## Basketball Predictability using Game Theory

Applying a little game theory can help you increase your chances in winning a basketball bracket. According to http://measureofdoubt.com/2011/06/13/game-theory-and-basketball/, a friend was able to gain the upper hand in predicting the outcome of the most NBA playoff games as possible through the use of some game theory. In the scenario, correctly predicting an NBA game was 5 points. After several predictions before using game theory, the count was Ben in second and Ilardi in first. It was the final game between Miami and Dallas and according to analyst predictions; Miami had a 63% chance of winning. However, if both Ben and Ilardi chose Miami, then they would both receive the same amount of points which would not change the gap, and Ben would still lose. Thus, this creates a game theory situation regarding which team Ben should pick.

In class we learned about Nash equilibriums which would state that Ben’s Nash equilibrium would be to pick Miami with the same probability of Miami losing which is 0.37 and for Ilardi to pick Miami with the same probability of Miami winning which is 0.63. However this only gives Ben a 23.3% chance of defeating Ilardi which is ok, but could be better. Thus, another possibility is for Ben to ignore choosing his Nash equilibrium strategy and instead predict Ilardi’s action if he was confident enough. This means that Ben should pick Dallas if he thinks that Ilardi is 63% or more likely to choose Miami as opposed to Dallas. The resulting probabilities of each of the outcomes according to the site with “p” equated to the chance that Ilardi picks Miami and “q” equated to the chance that Ben picks Miami would look like this:

Outcome where Ben wins |
Probability |

Ben chooses Miami, Ilardi chooses Dallas, and Miami wins | q(1-p)(0.63) |

Ben chooses Dallas, Ilardi chooses Miami, and Dallas wins | p(1-q)(0.37) |

And the total probability that Ben wins would be the sum of the two, which yields .37p+.63q-pq. Obviously different “p” values would change Ben’s chance of winning, but in this case, Ben believes that the chance that Ilardi will pick Miami is greater than .63% since people generally pick the team that usually wins as opposed to the underdog. If Ben is correct in his prediction and chooses Dallas, this would give him a 37% chance of winning as opposed to his original 23.3% if he followed Nash equilibrium. And as predicted, Ilardi picks Miami and Ben scores with Dallas winning.

Of course since this is a one-time situation, game theory won’t always be accurate in picking the correct team. This prediction was based on people’s general tendencies and not the specific person’s decision making process so the success rate varies person to person. However more than likely using simple game theory will improve your chances in reaching the goal, as opposed to pure luck.