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Be Less Than You Can Be

Brian Skinner’s presentation of his paper, “The price of anarchy in basketball,” at the Sloan Sports Analytics Conference hits in two distinct ways:

  • One hand hand, Skinner’s proposal is so dreadfully counter-intuitive on a conceptual level that it could make a lot of NBA fans turn up their noses.
  • But on the other, that concept is such a deeply-seated part of sport as we know it, that any self-respecting follower of sports would be deemed foolish for turning a blind eye.

His work appropriately brings the contrast between macro and micro into broad daylight, but in a completely different way than many NBA fans are used to. The struggles to find balance on a basketball court typically occur in an effort to best determine the optimal method of achieving a common goal…assuming that there is a common goal. One guy may be playing for a contract, another just for the joy of scoring more than anyone else on the floor, one just because basketball is the only thing he’s ever been good at, and finally, there may actually be some players who want to win games. More realistically, their interests are some combination of those mentioned above, in the form of a veteran athlete drifting through the regular season almost out of habit, and shooting/scoring because that’s what he’s always done.

Somehow, someone has to take all of those intentions and all of the production, potential, and talent that comes along with it, and figure out the best possible way to win. It’s not an easy task, and the natural inclination is to break the incredibly complex, holistic game on the hardwood into its most basic components: Steve Nash is effective bringing the ball up the floor and running the offense, but Amar’e Stoudemire is probably not. Kobe Bryant is an excellent shooter, and D.J. Mbenga is not. Then, we can take all of these things, take into account all of the players on the floor and their relative strengths and weaknesses, and decide which conceivable outcome will give you the best possible chance of scoring points on a given possession. Our logic and reasoning processes tell us that choosing the option with the greatest probability for success is an easy call. Skinner tells us that your logic and reasoning could be completely off-base.

One example that Skinner highlighted is Ray Allen. Allen’s shot usage over the course of his career makes him an easy candidate; in Milwaukee and Seattle he was called upon to be The Man, but in Boston, he’s simply a man. He’s a shooter, a scorer and leader, and one of the three. He offers plenty on the court but in a completely different capacity, and with a markedly lower percentage of his team’s total shots. There is power in variety, and with the offensive options that have been available in Boston (in 2008, namely, though still today on a theoretical basis, if nothing more), Allen, a talented offensive player, actually benefits his team by not shooting. Not because his teammates are better shooters than he is on a per-possession basis necessarily, but because putting so much of the offensive production on one source creates myriad problems. Fatigue. Defensive attention. Heat checks. Skinner invokes Dean Oliver in stating that as usage goes up, a player’s offensive efficiency goes down, and that makes a ton of sense.

But at the same time, that creates a bit of a boggling result: a team’s best play is sometimes to have their best shooter not shoot. That conclusion naturally led Allen’s former teammate, Brent Barry, to pipe up from the audience and announce that he texted Ray the results of the study with a note to not shoot so much. I’m pretty sure Denzel Washington told him the same thing over ten years ago, though, so I wouldn’t expect some kind of drastic change.

It’s also interesting to note that such an idea is pretty much in direct conflict with the love of excess when it comes to sports. We want a player to one day hold up a piece of paper reading “101″ in a locker room, to waltz into Madison Square Garden and drop 50, to average a triple-double for an entire season. America is a nation of decadence and sports are absolutely no exception. But the underlying mentality that drove guys like Michael Jordan or Larry Bird to greatness is, despite each player’s phenomenal success, not the best possible approach.

Think about that. It’s completely possible, supposing you buy Skinner’s basic argument, that Jordan and the Bulls underachieved. If they had achieved the perfect offensive balance — where Jordan may have stopped scoring well before the point which Skinner describes as something akin to the Nash equilibrium, in which a player’s likelihood of scoring is equivalent to that of his teammates scoring — the ’96 Bulls could very well have improved upon their 72-10 record. Or maybe that’s exactly what allowed that particular team (and all of Chicago’s championship teams, really) to excel compared to some of Jordan’s earlier campaigns.

When you think about it that way, it’s the same argument we’ve heard over and over again: Player X should shoot less for the benefit of the team. It’s disguised as “trusting their teammates” and, as Skinner noted, “keeping the defense honest,” but it’s probably as old as winning itself. Where this argument differs from others is the disregard of our micro-obsessed desire to dissect the game’s minutiae. We do possession breakdowns and pick apart the decision-making of every player on the court, but sometimes the view is so narrow that it obscures the bigger picture. Your best player getting a good shot isn’t always the best case scenario for an offense in the long-run…even if it’s LeBron James kicking it to an open Donyell Marshall in the corner.

