Fly Into Tomorrow

Ok. Back to what's important.

If you haven’t been following this week's PER debate it probably isn’t worth starting now. And if you have been following it, chances are you’re bored sick. But for those eight or nine of you out there actually looking forward to the next installment, come and join me for one final ride.

When we last left off, the theory of PER inflation was under fire from the gentlemen at BallHype, who put together an impressive study showing that season-to-season increases in minutes actually correspond to increased, not decreased, productivity – even for the subgroups we argue are inflation-prone. The problem with looking for the minutes-productivity relationship in this data is that causation may very well run the other way, like when players get more minutes because they've improved. I originally thought this problem could be avoided by looking at intra-season (i.e. game level) data. But as commenter Brian M wisely points out, the problem remains that coaches generally let players play when they’re hot, and bench them when they're cold - so we still won't know if minutes increase productivity, or the other way around.



Rather than look directly at the mpg-PER relationship, I thought I’d try approaching the problem from another angle. Our original hypothesis was that per-minute productivity will decline with large jumps in mpg because of a) the increased quality of teammates with whom production is shared, and b) the increased quality of defenders. My idea is pretty simple: if we can show the (negative) effect of match-up quality on productivity, and the (positive) effect of minutes-played on match-up quality, this would provide some indirect proof that per-minute adjustment creates inflated PERs.

The raw data I use are from the bizarrely under-the-radar +/- stats website basketballvalue.com. For each game, they provide data on every 5-on-5 combination that takes the floor and the total number of minutes elapsed for each match-up. Thus, for every player-game observation it is possible to calculate the average quality of teammates and defenders in that game- first, by taking each player’s 2006-2007 PER ratings, then multiplying that figure by the fraction of time they share the floor. For example, if Ginobili plays 30% of a 2-on-2 game with Duncan (PER 26) and 70% with Oberto (PER 12), then the average PER of his teammates would be 16.2 (.3*26 + .7*12). By applying the same method to our 5-on-5 data we derive our two independent variables, "Teammate-Per" and "Opponent-PER", for each player, for each game. Then, by linking these match-up variables with boxscore data from the same games, we can analyze the effect of both Teammate- and Opponent-PER on individual game-level production.



The results of our regression analysis are given in the tables below. For the first model, we test the effect of Teammate and Opponent-PER on three different measures of per-minute production (that is, our dependent variable): the NBA efficiency metric (NBA48), a simplified Hollinger metric (Hollinger48), and Dave Berri’s Win Score (WS48), each of which are normalized a la PER. We use a linear fixed effects model to control for both individual and team effects. (Without getting to technical, what this basically means is that we cancel out the effects of fixed differences in individual and team productivity, i.e. the fact that Kobe or the SUNS are more productive on average, and in ways that are unrelated to Opponent-PER.) For the second model, we test the effect of Opponent-PER on WS48 using different subgroups and controlling for minutes played.

We find that the effect of Teammate-PER is weaker than expected, and its significance is sensitive to the metric we select. For both NBA48 and Hollinger48, increasing Teammate-PER has a small and significant negative effect on productivity, but using Berri’s WS48 metric, that significance disappears. (This makes some sense, since Berri’s system emphasizes shot efficiency over point totals, making the benefit of high-quality passing more important than the cost of reduced attempts). Moreover, when included in a model with Opponent-PER, the effect of Teammate-PER drops out entirely (see table 2).

In contrast, the effect of Opponent-PER (i.e. the quality of defenders) is robust for all three performance measures. In the first model, the effect is still quite small – a negative .06 decline in WS48 for every 1 unit increase in Opponent-PER. However, that effect increases significantly with the addition of further controls (i.e. mpg). And when we focus only on our original subgroups - i.e. players with 15+ PERs and high mpg - the effect jumps to –0.20. This means that increasing the average quality of the opposition from 10 to 20 PER – that is, going from a match-up with bench players to a match-up with starters – leads to a 2pt decline in per-minute Win Score (where WS48 is normalized with a mean of 15). Not an enormous decline, but still significant.



Going back to our original theory of PER inflation, we also tested to see if Teammate-PER and Opponent-PER are indeed correlated with the number of minutes an individual plays. As one might expect, we find that yes, the longer a player stays on the floor, the higher the quality of both teammates and defenders. Thus, given the positive effect of minutes-played on match-up quality, and the negative effect of match-up quality on individual production, it seems plausible that – all things really being equal – an increase in minutes will lead to (slightly) decreased productivity, on average. And that this is especially true for above-average bench-players who get a large bump in mpg - that is, the subgroup we originally hypothesized would be subject to inflation. In short, THE THEORY OF INTERTEMPORAL HETEROGENEITY LIVES.




A couple quick caveats- first, these are the results of a pretty quick and dirty analysis, so please judge them accordingly. Also, while I do know my way around this kind of analysis, I'm far from an expert, so consider that as well. Finally, it's true that the problem raised by Brian M still applies: players who are more productive will stay in games longer, and thus face better defenses. However, this just means that if anything, the effect we observe is understated, and so it hardly undermines our case.