NCAA 2016
Predict the 2016 NCAA Men's Basketball Tournament.
Data
The data analysts at FiveThirtyEight have crunched the numbers and determined the Expected Winning Percentage for every team in the tournament this year. This number is an estimation of what percent of the time a given team will win against a random opponent on a neutral court. The teams, expected winning percentages, regions, and seeds are located in ncaa_data_2016.csv.
Predicting the Tournament
Your job is to determine the chances for each team to win the entire tournament. You will use a Monte Carlo Simulation of the tournament, basically by simulating each of the 63 games based on the team winning percentages lots and lots of times and collecting the results.
Setting up the Bracket
Open bracket_2016.pdf. Make sure to set up the initial state of the tournament correctly. Teams are separated into one of 4 regions: East, West, South, and MidWest. Each of the teams in a region is given a seed. The lower the seed, the better the team. The teams are pitted based on their seed, a 1 seed always plays a 16 seed first, and then would play the winner of the 8 vs. 9 seed matchup, and so on. You must carefully set up your program to create these specific matchups and not others. The winners of each region meet in the Final Four, with the South playing the West and the East playing the Midwest. The winners of those two games then play for the National Championship.
Predicting a Game
To determine the odds of Team A winning a game against Team B you can use the Log5 Method invented by famous baseball sabermatrician Bill James.
Given the probability P[a] of Team A winning any game (ie. expected winning percentage), and also the probablility P[b] for Team B, the probability that Team A wins a game against Team B, P[a],[b] is:
P[a],[b] will be a number in the range [0, 1]. To determine the winner of a game in a given turn of the simulation compare this number to a random number r. If r is <= P[a],[b] then Team A wins the game. Otherwise Team B wins the game. For example, if Team A would beat Team B 75% of the time, the random number 0.3676376 would predict a win by Team A and the random number .818228 would predict a win by Team B. This process will result in Team A winning approximately 75% of the simulated matchups with Team B.