raise their win percentage. In most cases, a differential of -2 (the away team leading by 2) is what corresponds to an even winning percentage between the two teams.
  • Even more notable is that the home team still has a strong chance of winning as long as they’re losing by 3 or less points at the end of the first half. We covered in great length the fact that a 3-point halftime deficit this season still resulted in a winning record for the home team – but after 3, the drop is significant – trailing by four only brings victory 41% of the time, and the ratio decreases steadily after that. And, conveniently, the different between -3 and -4 is statistically significant, adding to the intrigue of the -3 differential.
  • We mentioned this earlier, but it’s also notable how delicate the through-three differential is – one 3-pointer drastically changes the odds of victory from the home team’s favor (70% when winning by 2 entering the fourth) to the away team’s (62%), a pretty ridiculous 32% swing.

As I said above, no causation is implied here; I’m not trying to say that the act of winning the first quarter by 2 points causes the home team to be substantially more likely to win. Instead, I’m suggesting that whatever causes the home team to be up by 2 or more also causes the home team to eventually win the game. Leading by those differentials is a sign that they stand a good chance of winning the game – not the reason they do.

Regression Analysis

Like last time, I ran a regression analysis, seeking a correlation between differential (for each quarter and half) and winning percentage.

There is one – an incredibly strong one. The second, third and fourth quarter differentials each correlate incredibly strongly to winning percentage (the first quarter differential correlates as well, but not quite as strongly – R=.9 for the first quarter whereas R=.94 for two, three and four). What this means is basically, outscoring your opponents by more points during a certain period of time does raise your chance of winning. We’re really uncovering deep, hidden secrets now, aren’t we? I think we just statistically proved that you win a game by outscoring your opponent. Groundbreaking, absolutely groundbreaking.

The slopes of these regression lines border on relevant, though. The quarter regressions all hold slopes of roughly .023, implying that for every point added to the differential, winning percentage increases by .023. To put that in terms that make sense, it means statistically if a team outscores its opponent by 5 points in the second quarter in every game, they’ll likely win two more games (over a season) than if they outscored their opponent by only 4 points in those quarters.

More relevantly, that means that if a team raises its average differential in one quarter by 1 point, it’ll average 2 more wins over an 82-game season. For a long-term coach, that’s a great goal. Raise it by 1 point per quarter and that’s possibly an 8 game improvement. That might sound drastic, but consider how strong a 4-point average differential difference makes in the league – in 2007-08, a 4-point difference is what separated the Jazz and the Raptors.

Miscellaneous

And beyond all of the above, there are a few things in this analysis that I just find flat-out interesting. There’s no statistical relevance to any of them, but they’re interesting observations.

  • No home team recovered from being down 16, 17 or 19 points after one quarter (total of eight occurences), but two of the three home teams down 20 after the first recovered: Minnesota against Indiana and Phoenix against Seattle. Minnesota completely erased the 20-point deficit and led at halftime by 1, whereas Phoenix trailed by only 2.
  • The home team actually held a winning record when being outscored by 10 in the second quarter, or by 6, 7 or 10 in the third. They did not, however, hold a winning record when being outscored by anything more than 4 in the first quarter, or 5 in the fourth.
  • The lowest quarter differential to yield a 100% winning percentage was 13, when scored in the fourth quarter by the home team. The away team required a 16-point quarter-differential, but could have it occur in either the first or third quarters.
  • The away team won 3 times when being outscored by 19 points in the second half, but never won when being outscored by more than 16 unless it was 19.

One of the things I plan to do later in the summer is re-hash the more ‘controversial’ or ‘fuzzy’ conclusions from this analysis by expanding the sample pool ten-fold and looking at the statistics for every game over the past ten years. If the conclusion on halftime differential holds up then, it’ll be only a one in a trillion (in other words, impossible) chance that it’s by coincidence.

I think that’s about all the information I can beat out of this data without stepping into the second half of our analysis. If anyone has any other questions that might be answered by this data, feel free to e-mail me at the heavily disguised e-mail address on the left. Wait until tomorrow though, since I’m only half-done with this portion of the analysis. Now, on to the takeaways.

LITTLE WHITE TAKEAWAYS

So, in this analysis, we looked at how often each point differential led to a win (or, more specifically, the winning percentage associated with each point differential). As always, teams were separated by location, since it’s been thoroughly discovered that differential trends are very different between home and away teams.

  • Halftime Differential: Crazy stuff – I recommend reading this part regardless of your knowledge or interest in statistics. Basically, there’s evidence that the home team wins more often when trailing by 3 points at halftime than if the game is tied at halftime. It sounds bizarre, but the statistics behind it are extremely straightforward. Later this summer I’ll look at this again with data from the past 10 years (or 7, depending on how far back Yahoo!’s box scores go) and see if it still holds true.
  • Through-Three Differential: The team leading at the end of three quarters, regardless of home or away and regardless of the amount they lead by, is always statistically more likely to win the game (though not extensively – 82% of games are won by the team leading after three, but only around 60% are won by the team leading if they lead by less than 3).
  • Critical Points: There are critical points in the differential for each quarter and half, meaning that there is a certain differential that begins to lead to a much larger chance of winning. For example, a 1-3 point advantage for the home team in the second quarter (only the second quarter, not first and second) yields about a 57% chance of victory – however, 4 and above yields a 70%+ chance.
  • Regression Analysis: A regression analysis showed there’s a very strong correlation between quarter differentials (in every quarter) and final result. Especially interesting from this part is the impact that a small improvement in differential can have – this part is also interesting reading even for those not interested in statistics.
  • Miscellaneous: Weird stuff happens.

Don’t miss next entry, though. In the next entry we unveil some very interesting statistics about the power of individual quarters, and what periods of the game are most important to perform well in. It’s definitely interesting even to the casual fan, so come back tomorrow when it’s finished and posted. Until then, wish me luck on my last week as a college student.

-DJ

June 13th, 2008, posted by joyner