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Love and Mathematics Pt. 2: The Paul Millsap Quandary
tziller posted 9/12/2007 from ballhype.com
Over the past few days, there's been lots of discussion about advanced basketball metrics -- and specifically per-minute statistics -- among bloggers. Skip this paragraph if you know what's going on. Otherwise: It started with Carter Blanchard of Plissken at the Buzzer, who refuted the usefulness of John Hollinger's PER and the basic per-minute statistic. I defended PER on Saturday, here at Ballhype. Thank You Isiah and We Rite Goode jumped in, followed by a response at Plissken, followed by a controversial entry at Free Darko, which set off any number of responses and mini-battles. All the while, we've had some terrific conversation in the comments to my post. Awesome.
But one of the things which kept popping up was this assertion I'll hereby credit to Free Darko: "Insofar as the problem here is one of rotation, small-scale adjustments in minutes played shouldn't create major distortions. [...] 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)." Shoals and Silverbird are arguing that because low-minutes high-PER guys typically play against fellow bench players, their PER is higher than it would be if they played starter minutes. They aren't arguing (as some surmised) that PER is useless, just that it is prone to inflation. The argument, from seemingly everyone on the 'anti per-minute statistics' side, is that if you increase a player's minutes, his efficiency will suffer.
There's a problem with this oft-repeated claim: It's not true.
Thanks to the data-collection efforts of Ballhype's own Jason Gurney, I'm going to try to ensure this claim never gets stated as fact ever again. Using seasons from 1997-98 to the present, we identified all players whom played at least 45 games in two consecutive seasons and whom saw their minutes per game increase by at least five minutes from the first season to the second. The players must have played between 10 and 25 minutes per game in the first season, to ensure we were not dealing with either folks who went from none-to-some playing time or superstar candidates who took over an offense and thus got a minutes boost. This is aimed at roleplayers whose role becomes more prominent -- exactly the candidate FD's Theorem of Intertemporal Heterogeneity implies will suffer from increased minutes.
Since I seem to express myself more clearly via Photoshop, here is the result of our mini-study.
No, increased minutes do not seem to lead to decreased efficiency. In fact, the data indicates increased minutes lead to... increased efficiency. More than 70% of the players in the study (there were 251 in total) saw their PER (which is, by definition, a per-minute summary statistic) increase with the increase in minutes. Players whose minutes per game increased by five saw an average change of +1.38 in their PER. The correlation between increased minutes and change in PER in this data set was +0.20.
One step further: Players who had at least five years of experience including their first-season in this study and got the requisite 5-minute increase (106 such players) saw an average change of +1.26 in their PER. It's not just young kids who happen to improving and getting more minutes all at the same time -- vets who get more minutes typically see their per-minute production rise. A full 67% of these players so positive changes in PER with the increased minutes. (And this answers one of Carter's concerns with existing studies.) Let's bump this up to players who had at least eight years of experience going into their minutes increase; we had 52 such cases. The average change in PER: +1.31. Of these players, 69% saw their PER increase with more minutes.
One concern I had: Players who started with above-average PERs and then saw a big bump in their minutes; call it The Paul Millsap Quandary. (Ty Keenan of Plissken also alludes to this problem here, though he brings up a separate issue which I don't intend to address... mainly because I don't think value quantifications must be coupled with some static unit of measure. 15 is better than 14, 20 is a lot better than 15, etc. I depend on sheer logic in these cases, and I don't think there's a problem with that.) ANYWAY, Paul Millsap. So I looked at players who had a PER of at least 15 in the first season and then saw at least a 5-minute increase. There were 53 such players, and the average change in PER was -0.22. Ooh, ouch. But critics, don't seek shelter here -- the negative average is completely erased when you take out Malik Rose's barely viable (600 total minutes) 1998-99 season and Nazr Mohammed's inexplicable career. But we don't even need to tamper with the evidence to feel sure our theorem that increased minutes does not necessarily lead to decreased efficiency for even above-average players is correct: Look at the reported decline here (-0.22) when compared to the reported performance increases above (+1.26 to +1.38). An average drop so small is negligible. More proof: of those 53 players with over-15 PERs who get the big minutes increase, 27 saw their PERs decrease (range of -0.1 and Malik's -6.5) and 26 saw their PERs increase (range of +0.1 and David Lee's +4.8). In fact, for over-15 PERs who then got at least 10 extra minutes per game the following season, the average change in PER was +0.18.
So how do we settle The Quandary? By admitting it is highly contextual and case-based at this level. The data does not say whether Millsap's per-minute production would suffer, improve or be maintained given more playing time. The data is inconclusive -- even if it were more conclusive, such as the previously highlighted notes -- we cannot ascertain motive from these relationships. As the adage goes, correlation does not mean causation. Or in terms I prefer: We don't know.
I want to emphasize this again: We don't know. We cannot look at any of this data and say "Increased minutes leads to increased per-minute production (aka efficiency)" just as we cannot and should not say "Increased minutes leads to decreased per-minute production." But this data does indicate a positive relationship between minutes and efficiency. The factors and/or causes of the relationship aren't known to us at this point -- some folks deeper in the muck might have private inklings; perhaps deeper investigation has been hashed and fried in the bunkers of Quicken Loans Arena or the Pepsi Center, or even in John Hollinger's basement. Who knows? All we do know -- based not only on this study, but the previous (exemplary) work of Basketball-reference.com's Justin Kubatko and Hollinger (via Knickerblogger) -- is that an increase in playing time DOES NOT cause a player's efficiency to falter as a rule. So stop saying it does.
