KRACH applied to Division I-A college football
Background
A few years ago I applied Ken's Rating for American College Hockey (KRACH), or Bradley-Terry statistics, to ACHA club hockey teams. At the time, participants for the national tournament were determined by an opinion poll, and there wasn't enough interplay for that to be meaningful (sound familiar?).
In an earlier post here, I intimated that I'd like to see someone crunch the numbers as a mechanism for rating Division I-A college football teams. It's something I've been thinking about for quite some time, just to see what would happen. So tonight I threw something together.
Brief Summary:
"The KRACH rating system is an attempt to combine the performance of each team with the strength of the opposition against which that performance was achieved, and to summarize the result as one number, a "rating", for each team. The higher the rating, the better the team."
"Interpreting the ratings
The ratings are given on an "odds scale": that is, if team A is rated at 400 and team B at 200, team A is reckoned to have odds of 2 to 1 of defeating team B when they meet (since 400 is twice 200). Equivalently, team A is reckoned to have probability 2/3 of defeating team B (since 400/(400+200) is 2/3)."
"There are two things we need to check, to make sure that the rating system is sensible:- If you win more against the same opposition as another team, your rating will be higher.
- If you have the same record as another team, but against tougher opposition, your rating will be higher."
Methods
So, I took the season results from the official NCAA page. I excluded results against FCS competition, as a matter of principle.
One caveat here - I haven't yet worked out what to do exactly with undefeated and winless teams. This will become meaningful at the end of the season if there are multiple undefeated teams (I'm not sure I really care about the winless teams). While I sort that out, I've done the following:
- Verified my calculated rating by calculating the predicted number of wins;
- Determining a percentage difference between the predicted and actual number of wins;
Results
Without further ado, the first KRACH rating for Division I-A college football:
KRACH | Predicted Wins |
Actual Wins |
% Difference |
||
1 | Texas | 200.000 | 8.937 | 9 | 0.702 |
2 | TCU | 200.000 | 7.928 | 8 | 0.898 |
3 | Boise State | 200.000 | 7.848 | 8 | 1.906 |
4 | Cincinnati | 200.000 | 7.830 | 8 | 2.131 |
5 | Florida | 200.000 | 7.752 | 8 | 3.104 |
6 | Alabama | 200.000 | 8.716 | 9 | 3.160 |
7 | LSU | 39.863 | 6.999 | 7 | 0.011 |
8 | Georgia Tech | 35.246 | 7.998 | 8 | 0.024 |
9 | Oregon | 32.752 | 6.998 | 7 | 0.021 |
10 | Iowa | 28.690 | 7.998 | 8 | 0.026 |
11 | USC | 21.015 | 6.999 | 7 | 0.021 |
12 | Pittsburgh | 17.119 | 6.998 | 7 | 0.024 |
13 | Arizona | 14.574 | 4.999 | 5 | 0.025 |
14 | Oregon State | 14.533 | 4.999 | 5 | 0.021 |
15 | Miami (FL) | 13.562 | 5.999 | 6 | 0.022 |
16 | Ohio State | 13.418 | 7.998 | 8 | 0.026 |
17 | South Florida | 12.804 | 3.999 | 4 | 0.021 |
18 | Penn State | 12.186 | 6.998 | 7 | 0.025 |
19 | Virginia Tech | 10.888 | 5.999 | 6 | 0.020 |
