The Interpretation of Symbols
A Joint-post by Silverbird5000 and Bethlehem Shoals
Some of you may be following the latest blogosphere contretemps over Hollinger's Player Efficiency Ranking (PER)- that great Rosetta Stone of NBA statistical analysis, whose benevolent tyranny over our league it is our duty as fans to periodically resist. The argument comes down to the wisdom of the per-minute adjustment, which is a central part of PER, along with pretty much every other Ultimate Metric in the marketplace. On the one hand, adjusting for minutes played seems like a good idea, insofar as it immunizes our judgment from the folly of coaches. If a player who should be getting 40 minutes a game only gets 20, his per-game stats will understate his true value. What per-minute adjustments do is control for mismanagement, as Ziller correctly points out.
The problem with this line of reasoning is that it assumes the homogeneity of court time. It assumes that if a player scored 20 points in 20 minutes, he would also score 40 points in 40 minutes. That there will by systematic differences between these two situations is almost too obvious to point out. It's the difference between sharing the ball with Jordan Farmar while being guarded by Kenny Thomas, and sharing the ball with Kobe Bryant while being guarded by Ron Artest.
Insofar as the problem here is one of rotation, small-scale adjustments in minutes played shouldn't create major distortions (it isn't unrealistic to think that if Tim Duncan played 5 extra minutes per game, his per-minute production, as influenced by the level defense he'd face, would basically be the same). But when PER catapults bench players into the starting five (or vice-versa), be on the look-out for inflation. Call this the Silverbird-Shoals Hypothesis, or the THEOREM OF INTERTEMPORAL HETEROGENEITY (TOIH).
By way of proof, we propose the following experiment: imagine a league in which the distribution of minutes perfectly reflected the PER rankings, such that the top-ranked player played the most minutes per game (43mpg), the 100th-ranked player played the 100th most minutes (31mpg), and so on and so forth. Now, compare this projected distribution of minutes to that of the actual league. For most players, the difference between actual and projected mpg is fairly small - high PER players play high minutes, low PER players play low minutes. But for a significant minority of players, actual mpg falls far short of what Hollinger's rankings predict. If TOIH is correct, we should observe inflation in the value of these players' PER. We invite you to consider the evidence and decide for yourself.
The following table shows all players (PER rank < 150) whose actual-projected mpg differential is 12 minutes or more:
[That pretty much every player on this list is vastly overrated by PER is, ultimately, a subjective judgment. But it is the kind of subjective judgment only a lunatic doesn't share.]
Note that everyone here ranks in Hollinger's top 150; if PER accurately reflected productivity, then leaving aside issues of position, age, etc., every one of them should be on some team’s starting five. But none of them are, not even Ginobili. Indeed, despite their high per-minute productivity, many of these players see no more than 15 minutes a game. Somewhat paradoxically, this suggests that PER inflation is a matter of being both overvalued AND underplayed; or, more accurately, being overvalued per-minute but under-valued per game.
If PER inflation is basically the problem of over-qualified bench players, it would seem that PER deflation, its counterpart, is somewhat more complicated than just under-qualified starters. Among the worse 150 players in Hollinger’s rankings, the following play significantly more minutes than projected: Bruce Bowen (#372/+19mpg), Speedy Claxton (#371/+14), Adam Morrison (#366/+14), Trenton Hassell (#331/+14), Desmond Mason (#307/+17), Raja Bell (#262/+18), Shane Battier (#261/+17), Larry Hughes (#252/+17), and Marvin Williams (#239/+14). Given our hypothesis, it would stand to reason that all or some of these players have no business regularly facing top-tier competition.
Bowen, Bell, and Hassell can be excluded, for their defensive contributions are partly invisible. But Claxton, Morrison, Mason, Hughes (as currently constituted) and Williams (at this point in his career) are all players who, in a perfect world, would be used more sparingly. That they are not is a function of either missing resources or incompetent coaching. It is interesting to find fantasy and Right Way figurehead Shane Battier on here; 'twould appear that his production is a function of minutes, not value.
To conclude, the virtue of per-minute adjustment is that it adjusts for bad coaches. But in the process it runs afoul of a far greater and more systemic problem: that is, the unequal distribution of talent in the league. In a world of perfect balance, where starters played equal starters, bench players played equal bench players, or everybody just played everybody all at once, then each man’s productivity could be measured under equal conditions, and so without fear of distortion. This world would be called baseball, a sport whose statistical models we have borrowed without regard to their unspoken assumptions. As it happens, our sport is basketball, and its time is ineluctably structured by the inequities below. Whether our statisticians can ever overcome this problem remains to be seen.
Silverbird5000, Bethlehem Shoals
September 10th, 2007