Yet Another CBB Rating System

It’s here! March Madness, that time of year where we all try to predict how a bunch of 20-year-olds playing a game filled with randomness will perform. It’s fun! But we sure don’t bet real money on it, cause that would be illegal!

Actually guys, it’s not as much fun for me again this year, because, for the 3rd consecutive season, my team was not invited to keep playing. Someone please fix this. Sigh…

Anyway, this year I decided to build my own quantitative rating and prediction system to help me fill out my bracket. Here’s how my system works:

I define a numeric rating, R(i), for each team i. I also define the probability of team i defeating team j on a neutral court as

P(i->j) = R(i) / (R(i) + R(j)).

I then create a cost function, defined over all games played during the season, which is the sum over

[P(i->j) – GP(i->j)]^2,

where GP(i->j) is an estimated game probability that depends only on the result of each individual game. The GP probability value for each game must be provided as an input to the algorithm.

Of course, coming up with a good value for GP(i->j) is tricky, since we only have one occurrence (one result) for each game. The simplest method for determining GP(i->j) is to assign 100% probability if team i defeated team j, and 0% otherwise. But this ignores home/away, so it’s not ideal.

For my system, I decided to build a model based on the home/away adjusted margin of victory for the game. If team i wins by a large margin, P(i->j) will be close to 100%, but if it’s a close game, the value will be closer to 50%. (The home/away factor adjusts the margin in favor of the road team by 3.5 points)

To compute the final ratings for all teams, I initialize all teams with an equal rating (1.0) and perform an iterative optimization that minimizes the overall cost function with respect to the ratings. I use gradient descent as the optimization procedure.

Below, I list my ratings for the top 100 teams in division 1. (My Marquette Golden Eagles just managed to sneak in at #99, woo!). Note that the value of a team’s rating carries no particular meaning by itself – it’s only useful when compared to the other team ratings.

Rank Team Rating
1 Kansas 8.779
2 Michigan St 8.317
3 North Carolina 8.174
4 Villanova 7.717
5 West Virginia 7.504
6 Virginia 7.149
7 Louisville 6.637
8 Oklahoma 6.602
9 Purdue 6.035
10 Kentucky 5.737
11 Duke 5.483
12 Arizona 5.342
13 Xavier 5.200
14 Miami FL 5.199
15 Oregon 5.151
16 Indiana 5.136
17 Iowa St 4.919
18 Texas A&M 4.802
19 Baylor 4.700
20 Maryland 4.601
21 SMU 4.514
22 Utah 4.400
23 Iowa 4.390
24 California 4.266
25 Vanderbilt 4.246
26 Wichita St 3.983
27 Gonzaga 3.842
28 Connecticut 3.827
29 Pittsburgh 3.552
30 Butler 3.543
31 Seton Hall 3.538
32 VA Commonwealth 3.531
33 Notre Dame 3.496
34 Texas 3.487
35 USC 3.465
36 Cincinnati 3.444
37 Florida 3.443
38 St Mary’s CA 3.221
39 Creighton 3.182
40 South Carolina 3.154
41 Kansas St 3.117
42 Michigan 3.107
43 Syracuse 3.057
44 Texas Tech 2.990
45 Colorado 2.969
46 Wisconsin 2.953
47 St Joseph’s PA 2.882
48 Washington 2.825
49 Florida St 2.791
50 Valparaiso 2.700
51 Dayton 2.682
52 Yale 2.671
53 SF Austin 2.620
54 Oregon St 2.617
55 Georgia Tech 2.589
56 Clemson 2.589
57 Providence 2.559
58 Northwestern 2.529
59 Ohio St 2.515
60 Georgia 2.467
61 Hawaii 2.400
62 San Diego St 2.388
63 BYU 2.353
64 Arkansas 2.330
65 UCLA 2.309
66 Tulsa 2.297
67 G Washington 2.284
68 Virginia Tech 2.209
69 Arizona St 2.182
70 Georgetown 2.167
71 Houston 2.114
72 Ark Little Rock 2.110
73 Rhode Island 2.089
74 Nebraska 2.072
75 UC Irvine 2.046
76 Mississippi 2.045
77 Stanford 2.029
78 LSU 2.023
79 Princeton 2.012
80 NC State 2.006
81 Memphis 2.003
82 Monmouth NJ 1.994
83 Evansville 1.949
84 Alabama 1.925
85 St Bonaventure 1.921
86 UNC Wilmington 1.896
87 Richmond 1.896
88 S Dakota St 1.887
89 Temple 1.884
90 Mississippi St 1.881
91 Stony Brook 1.806
92 Oklahoma St 1.794
93 Akron 1.787
94 Tennessee 1.764
95 Davidson 1.751
96 William & Mary 1.749
97 Santa Barbara 1.732
98 James Madison 1.731
99 Marquette 1.727
100 Iona 1.674

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