## The Quandary that is Hero Ball

In the modern world of professional sports it is safe to say that statistics and game theory reign supreme.  That is, while purists who judge solely by gut feeling and conventional wisdom still exist, phenomena like “Moneyball” have revolutionized sports and turned them into numbers based games.  However, despite these radical changes, there are still circumstances in which professional sports teams continue to play against the odds.  Abbott and Ruminsky highlight one example in particular – when a basketball team is down by two points at the end of the game and must decide what to do with the ball.  Very often NBA teams will elect to play Hero Ball.  That is, give the ball to their best scorer and let him try to score in isolation against the opposing team’s best defender.

While conventional wisdom suggests that situations like this are the very reason why NBA teams are willing to pay so much money for superstars, game theory suggests otherwise.  Out of the 10 different types of plays tracked by Synergy Sports, isolation plays are by far the least efficient, only yielding an approximate 0.77 points per play (ppp).  For comparison sake, plays involving off-ball cuts and transition plays are far more efficient at 1.18ppp and 1.12ppp respectively.  Thus, isolation plays would be fine if they were only used infrequently, but in fact they are the 4th most commonly used type in the NBA at 12% and, what’s more, this percentage actually rises in pressure situations to 19%.  Clearly, something is not right here.  Furthermore, one would think that an easy way to overcome stiff defenses designed to smother isolation plays would be to pass the ball to another player.  Sure enough, doing so causes the average number of points scored per play to increase by 21% to 0.93.  Unfortunately, this doesn’t happen often – only 20% normally and 16% in the last 5 minutes of the game.  So why is this?

In his article, Ruminsky even diagrams a simple zero sum game based on situations where it is the final play of a game, a team is down by two, and must choose whether to take a two or three:

In the diagram, the numbers come from league wide shooting percentages for open/contested 2 and 3 point shots.  Namely, if the offensive team designs a play for a two point shot and the defending team chooses to defend the two, the resulting shot would have the percentage associated with a contested 2 pt.  Ruminsky also assumes that a successful two point shot sends the game goes into overtime where both teams are equally likely to win.  As we learned about in class, it turns out that this game has a Mixed Nash Equilibrium.  Specifically, the defense should defend the three pointer approximately 79% of the time and the offense should shoot the three approximately 33% of the time.  Obviously this game has flaws because it uses league wide statistics, oversimplifies the situation, and is for a very specific scenario, but on the whole it explains why many situations like these often involve the defensive team closely guarding the perimeter while the offensive team tries to go for an easy 2 pointer even though it may appear counter-intuitive to do so.

How does this relate to Hero Ball?  By giving the ball to their star in isolation, the offensive team is essentially resigning itself to taking a contested shot, and it goes without saying that these are harder to make than open ones.  So why do teams continue to play Hero Ball when better options clearly exist?  Paraphrasing from Bucks assistant coach Jim Boylan, if somebody other than the best player takes the last shot of the game and misses, everybody wonders why the star didn’t demand the ball and he gets blamed for their loss.  Thus, even though game theory clearly supports sticking to team oriented strategies by passing the ball and finding the open man, many times teams fail to do so and utilize sub-optimal strategies due to social pressure.

-porcupineh

Sources:

http://espn.go.com/nba/story/_/id/7649571/nba-kobe-bryant-not-money-think-espn-magazine

http://mindyourdecisions.com/blog/2012/06/19/game-theory-applied-to-basketball-by-shawn-ruminski/