Game Theory and Basketball: A Look Into Crucial Decision Making
http://mindyourdecisions.com/blog/2012/06/19/game-theory-applied-to-basketball-by-shawn-ruminski/
Ever since 1891, basketball has been a team based game that takes into account teamwork and individual skill. Each individual player on each team needs to take into account various factors in order to achieve the goal of the game, which is to score more points than the opposing team. Choosing between these various options as a player make up the set of possible strategies that the player can implement. Each strategy has a specific payoff, with some strategies having higher payoffs than others. It is up to the player to identify which strategy has the highest payoff and execute it. At the same time, since basketball is a zero sum game, where winning is also dependent on the performance of the opposing team. Thus, the player needs to account for the strategy utilized by the other player, or tap into their rationality, which can affect the payoff of your own set of strategies. Because of all these factors that come into play, it is often the case that there does not exist a strictly dominant strategy, so deciding between these options becomes very difficult on the fly.
Analyzing every possible decision within a game is a huge endeavor, but Presh Talwalkar has attempted to analyze two specific situations made by the coach of the game: handling players in foul trouble and deciding to shoot a 2 or 3 in late game situations. Presh Talwalkar is a graduate from Stanford in Economics and Mathematics, and is also the author of The Joy of Game Theory: An Introduction to Strategic Thinking.
When addressing the first decision of handling foul trouble, after doing some numeric calculations on the payoffs for each decision, he came to the conclusion that the benefit of having your star player in the game out-weighs the possible drawbacks of them fouling out. Some of the factors in this calculation include the disparity between the star and bench skill, as well as the “quality” of the minutes, since each second becomes more and more important as the game progresses.
For the second situation of choosing to shoot a 2 or 3, Talwalkar takes into account various percentages, such as open and contested 2’s and 3’s. With these values, Talwalkar is able to create a payoff matrix:
| Defense | |||
| Offense | Defend 2 | Defend 3 | |
| Shoot 2 | Contested 2: 0.357
OFF: 0.357*0.5 = 0.178 DEF: 1 – 0.178 = 0.822 |
Open 2: 0.625
OFF: 0.625*0.5 = 0.312 DEF: 1 – 0.312 = 0.688 |
|
| Shoot 3 | Open 3: 0.50
OFF: 0.50*1=0.50 DEF: 1 – 0.50 = 0.50 |
Contested 3: 0.228
OFF: 0.228*1 = 0.228 DEF: 1 – 0.228 = 0.772 |
|
The implication of this matrix is that it is in the best interest of the losing team to shoot the three almost all the time. As long as the defending team guards the three less than about 80% of the time, the losing team should seek to end the game in regulation. Likewise, the team that is ahead should fear the three more than overtime. As long as the losing team shoots the three at least a third of the time, the defending team should always defend the three. Overall this article was a very interesting look into the decision making that the coach goes through during a game of basketball. It is interesting to analyze the situation systematically and reach the best possible strategy using this system. Of course, this look into these two decisions can’t possibly account for all possible factors and circumstances, so these outcomes should not be the end all be all for making such a crucial decision.
It is unquestionable how this article relates to the class. The entirety of this article is application for game theory to the sport of basketball. After attending lectures and reading the sections of the book about game theory, a lot of the key terms that Talwalkar uses became immediately recognizable to me. I appreciated how this example of game theory was actually applied to a game. Situations we covered in class, such as the Prisoner’s Dilemma and the Hawk-Dove game are much simpler examples. I like how I was able to apply concepts in class to a game that I quite enjoy such as basketball.