Article link: http://arbitrarian.wordpress.com/2008/01/28/nba-game-theory/

From this article about NBA Game Theory, I find out that in basketball game, there is a high correlation between assists ratio and field goal percentage. If players try to find the other open players, open players will be likely to score with high percentage shooting. However, if players try to shoot even though defense players tightly guard in front of them, the field goal percentage will be dropped significantly. Therefore, in the view as a team, high field goal percentage will lead team to win more. However, as a view of players, players should score more and make their statistics look good for future salary contracts because salaries are highly depended on statistics. Therefore, like shown in the article, in some team like New York Knicks, players face prisoner’s dilemma between passing to other players and shooting in front of a tightly defense player. The best outcome from this dilemma is passing to other players, but since some players are selfish enough to think more about their salaries over team’s wins, they just try to shoot the ball on their own with low field goal percentage. These are differences between winning teams and losing teams in NBA.

Like a prisoner’s dilemma above, game theory can be applied to strategies of offense and defense players. San Antonio Spurs was a champion team last year. In addition, they won four of last 9 seasons with their best player, Tim Duncan who is an arguably best power forward in NBA history. Since players like Tim Duncan dominate their opposing defense players easily, it’s almost impossible to guard him by a single defense player. Therefore, many times other teams try to guard Duncan with two players, but at that moment, Duncan passes the ball to other players and they score with ease. In this situation, game theory can be applied.

Tim Duncan’s filed goal percentage is 50%. When he is guarded by a single player, he can score with 70%, while if he is double teamed, percentage is dropped to 30%. Also, shooters in every NBA team can shoot 3 pointers with 70% chance, if they are opened. If they are guarded, the percentage is dropped to nearly 30%. Therefore the payoffs of Duncan’s play will be 0.6(if he shoots with double teamed), 1.4(if he shoots with one defense player), 2.1(if he passes when double teamed), and 0.9(if he passes when one player guards him).

Double-teamed Not double teamed

Shoots (0.6, 0.7) (1.4, 0.3)

Passes (2.1, 0.3) (0.9, 0.7)

In this situation, there is no Nash Equilibrium. This is the reason why there is a no a dominant strategy for opposing teams to guard Tim Duncan or dominant offense strategy for Tim Duncan. And, that’s why basketball is complicated and has many different offence and defense strategies. Surely, in the situation above, Tim Duncan will look for other players when he is double-teamed. If he is not double teamed, he will shoot by himself. Those two strategies make most payoffs for him. In contrast to Tim Duncan, opposing teams will try to defense Duncan with two players while he is shooting, and will try not to guard with two players if Duncan tries to pass. For sure, the team that uses its beneficial strategies more fluently will win the game. But, as you can see above, Tim Duncan’s team has a higher chance to make efficient plays and that’s why San Antonio Spurs are still top ranked in NBA standings.

(http://sports.yahoo.com/nba/standings)