But Skinner’s study, while deeply theoretical, lacking in obvious applications, and definitely limited and assuming in a lot of respects, represents a pretty interesting intersection that occurs at places like Sloan; new, innovative research confirms something that we already knew, but in such a way that offends even our modern sensibilities. That the Lakers could actually benefit from Kobe Bryant passing to Smush Parker? That the Nuggets could run a more efficient offense by having Chauncey Billups pass up a shot in favor of Joey Graham? It’s not always an easy fact to stomach, but the research shows, at least at a basic level, that those plays are so wrong that they’re right.

You can read Skinner’s paper in its entirety here.

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@Tom Pestak: Actually, Skinner's analysis is not supposed to be applied to the endgame. (I don't think.) At the end of the game, you take the option that gives you the best chance of winning the game, not the option that's most efficient. Those are not always the same thing; in fact, I'd say a rough definition of "endgame" is the period of time when they aren't the same thing.

So, if LeBron (or any player) presents the best chance of winning at the end of the game, then he's the option to take, regardless of any game theory considerations that might govern the midgame.

That being said, I think LeBron has as good a mix as anyone, which is to say, still too predictable. But no more predictable than any of the other "closers."

As a Cavs fan, we have been dealing with this topic for years. LeBron doesn't have "killer instinct" therefore... LeBron shies away from the "last shot" therefore...

Therefore he's making the right basketball decision most of the time.

Check out what Brian Windhorst wrote years ago. http://sports.espn.go.com/nba/playoffs2008/columns/story?page=WizCavsGame4-080427

And here I thought A Nash equilibrium was a scenario in which one player knows the defensive strategies of all of the other players, but unilaterally makes the decision to pass anyway :)

@Mike A: The question is what helps the team the most. Statistics like +/- and its analyzed brethren look at this at a large scale; game theory can address it at the scale of an individual possession.

To that end, shooting percentage is a crude parameter as an objective to aim for. It may be that 79 percent of teams with the higher shooting percentage win, but a much higher percentage of teams with the higher points per possession win. (Not quite 100 percent, but it's darned close.) So the game theory approach looks for strategies that optimize for PPP, rather than shooting percentage (or even true shooting percentage). My guess is that the current state of the art isn't advanced enough to support a full analysis this way, but even an examination of the starts of possessions is feasible and might open some eyes.

It must be emphasized that this is a midgame consideration, not an endgame one. It is the midgame that aims to maximize expected PPP; the endgame aims to maximize probability of winning from specific game positions. So in the endgame you may choose tactics that would be distinctly suboptimal from a PPP perspective, but improve your chances of winning the game. You'd only do that in the midgame if you were much, much worse of a team than your opponents; in fact, you might consider that to be the start of a very long endgame. The classic example is taking the trey at the end of regulation with a two-point deficit, even when the trey is less than two-thirds as likely to go in as the deuce (and therefore sub-optimal from a PPP point of view).

Dee is basically right. A Nash equilibrium is one in which neither side (in a competitive game) can improve their result unilaterally. In a sense, neither side really bases their play on their assumption of what the other side does; instead, they set their strategy so that they don't care what the other side does, it can never diminish their own result. It might improve it, but it won't make it worse. See Wikipedia's entry on NE for more details (last I checked, some minor errors, but nothing to worry oneself over).

Skinner does acknowledge that he's not talking about true Nash equilibria, and throughout his paper he uses the term "Nash equilibrium" to refer to this pseudo-Nash equilibrium. However, his paper is considerably weakened by not actually taking a game-theoretical approach to the problem. He assumes that any player's efficiency is a decreasing function of usage rate. While that's plausible (though Berri has conducted some studies that appear to contradict it), using that as a fixed condition obscures some more interesting relationships between the defense and offense.

I took some time out yesterday to suss some of these out and for those of you with a mathematical bent, you can find it at

http://www.astronomycorner.net/misc/skinner.pdf

Very quick and dirty, so some errors still floating around in there, and some shorthand notation I don't take any time to explain. Hopefully they won't be too difficult to interpret.

that's not a nash equilibrium. a nash equilibrium is in a competitive situtation where both opponents base their play/method/move on their assumption of what the other person will do, and both persons are correct thus each assume that they are making the best move in anticipation.

This can all be broken down into trying to maximize shooting %. In my studies of the NCAA Tournament the team with the highest overall shooting % wins 79% of the time. The great player not only creates high % shots for himself, but also draws the attention of the defense creating higher % shots for his teammates. If the "high volume" guy is a low % guy then you have a high scoring avg and a losing team. Ideally, you want 5 guys who can create easy shots for themselves and recognize draw enough defensive attention to get easier shots for others..ie 5 megastars.

Fascinating take on this long-standing dilemma. Of course, it would also mean redefining our ideas of who is a 'good' player and who is a 'shitty' player into who is 'efficient' and who is 'inefficient.'

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