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Category: Math & Statistics

College Football Rankings, Pre-Bowl

Published 2024-12-11

You make like or despise or completely not care about the College Football Playoff committee rankings. I have an interest and am curious about how “right” they get things. (There is a serious contention that they don’t care about getting it right, just about creating profitable matchups in the post-season.)

I have my own method to rank teams. I use a modified Elo ranking system which is non-discrete. The system considers strength of schedule, home field advantage, and point spreads up to 19 points (because anything beyond that is functionally meaningless). The systems first ranks the FBS, FCS, Division II and Division III divisions based on cross-division games. The system then ranks the conferences, using the division rankings as the starting points, based on cross-conference games. The system then ranks the teams based on all games.

Disclaimer: I am a BYU fan. I have thought all season that BYU should be ranked above Miami and Boise State. You can see that my math does not agree with me. Here are the rankings based on my system.

RankTeam
1Oregon
2Indiana
3Ole Miss
4Texas
5Georgia
6South Carolina
7Notre Dame
8Tennessee
9Alabama
10Florida
11Miami
12Ohio State
13LSU
14Army
15Arizona State
16Penn State
17Missouri
18Texas A&M
19Memphis
20Kansas State
21BYU
22Vanderbilt
23Minnesota
24Clemson
25Iowa

World Cup probabilities

Published 2018-06-11

With the World Cup starting this week, I had to create the obligatory probability models. I’ve used the FIFA ratings as my starting point, adjusted for geographical differences in travelling to Russia, and crunched the numbers. I get the follow for the top five teams and their associated probability of winning the championship.

Team p
Germany 6.8%
Portugal 4.9%
Belgium 4.4%
Brazil 4.2%
France 3.5%

Interestingly, the percentages here give Portugal a slight edge over Belgium, even though Belgium is ranked higher in the FIFA rankings. This has to do with the first round groupings and the way the bracket gets structured. Even though they are the higher ranked team, Belgium’s path to the championship likely goes through more difficult teams than Portugal’s path. Even so, what should be very apparent is that any team’s path is difficult as evidenced by the favorite’s probability sitting at only 6.8%.

Worth noting is the presence of only one South American team among the model’s favorites. Going into the World Cup, Brazil is ranked second in the world. However, the historical data suggests that South American teams will under perform in Europe (and yes, I am counting Russia as geographically Europe for this World Cup). Applying a 10% deduction to the South American teams, the model takes both Brazil and Argentina out of the tournament in the quarterfinals matches.

Most probable results:

1st place Germany
2nd place Belgium
3rd place Portugal