More Thoughts On Duck on a Rock

My post on PERs a couple of days ago led to a few interesting comments. Let me respond with a few more observations about evaluating player productivity in Duck on a Rock – I mean basketball.

Evaluating the Average Player

Imagine a team had a player that was average in every respect. For his position, he was average in shooting efficiency, rebounding, creating steals and assists, blocking shots, and committing turnovers and personal fouls. If we looked at this player via Win Score or NBA Efficiency, we would see an average player.

Now we take that same player and we increase his shot attempts. He is still average in shooting efficiency and every other aspect of the game. But he is now taking more shots. Win Score still tells us that this player is average. NBA Efficiency, which over-emphasizes scoring, now tells us that this player is above average. In fact, a player can be below average in shooting efficiency, and if he takes enough shots, be considered above average in NBA Efficiency.

The problem for decisi0n-makers is that in terms of offensive and defensive efficiency, teams lose when shots do not go in. If you take ten shots at a below average rate you hurt your team. If you take twenty shots at a below average rate you hurt your team even more. But NBA Efficiency, and PERs – two metrics that set the break-even point on shot attempts at a very low rate – will tell you that the player is actually above average when he takes a large number of shots at a level of shooting efficiency below the league average. Again, I need to emphasize this observation. As long at the player exceeds the very low break-even points set by NBA Efficiency and PERs, the more shots he takes, the higher the player’s rating.

In fact, one can do nothing else but score – either at a below or above average rate of efficiency, and NBA Efficiency and PERs will tell you a player is great. And furthermore the NBA player’s market will likely give our one-dimensional scorer significant money. But our model of offensive and defensive efficiency tells us quite clearly that the one-dimensional inefficient scorer will not create many wins.

Creating Shots and Confusing How and Why

People will argue that there is value is creating a shot. And that is true, if the shots you create go in. If you are simply chucking the ball in the directions of the basket, though, you are not helping your team win games.

But isn’t it the case that the more you shoot the lower your efficiency, and the less you shoot the higher your efficiency? If this is true, a high volume shooter may be helping his teammates take fewer shots and become more efficient.

There are two answers to this question. First, as Marty detailed last June, there is very little evidence that shot attempts and shooting efficiency have a strong relationship. But let’s ignore that point.

Let’s say the argument is true, shooting efficiency and shot attempts are indeed linked. If it is true, shouldn’t we adjust our performance metrics to take this into account?

Those who think we should are confusing how productive a player is with why that player is productive (a point I made last June).

Consider baseball for a moment. Imagine a hitter with a 0.350 batting average. This is pretty good. What if I said he only has this batting average because his manager only has him face left-handed pitching, and if he faced right-handers he would bat 0.150? Does this fact change his 0.350 batting average? No, he did what he did. The information on who he faced allows us to understand why he has this batting average.

In making decisions you need to consider both questions. But to answer the “why” question you first must know “how.” And when people rely on PERs and NBA Efficiency to determine “how”, the picture of productivity they are using is flawed.

Over Valuing Rebounds, Again

Is our model an accurate picture of “how?” It has been said that our model clearly overvalues rebounds. A few days ago I wrote an essay addressing this argument. I would add to that story by referencing the wisdom of Milton Friedman.

In 1953 Friedman published Essays in Positive Economics. In this work Friedman argued that you cannot refute a model unless one has an alternative that provides better predictions. In Friedman’s words, “criticism of this type is largely beside the point unless supplemented by evidence that a hypothesis differing in one or another of these respects from the theory being criticised yields better predictions for as wide a range of phenomena.”

People have argued that our model overvalues rebounds because its conclusions are inconsistent with their prior beliefs. Specifically people believe Dennis Rodman is not a very good player. Because our model says he is quite productive they conclude our model must be incorrect. But prior beliefs are not evidence against our approach. Evidence against our approach would come in the form of an alternative model that offers a better explanation of the evidence. From this perspective, our model only over-values rebounds if another model with an alternative value for boards explains and predicts better. To date, I have not seen this alternative model.

I do see evidence, though, that whatever model the NBA employs has trouble explaining and predicting. Wins and payroll are not strongly linked in basketball despite the fact player performance is relatively consistent across time. Player salary is primarily determined by scoring, not other factors like shooting efficiency and turnovers. And the metrics people have offered – NBA Efficiency and PERs – confirm this bias towards scoring.

Taking Rebounds from Teammates

And to conclude this essay, let me address the question, do players take rebounds from their teammates? The answer is “absolutely.” Of course they also take shot attempts from their teammates. In fact, we show in The Wages of Wins that the more productive your teammates the less productive you will be. But people tend to exaggerate this effect. We found the interaction effect to exist but it appears to be rather small.

To see this point, consider the consistency in player performance across time. If your performance depended entirely on your teammates, player performance would fluctuate dramatically across a player’s career. This is indeed what we see in football. But in basketball we see much more consistency, suggesting the size of the interaction effects have been exaggerated.

– DJ

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