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The play-in games and the first round of the NCAA tournament featured a number of upsets. The Bradley-Terry model predictions from my previous post took a beating the first two days but somehow managed to make a number of good predictions later in the first round.

### Accuracy of Play-in and Round 1 Predictions

Overall, the model was correct on 72% of all predictions. I’m pretty sure the model and most peoples’ brackets took a beating in the same places- the big upsets of the first day of the round of 64.

The table also lists proportion correct by probability. These are helpful to see if the model’s probabilities are either over- or under-confident. If neither were to happen, we should expect that over the long run, the model will have a proportion correct equal to it’s predicted probability. That is, for all predictions of winning with probability of .9, we would expect the model to predict 90% of the games correctly. The table shows a rough alignment with proportion correct and predicted probability, but then again, our sample of games is very small so far.

Predicted ProbabilityProportion CorrectNumber of Predictions
All0.7236
0.5-0.60.5511
0.6-0.70.676
0.7-0.80.676
0.8-0.91.004
0.9-10.899

### Updated NCAA Tournament Probabilities

Using the methods described on the previous post, the updated probabilities for winning are listed in the table below. Of note: the team with the biggest increase in probability for winning the tournament was Gonzaga, which was aided by two upsets in their half of the South bracket. Also interesting is that despite winning their first game, Kansas has a decreased chance of winning in each of the next rounds, likely due to the Big 12 having a terrible showing in the tournament so far.

In the table, the last three columns represent the change in championship winning probability, change in Bradley-Terry effect, and change in expected number of wins over the pre-tournament predictions.

TeamBT EffectSweet 16Elite 8Final 4Final GameWinnerExpected # WinsChange WinProbChange BT EffectChange # Wins
Kentucky6.3710.9370.8020.6700.5350.4144.3580.0040.0170.103
Virginia5.3480.8120.6740.3900.2600.1123.2480.0070.0680.128
Villanova5.2700.8690.5790.3440.2230.0983.1130.0180.0690.313
Wisconsin5.2110.8010.6550.4430.1730.0983.1700.0130.061-0.030
Gonzaga4.8360.7730.6900.4030.1810.0663.1130.046-0.0280.658
Arizona4.8310.8360.6780.3590.1150.0543.042-0.0060.0730.317
Duke4.8960.7720.5470.3350.1510.0492.8530.0140.0700.178
Northern Iowa4.5830.6080.2560.1280.0710.0242.087-0.0260.0810.127
Notre Dame4.5100.6500.3530.0890.0440.0192.155-0.0110.0860.135
Kansas4.4770.5750.3040.0720.0340.0131.999-0.002-0.067-0.096
Maryland4.4110.6960.1440.0740.0310.0121.9580.0020.0730.273
Wichita St4.1720.4250.2060.0490.0220.0091.710-0.0060.1100.365
Louisville4.0890.3920.1310.0490.0230.0051.599-0.0050.0870.214
Utah3.7920.4860.1690.0700.0200.0041.749-0.0010.1060.379
Georgetown DC3.8510.5140.1820.0770.0200.0041.796-0.0010.0880.386
Oklahoma3.8320.6760.1690.0460.0180.0041.913-0.016-0.0500.453
Butler3.8570.3500.1370.0270.0100.0031.526-0.0020.1060.466
North Carolina3.6610.5300.1300.0520.0090.0021.723-0.0030.1090.488
Oregon3.5760.1990.1050.0370.0070.0021.3500.0020.1230.600
San Diego St3.5710.2280.1020.0400.0080.0021.3800.0020.0900.650
Xavier OH3.3730.6550.1780.0460.0070.0011.8870.0010.1061.072
Iowa3.4130.2270.1660.0510.0090.0011.4540.0010.0960.614
Michigan St3.6770.1880.1080.0280.0100.0011.3350.0010.1180.570
West Virginia3.4930.3040.0350.0130.0030.0011.3550.001-0.0260.465
Arkansas3.5060.4700.1100.0370.0050.0011.6230.0010.0610.578
Cincinnati3.0900.0640.0190.0060.0020.0011.0900.0010.0830.605
Ohio State3.0090.1640.0810.0150.0020.0011.2620.0010.1440.752
Georgia St2.7370.3450.0630.0110.0010.0001.4210.0000.1891.166
Dayton3.0440.3240.0500.0070.0020.0002.3830.0000.0341.733
Alabama-Birmingham1.7400.2820.0240.0020.0000.0001.3090.0000.1881.219
North Carolina St3.1940.1310.0350.0080.0020.0001.1750.0000.1110.510
UCLA2.7180.7180.1200.0240.0030.0001.8650.0000.1811.540