20 | Clemson | 9.944 | 4.999 | 5 | 0.023 |
21 | Wisconsin | 9.061 | 5.999 | 6 | 0.023 |
22 | Oklahoma State | 8.788 | 5.999 | 6 | 0.020 |
23 | Temple | 7.966 | 6.998 | 7 | 0.026 |
24 | Stanford | 7.682 | 5.999 | 6 | 0.021 |
25 | Houston | 7.679 | 6.998 | 7 | 0.024 |
26 | Utah | 7.215 | 7.998 | 8 | 0.024 |
27 | California | 7.194 | 4.999 | 5 | 0.024 |
28 | Auburn | 5.098 | 5.999 | 6 | 0.021 |
29 | Navy | 4.686 | 6.998 | 7 | 0.026 |
30 | Georgia | 4.627 | 3.999 | 4 | 0.019 |
31 | Rutgers | 4.399 | 3.999 | 4 | 0.022 |
32 | Boston College | 4.292 | 4.999 | 5 | 0.025 |
33 | West Virginia | 3.877 | 5.999 | 6 | 0.020 |
34 | Tennessee | 3.789 | 4.999 | 5 | 0.018 |
35 | Notre Dame | 3.761 | 5.999 | 6 | 0.022 |
36 | Arkansas | 3.534 | 3.999 | 4 | 0.022 |
37 | UCLA | 3.515 | 3.999 | 4 | 0.016 |
38 | Florida State | 3.103 | 2.999 | 3 | 0.019 |
39 | North Carolina | 3.030 | 3.999 | 4 | 0.020 |
40 | Brigham Young | 2.787 | 6.998 | 7 | 0.025 |
41 | Washington | 2.689 | 3.000 | 3 | 0.013 |
42 | Central Michigan | 2.345 | 5.999 | 6 | 0.024 |
43 | South Carolina | 2.315 | 4.999 | 5 | 0.017 |
44 | Minnesota | 2.130 | 4.999 | 5 | 0.023 |
45 | Mississippi State | 2.117 | 3.000 | 3 | 0.016 |
46 | Fresno State | 2.057 | 4.999 | 5 | 0.025 |
47 | Kentucky | 1.951 | 3.999 | 4 | 0.021 |
48 | Mississippi | 1.905 | 3.999 | 4 | 0.020 |
49 | Arizona State | 1.582 | 2.999 | 3 | 0.024 |
50 | Texas Tech | 1.541 | 4.999 | 5 | 0.020 |
51 | Northwestern | 1.260 | 4.999 | 5 | 0.023 |
52 | Michigan State | 1.219 | 3.999 | 4 | 0.022 |
53 | Oklahoma | 1.196 | 3.999 | 4 | 0.017 |
54 | Nebraska | 1.172 | 5.999 | 6 | 0.022 |
55 | Wake Forest | 1.133 | 3.000 | 3 | 0.015 |
56 | Connecticut | 1.010 | 2.999 | 3 | 0.023 |
57 | Duke | 0.905 | 3.999 | 4 | 0.025 |
58 | Purdue | 0.865 | 3.999 | 4 | 0.018 |
59 | Syracuse | 0.836 | 2.000 | 2 | 0.017 |
60 | Air Force | 0.729 | 4.999 | 5 | 0.025 |
61 | Virginia | 0.719 | 3.000 | 3 | 0.017 |
62 | Missouri | 0.718 | 3.999 | 4 | 0.020 |
63 | Troy | 0.690 | 6.998 | 7 | 0.022 |
64 | North Carolina State | 0.561 | 2.000 | 2 | 0.017 |
65 | Kansas State | 0.555 | 3.999 | 4 | 0.020 |
66 | Michigan | 0.545 | 3.999 | 4 | 0.023 |
67 | Texas A&M | 0.536 | 4.999 | 5 | 0.020 |
68 | Baylor | 0.476 | 2.999 | 3 | 0.025 |
69 | Idaho | 0.466 | 6.998 | 7 | 0.024 |
70 | Iowa State | 0.437 | 3.999 | 4 | 0.023 |
71 | Kansas | 0.434 | 3.999 | 4 | 0.020 |
72 | East Carolina | 0.413 | 3.999 | 4 | 0.024 |
73 | Middle Tennessee State | 0.363 | 5.999 | 6 | 0.022 |
74 | Illinois | 0.358 | 1.999 | 2 | 0.026 |
75 | Southern Methodist | 0.333 | 3.999 | 4 | 0.022 |
76 | Louisville | 0.305 | 2.000 | 2 | 0.020 |
77 | Northern Illinois | 0.304 | 4.999 | 5 | 0.024 |
78 | Indiana | 0.289 | 2.999 | 3 | 0.023 |
79 | Nevada | 0.287 | 5.999 | 6 | 0.022 |
80 | Marshall | 0.259 | 3.999 | 4 | 0.021 |
81 | Southern Miss | 0.240 | 3.999 | 4 | 0.020 |
82 | UCF | 0.223 | 3.999 | 4 | 0.018 |
83 | Bowling Green | 0.206 | 3.999 | 4 | 0.024 |
84 | Colorado | 0.203 | 2.999 | 3 | 0.025 |
85 | Ohio | 0.181 | 4.999 | 5 | 0.020 |
86 | Louisiana-Monroe | 0.177 | 3.999 | 4 | 0.018 |
87 | Maryland | 0.149 | 1.000 | 1 | 0.021 |
88 | San Diego State | 0.147 | 2.999 | 3 | 0.019 |
