Chamberlain Theory: The Real Price of Anarchy in Basketball
A recent post by ElGee over at Back Picks talks about something I’ve been wanting to chime in on, and I want to go over it and then point something out that I haven’t seen discussed, other than in conversations I’ve had with ElGee and a few others. The back story:
The Price of Anarchy is a game theory concept describing the difference between actual and optimal performance in a network where individuals in the network behave selfishly. One of the amazing counterintuitive epiphanies relating to this is called Braess’ Paradox which describes how in a transportation system, building a new road can actually slow traffic down. I’m going to skip an explanation of exactly how this is so and go straight to the analogy to basketball because it’s most relevant, and actually easier to understand.
People in the basketball world started talking about this when Brian Skinner wrote a paper and gave a talk at the Sloan Sports Analytics conference last year. Skinner broke down the situation admirably: If you keep running the same play, even if it’s easily the best play you have, the opponent is going to catch on, and it’s not going to be as effective. Hard to argue with the man, he’s clearly right – but how big of a problem is this?
Ewing Theory…is not caused by Braess’ Paradox
Skinner mentioned the humorous Bill Simmons‘ Ewing Theory as a possible consequence of this. Ewing Theory is based on the idea that Patrick Ewing was the team’s star, but the Knicks did better when he got injured. The most intuitive explanation for such an event is that the star might not be as good as people thought he was. Skinner puts forward the idea that maybe it’s not that Ewing was overrated, maybe the issue was that the Knicks were just overusing him, and thus improved because his absence forced a better distribution of usage. Hence in Skinner’s words, “The apparent improvement of the team upon losing its center, and, indeed, any instanceof the “Ewing Theory”, is a consequence of this short-sightedness.”
Now, the first thing to check here is the specifics of Ewing’s situation. The most notable absence of Ewing came last in Ewing’s career (’97-98 and ’98-99) at a time when Ewing was not scoring at huge volumes (20.8 PPG and 17.3 PPG respectively). So it’s hard to imagine this was a situation where Ewing was getting used so much that the team was suffering. Also of note is that the Knicks offensive efficiency went down in ’97-98, down further in ’98-99, and then went back up the next year with more Ewing, and then down again the year after that when Ewing went to Seattle. A superficial glance would show no signs that Ewing’s presence was hurting his team’s offense, so there doesn’t seem to be any basis for attributing Ewing Theory to Braess’ Paradox.
The phenomenon of some teams being surprisingly resilient without their stars is quite real, and Ewing is an example of that. There are many reasons for this, but I’m going to talk about one broad attribute of basketball and then dive into what I see as the key example.
Basketball is a sport where there are 5 teammates who could have the ball in their hands at any one time, but only one does. The team’s coach needs to decide not simply who will play, but who will play what role. Since only one player can have the ball in his hands at a given, this means that having two players with great ability to help the team when they have the ball in their hands can result in one of those players contributing significantly less value to the team due to the coach deciding to put the ball in the other player’s hands most of the time.
ElGee uses Wilt Chamberlain in his post as the example for the Price of Anarchy in basketball Wilt Chamberlain, and this was a superb choice. He focuses on how the Philadelphia 76ers improved drastically in their offense from ’65-66 to ’66-67 when the team stopped using Chamberlain as a volume scorer. And by drastically I mean a far greater improvement than we had ever seen involving Wilt, greater by quite a bit than when he joined his previous teams. However, he also points out something crucial which throws a wrench in things more than he expresses:
“His teammates scored at 50.7% efficiency. Wilt’s TS% went up as well. But, here’s the most interesting wrinkle: Even if Chamberlain’s TS% had remained the same, the overall team efficiency would have gone from 49.0% to 51.4%, and at well over 100 “attempts” per game, that results in a colossal shift in scoring efficiency. (As it were, the team’s TS% increased to 52.8% because Chamberlain’s TS% also increased.)”
Braess’ Paradox would seem a good explanation for the improvement based on more even distribution of possessions – until you realize that the key component was not that Chamberlain’s efficiency went UP when HIS usage went DOWN, but that his teammates’ efficiency went UP when THEIR usage went UP. At this point it’s clear we’re onto something that’s totally different than Braess’ Paradox.
So what happened? Well, I can’t give you an exact causal narrative, but here are some facts to consider:
1) New coach Alex Hannum joined the 76ers in ’66-67. This was actually his 2nd stint with Wilt, the first came on the San Francisco Warriors where in his first year the team became much better with the bulk of the improvement being on the defense. So this was a smart coach, not simply saying “Hey Wilt, shoot less.”, he was putting a new system in place.
2) When Hannum arrived in San Francisco, there are anecdotes about him being completely shocked at how badly Chamberlain’s teammates had regressed because of their roles, i.e. “Pass to Wilt, and stand there.”
3) Wilt’s new role wasn’t simply to score less, but to act as distributor. Wilt thus had a new focus on getting the teammates the ball in a position where they could do something with it.
4) If we had all relevant data relating to a scorer, this would include the turnovers caused getting him the ball, the turnovers of the player once he gets the ball, and how effective a position players are in when they get the ball back from him.
This all leads to what I’ll call Chamberlain Theory, in honor of Simmon’s theory: There is more to judging the effectiveness of a scorer, or a player in general, than simply his most obvious related statistics, and pursuit of those obvious statistics without proper awareness for the rest of the court can erase most if not all of a scorer’s positive impact, even when those obvious statistics are as great as any in all of history.
Last, when I consider all of these factors, it seems so strange to me that Skinner’s article caused such a fuss. And I don’t mean to knock him, every piece of communication I’ve seen from him shows him to be a humble guy who himself is surprised by the fuss. I think to some degree, people latch on to a phrase like “Price of Anarchy” and think it means something more specific than it really does. The idea that teams aren’t always run optimally I don’t think would surprise anyone close to the game. The skepticism expressed by “the jocks” toward basketball statisticians isn’t based on an assumption of their own infallibility, but rather on the idea that abstract concepts from “the nerds” can tell them something huge that they don’t know. The jocks who believe this, I think, often underestimate just how much the brainiacs can help them. On the other hand, I think we nerds have a tendency to drastically oversimplify things.
The real Price of Anarchy in basketball is best personified by what happened with Wilt Chamberlain over 40 years ago. We know about it because a coach at the time recognized the problem and greatly improved it. Granted, it’s not the case that modern NBA coaches have these problems licked, but I think it’s a healthy lesson in modesty for statisticians to recognize how much the jocks have already accomplished in decreasing the price of anarchy already with issues that many advanced stats don’t diagnose, let alone solve.