# 2015 NCAA Tournament Predictions: Pre-Tournament

NCAA tournament predictions are pretty common these days, from FiveThirtyEight.com to Bing.com. Not to be left out of the fun, here are some predictions I put together using a fairly simple model and R.

### Prediction Methods

Using data from the 2014-2015 NCAA men’s basketball season (posted at http://prwolfe.bol.ucla.edu/cbasketball/scores.htm), I used a modified version of the so-called Bradley-Terry model to estimate a relative strength effect for each NCAA Division I team. The Bradley-Terry model predicts the outcome of an comparison (a game for this analysis) using a logistic regression where the winner of the game is predicted by who played and other covariates. I added in covariates to control for the location of the game (home, away, or at a neutral site). This model was estimated using maximum likelihood with the glm() function in R.

Using the estimates and the asymptotic covariance matrix, I then used a simulation to predict the outcome of the tournament. For each of 10,000 replications, I the team’s strength effect from a multivariate normal distribution. For each game in the tournament, I then proceeded to create the Bradley-Terry model predicted probability of a win. The results shown below are summaries of the simulation.

Time permitting, I will update the results of the tournament as the event progresses. I’m interested in seeing how effective a very simple model for the outcome of games can be considering all the varying complexities of the sport not incorporated into this analysis. For each subsequent analysis, a new Bradley-Terry model will be estimated using the results of any tournament games.

### Predictions for First Round (Play-in Games)

• BYU over Mississippi (58.3%)
• Manhattan over Hampton (66.2%)
• Boise State over Dayton (55.4%)
• North Florida over Robert Morris (a toss-up, really 50.2%)

### All Pre-Tournament Results

Perhaps the easiest way to summarize the table is to say it is Kentucky versus the field. Kentucky has an estimated .422 probability of winning the tournament. Only five teams (Kentucky, Virginia, Wisconsin, Villanova, and Gonzaga) have win probabilities of greater than .05.

The results are summarized in the table below. The columns are sortable with a click.

The BT Effect column is the estimated Bradley-Terry model effect. When comparing two teams who may meet in a tournament game, the team with the higher probability of winning is the team with the larger BT Effect number.

The columns for each of the varying the rounds are the probability a given team makes it to that round. For instance, Kansas has a .356 probability of reaching the Elite 8 round.

The wins column represents the expected number of wins in the tournament.

TeamSeedRegionBT EffectRound or 32Sweet 16Elite 8Final 4Final GameWinner# Wins
Alabama-Birmingham14South1.55.072.012.001.000.000.0000.09
Albany NY14East2.26.187.046.006.001.000.0000.24
Arizona02West4.75.940.752.544.295.095.0472.67
Arkansas05West3.46.620.336.090.032.005.0011.08
Baylor03West4.00.791.534.226.087.018.0061.66
Belmont15East1.82.040.007.001.000.000.0000.05
Boise St11aEast3.27.233.112.026.007.002.0000.93
Brigham Young11aWest3.16.287.117.035.010.001.0001.03
Buffalo12Midwest2.92.364.104.010.003.000.0000.48
Butler06Midwest3.75.660.270.104.017.006.0021.06
Cincinnati08Midwest3.01.516.034.011.003.001.0000.56
Coastal Carolina16West1.84.049.014.004.000.000.0000.07
Davidson10South2.98.428.089.028.008.001.0000.55
Dayton11bEast3.02.157.068.012.003.000.0000.69
Duke01South4.83.952.713.530.303.141.0482.69
Eastern Washington13South2.29.210.059.009.002.000.0000.28
Georgetown DC04South3.76.790.444.156.057.016.0031.47
Georgia10East3.23.428.077.032.006.001.0000.54
Georgia St14West2.54.209.078.018.004.001.0000.31
Gonzaga02South4.84.932.751.494.306.153.0582.69
Hampton16aMidwest0.66.003.000.000.000.000.0000.34
Harvard13West2.58.293.109.020.006.001.0000.43
Indiana10Midwest2.85.255.058.016.002.000.0000.33
Iowa07South3.31.572.145.050.013.002.0000.78
Iowa St03South4.32.928.608.287.147.054.0152.04
Kansas02Midwest4.55.921.596.356.091.044.0182.03
Kentucky01Midwest6.36.987.930.806.679.545.4224.37
Lafayette16East1.71.041.010.001.000.000.0000.05
Louisville04East4.00.862.391.139.055.022.0051.48
LSU09East3.07.497.082.025.006.001.0000.61
Manhattan16bMidwest1.40.010.003.000.000.000.0000.67
Maryland04Midwest4.34.769.548.120.060.027.0111.53
Michigan St07East3.56.572.128.064.018.007.0010.79
Mississippi11bWest2.80.172.058.013.002.000.0000.66
New Mexico St15Midwest1.85.079.014.002.000.000.0000.09
North Carolina04West3.55.707.383.108.039.007.0011.24
North Carolina St08East3.09.503.080.025.006.002.0000.62
North Dakota St15South1.92.068.016.002.000.000.0000.09
North Florida16aSouth1.53.023.004.001.000.000.0000.53
Northeastern14Midwest2.06.106.023.002.000.000.0000.13
Northern Iowa05East4.50.818.531.235.119.065.0221.79
Notre Dame03Midwest4.43.895.609.321.080.040.0151.96
Ohio State10West2.87.406.081.028.006.001.0000.52
Oklahoma03East3.88.813.440.137.045.017.0031.45
Oklahoma St09West3.11.417.072.034.010.002.0000.53
Oregon08West3.45.584.128.069.027.003.0010.81
Providence RI06East3.77.611.334.102.031.011.0021.09
Purdue09Midwest2.94.485.034.010.003.000.0000.53
Robert Morris PA16bSouth1.52.025.004.001.000.000.0000.53
San Diego St08South3.47.477.127.063.021.005.0010.69
SMU06South3.82.760.329.129.057.019.0051.30
St John's NY09South3.56.523.153.081.027.007.0010.79
Stephen F. Austin12South2.84.315.124.029.007.002.0000.48
Texas11Midwest3.03.340.098.025.003.001.0000.47
Texas Southern15West1.75.061.016.003.000.000.0000.08
UC-Irvine13East2.05.138.020.003.000.000.0000.16
UCLA11South2.53.240.051.010.002.000.0000.30
Utah05South3.68.685.372.131.050.014.0031.25
VA Commonwealth07West3.33.594.151.067.020.003.0010.84
Valparaiso13Midwest3.02.231.102.009.002.001.0000.35
Villanova01East5.20.959.829.561.331.211.0952.99
Virginia02East5.28.960.788.621.368.246.1093.09
West Virginia05Midwest3.52.636.246.034.011.004.0010.93
Wichita St07Midwest4.06.745.332.174.045.021.0091.33
Wisconsin01West5.15.951.786.638.432.170.0903.07
Wofford12West2.92.380.173.037.012.002.0010.60
Wyoming12East2.75.182.058.011.003.001.0000.25
Xavier OH06West3.27.542.213.067.017.003.0010.84

Let the games begin…