A Substitute for War

Basketball philosophy

Chamberlain Theory: The Real Price of Anarchy in Basketball

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Wilt Chamberlain and Bill Russell during a bas...

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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:

Braess’ Paradox

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 SimmonsEwing 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.

Chamberlain Theory

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.

10 Responses

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  1. Cool stuff. In particular, your concluding thoughts and the idea that there is a 2-way disconnect between the Boys Club inside the game and the stat-heads. Bridging that, like Dean Oliver has to a degree, is incredibly valuable.

    Also, I vote to call this “Dantley Theory” for obvious reasons.


    January 20, 2011 at 3:22 pm

  2. ‘preciate the kind words.

    Hehe, I get the wish for Dantley theory, but there are a few reasons why Chamberlain theory is better:

    -Because Chamberlain did indeed have great impact at times, it’s not so much a damning of a player as it is a recognition of how crucial it is to use your superstar talents properly.

    -Chamberlain has a particular event on which we can focus which makes clear the problem really exists.

    -I think it’s really useful to tie this concept to such an important player in the game’s history. If it can happen with Wilt, there will NEVER be a player so talented that this principle doesn’t apply to them.

    Matt Johnson

    January 20, 2011 at 3:30 pm

  3. The Lebron theory might be another wrinkle in that, although you’re removing his entire contribution rather than just that related to scoring efficiency. 😉

    I had dreams of him turning into Magic-lite in Miami, but that looks less and less likely now.

    Wilt’s a great outlier in a lot of respects, so this is a really great attempt to diagnose why that great basketball ability didn’t directly translate to dominant success.


    January 20, 2011 at 6:03 pm

  4. Thanks Raven. A LeBron Theory is begging to be developed eventually, but I think it’s too soon. We’ve got to see a few in Miami at least.

    And I’m with you that even though Miami still looks to me like they could become a dynasty, it’s a disappointment to realize that LeBron probably just doesn’t have the Magic brain in him.

    Matt Johnson

    January 20, 2011 at 7:04 pm

  5. I live in hope that back-to-the-basket will come as his explosive athleticism declines…


    January 20, 2011 at 10:32 pm

  6. Who is the best NBA basketball player of all time?…

    I would have to go with Bill Russell, though when you compare between eras there isn’t any one definitive answer. What Russell definitely is, is the answer to the question: “What player contributed the most value to his teams in his career?” The Bos…


    January 21, 2011 at 11:58 am

  7. I agree Dantley’s career and apparant lack of offensive impact is one of the most fascinating examples of this – as well as Corey Maggette, the poor man’s Dantley

    I wrote something a while ago on RealGM that I’d paraphrase as this

    “There are two ways a player improves his team efficiency compared to an average player in his palce. The first is by shifting his team’s ratio of shots towards efficient parts of the floor – at the rim/FT line and from 3, and away from the inefficient long guarded 2s. The second way is by improving the efficiency of either 3pt, midrange, or inside/FT line shots compared to the average”

    Shaq is a great example of the first type, someone who drastically increases his team’s ratio of shots at the rim and from 3 than opponents. I don’t think Shaq’s % at the rim is any higher than when perimeter players get inside (because of his poor FT shooting) – he just gives you more shots there. Dirk is a great example of the 2nd – he scores at an absurdly high percentage compared to the average from midrange, thus I presume Dallas has always had one of the best midrange scoring percentages in the league. Thus if you add that to shots at the rim and from 3 which are efficient for everyone, Dallas is always efficient

    If Dantley is a non impact offensive player (this is still an argument, but it’s hard to ignore his team’s bad ORTGs) – then the argument would be 1. His ballstopping is preventing his teammates high efficiency shots at the rim and thus the ratio is not shifting towards good shots and 2. The shots he is taking are not much higher than usual shots from those spots

    Julien Rodger

    January 24, 2011 at 1:31 pm

  8. […] I wrote an article describing what I called Chamberlain Theory.  Here’s how I put it: There is more to judging the effectiveness of a scorer, or a player […]

  9. […] a handy point to make when defending why offenses are so inept generally in the clutch.) However, as we’ve talked about before, contrary to common understanding, Wilt’s teams were not particularly good on offense when he […]

  10. […] not just so the star’s shooting efficiency doesn’t fall off a cliff. As I wrote in my Chamberlain Theory piece, just because a player can score at high efficiency while at volume doesn’t mean […]

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