Predict Win Probabilities in NCAA March Madness Tournament
Yearly Men’s and Women’s College Basketball host 'March Madness' where the top ranked 64 teams compete. Kaggle has hosted their own competition inviting data scientist to predict win probabilities for all possible team mach-ups in the tournament. Kaggle has provided historical data of wins in losses of regular season games back to 1985 and detailed game stats back to 2003.
* FGM - field goals made (by the winning team)
* FGA - field goals attempted (by the winning team)
* FGM3 - three pointers made (by the winning team)
* FGA3 - three pointers attempted (by the winning team)
* FTM - free throws made (by the winning team)
* FTA - free throws attempted (by the winning team)
* OR - offensive rebounds (pulled by the winning team)
* DR - defensive rebounds (pulled by the winning team)
* Ast - assists (by the winning team)
* TO - turnovers committed (by the winning team)
* Stl - steals (accomplished by the winning team)
* Blk - blocks (accomplished by the winning team)
* PF - personal fouls committed (by the winning team)
A common method is to apply a ranking metric to each competitor and predict the outcome using some combination of the rankings. Commonly used metrics are Elo and Glicko. One of the shortcomings of these metrics is the need for a user to designate a parameter (C) for the sensitivity to recent vs. historical matches. To bypass this shortcoming we will compute Glicko ratings using multiple values of this parameter and make our prediction using an ensemble of Glicko ratings.
Commonly these rating systems are just applied to the win state of competitors, but they aren't inherently limited to just that, so we will update a rating after each game for all statistics given in the detailed game file. This will allow us to capture more of the nuance of the games. Ex. Maybe Team A lost to Team B, but they out performed in their FGM3, so by considering all stats we develop a more detailed picture of each teams strengths and weaknesses.
We will then calculate the covariate matrix for these rankings from the regular season games. This will be used with numpy's multivariate sampling to simulate games between competitors. We now can get believable rankings for each competitor and how they might vary relative to whom they are competing against, but we need a method to combine these to a final metric to determine the outcome our simulated game. I have decided to use the 'GameScore' metric which was a linear combination of the stats we ranked. Since it isn't clear that the combination coefficients for the stats would also be appropriate for our ranking of these stats we will reevaluate appropriate coefficients.
We can then simulate thousands of games for each match-up for all Glicko ratings using different C values. Giving us a picture of game outcome between a more historical representation of each team (lower C), to a picture of more recent representation of each team (higher C). We can then use logistic regression to get a final probability of the outcome of the game.
To calculate the Glicko rating we must first compute the rating deviation for each competitor. This is where the C parameter from above comes into play. One of the benefits of Glicko is that the rating deviation provides a range around the current rating describing each competitor, instead of a fixed value like in the Elo system.
The Glicko rating can then be calculated using the following formula.
where:
ri represent the rating of the opponents
si represents the outcome of each match, Win:1, Tie:0.5, Loss:0
Women's Bracket
Men’s Bracket