89 | Wyoming | 0.140 | 2.999 | 3 | 0.017 |
90 | UAB | 0.134 | 3.999 | 4 | 0.015 |
91 | Toledo | 0.117 | 3.999 | 4 | 0.020 |
92 | Colorado State | 0.115 | 2.000 | 2 | 0.020 |
93 | UNLV | 0.103 | 2.999 | 3 | 0.019 |
94 | Kent State | 0.092 | 3.999 | 4 | 0.020 |
95 | Western Michigan | 0.088 | 3.000 | 3 | 0.013 |
96 | Washington State | 0.074 | 1.000 | 1 | 0.013 |
97 | Buffalo | 0.050 | 2.000 | 2 | 0.019 |
98 | Louisiana-Lafayette | 0.048 | 3.999 | 4 | 0.016 |
99 | Florida Atlantic | 0.036 | 2.000 | 2 | 0.021 |
100 | Tulane | 0.035 | 2.000 | 2 | 0.013 |
101 | UTEP | 0.033 | 3.000 | 3 | 0.016 |
102 | Memphis | 0.031 | 1.000 | 1 | 0.019 |
103 | Miami (OH) | 0.031 | 1.000 | 1 | 0.020 |
104 | Tulsa | 0.031 | 3.000 | 3 | 0.015 |
105 | Akron | 0.030 | 1.000 | 1 | 0.025 |
106 | Hawaii | 0.028 | 2.000 | 2 | 0.023 |
107 | Louisiana Tech | 0.021 | 2.000 | 2 | 0.019 |
108 | Arkansas State | 0.019 | 1.000 | 1 | 0.021 |
109 | Florida International | 0.018 | 2.000 | 2 | 0.018 |
110 | Army | 0.015 | 3.000 | 3 | 0.013 |
111 | New Mexico State | 0.009 | 2.000 | 2 | 0.017 |
112 | Utah State | 0.008 | 1.000 | 1 | 0.007 |
113 | North Texas | 0.006 | 2.000 | 2 | 0.012 |
114 | Vanderbilt | 0.004 | 1.000 | 1 | 0.005 |
115 | Ball State | 0.002 | 1.000 | 1 | 0.007 |
116 | Eastern Michigan | 0.001 | 0.442 | 0 | 0.000 |
117 | New Mexico | 0.001 | 0.162 | 0 | 0.000 |
118 | Rice | 0.001 | 0.259 | 0 | 0.000 |
119 | San Jose State | 0.001 | 0.006 | 0 | 0.000 |
120 | Western Kentucky | 0.001 | 0.216 | 0 | 0.000 |
November 11th, 2009 at 3:48 PM ^
November 11th, 2009 at 3:58 PM ^
November 11th, 2009 at 4:27 PM ^
November 11th, 2009 at 4:36 PM ^
November 11th, 2009 at 4:48 PM ^
November 11th, 2009 at 5:38 PM ^
November 12th, 2009 at 7:44 AM ^
November 12th, 2009 at 10:59 AM ^
November 11th, 2009 at 4:56 PM ^
November 11th, 2009 at 5:49 PM ^
November 12th, 2009 at 2:02 AM ^
November 11th, 2009 at 5:51 PM ^
One caveat here - I haven't yet worked out what to do exactly with undefeated and winless teams. This will become meaningful at the end of the season if there are multiple undefeated teams (I'm not sure I really care about the winless teams).I wrote a KRACH program a few years ago, and what I did for the undefeated/winless teams was create a fake "tie team", and then have every single team play that team and have a tie. I had built my program off the description at USCHO, so it already handled ties. This had a bit of a fudge factor, but you need to make sure everyone has greater than zero wins and losses unless you have figured out how to divide by zero. I also made just one "I-AA" team to use for whenever someone played against a team from the other division because I didn't want to have to keep track of all those teams too. It was nice in the middle of 2006 when I could use it to confirm that Michigan was better than their ranking in the polls, but in the following years keeping up the spreadsheet was too big a pain just to further my misery.
November 11th, 2009 at 6:55 PM ^
November 12th, 2009 at 1:02 AM ^
November 12th, 2009 at 1:16 AM ^
November 12th, 2009 at 1:57 AM ^
November 12th, 2009 at 3:16 PM ^
Comments