Monday, November 26, 2012

Going Whole Ballhog

If you're one of the tens of readers who follow me, then unless the bottom of your rock doesn't carry ESPN, you've probably heard something about this kid from Grinnell who dropped 138 on a hapless Faith Baptist Bible College basketball team.  Now, granted, this was a Division III basketball game—hardly the acme of organized basketball.  Still, as Kobe Bryant said, "I mean, I don't care what level you're at, scoring 138 points is pretty insane."  Jack Taylor is a household name now, people.

Rather predictably, there was some backlash, with some people claiming that it was rigged, or that it was selfish basketball, or at least not The Way That Basketball Should Be Played (because anything that portentous has to be written upstyle).   I can't say anything as to whether it was rigged, although it didn't look like it to me, and as with any conspiracy theories, it's easy to say something like that when you don't have to offer any proof.  All you have to do is throw out your hands and say, "It's common sense!"

But we can say something about whether it was selfish or bad basketball.  Some folks have taken it upon themselves to make a virtue out of evenly distributed teamwork.  That's fine as a matter of personal opinion, but they make a mistake, I think, who believe that it's an intrinsic virtue of basketball.  It wasn't an intrinsic virtue of basketball when Naismith put up the first peach baskets, and until someone invents a game that makes teamwork an explicit scoring feature, there won't be a sport where it's an intrinsic virtue.  (I also think that some of these folks could benefit from playing with a scoring phenom, just to see what it's like, but that's neither here nor there.)

What makes it a virtue—when it is a virtue—is that it makes a team more efficient, by and large.  On the occasions when a player goes out and consciously attempts to score a bunch, it quite frequently turns out that the other players on the team are more efficient, and thus the team as a whole would have been more efficient if the offense had been more evenly distributed.  This is a basic result from game theory.

But that didn't turn out to be the case here.  Taylor scored 138 out of his team's 179 points.  That's 77 percent.  To get those points, of course, he used up a lot of his team's possessions: 69 percent, according to ESPN.  It is a lot, but it shouldn't overshadow the fact that the rest of his team used up the remaining 31 percent of the possessions and ended up scoring only 23 percent of the points.

Let's see how that stacks up against two other phenomenal scoring performances of the past: Wilt Chamberlain's mythic 100-point night in Hershey, and Kobe's own 81-point barrage at home against the Toronto Raptors.  (Taylor nearly had 81 just in the second half.)  I'm going to ignore claims that the Warriors game was a farce in the second half, or that the Toronto Raptors were a defensive sieve; I'm only interested in the efficiency figures.

Chamberlain's Warriors scored 169 points that night, so Chamberlain scored 59 percent of his team's points, using (again according to ESPN) 47 percent of his team's possessions.  Kobe's Lakers scored 122 points, so he contributed 66 percent of his team's points, while using (ESPN again) just 51 percent of the team's possessions.

One way to look at these feats is to consider how much more efficient the individual players were than the rest of the team.  So, on a percentage basis, Taylor scored 77 percent of the points on 69 percent of the possessions, whereas the rest of the team scored 23 percent of the points on 31 percent of the possessions.  Taylor, therefore, was (77/69) / (23/31) = 1.50 times as efficient as his teammates.  Similarly, Chamberlain was (59/47) / (41/53) = 1.62 times as efficient, and Kobe was (66/51) / (34/49) = 1.87 times as efficient.

However, such a measure can easily be misleading.  If someone plays a single minute, puts up a single three-pointer, and makes it, they might (as a normal example) have 3 percent of the team's points with only 1 percent of its possessions.  By the same metric, such a player would be (3/1) / (97/99) = 3.06 times as efficient as his teammates.  What's missing is some measure of the magnitude of the player's impact.

A more representative measure of the player's efficiency impact can be obtained by considering how efficient the team would have been if the other players had managed to use up all of their team's possessions, at the same efficiency they had been exhibiting.  For instance, Taylor's teammates used up 31 percent of the possessions, scoring 23 percent of the points they eventually scored.  If they had continued at that same clip, but used up 100 percent of the possessions, they would have eventually scored 133 points—about 74 percent as much as they actually did.  To put it another way, the team with Taylor was 31/23 = 1.35 times as efficient as they would have been without him.

Using that as our guideline, the Warriors with Chamberlain were 53/41 = 1.29 times as efficient as they would have been without him, and Kobe's Lakers were 1.44 times as efficient as they would have been without him.

Just as a demonstration of how amazing all of these numbers are, if a team averages a true shooting percentage of 50 percent amongst four players, and the remaining player uses up half the possessions with a true shooting percentage of 70 percent, that team is only 1.20 times as efficient as they would be without that player.  To increase their teams' efficiency as much as they did, these three athletes had to be remarkably efficient and prolific.

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