Transitivity is the idea that if A beat B by 10 points, and B beat C by 10, then A must be 20 points better than C. Another form of the idea is to ignore points and just say "then A must be better than C." If we assume transitivity is meaningful in sports, we can seemingly prove that in 2000 Buffalo (a 2-9 MAC team in its 2nd year in Division 1A) was better than Florida State (#3), Washington (#8), and Miami (#2).

Scores from 2000:

1. Buffalo 20, Bowling Green 17
2. Bowling Green 18, Kent State 11
3. Kent State 24, Central Michigan 21
4. Central Michigan 17, Akron 7
5. Akron 23, Ohio 20
6. Ohio 23, Minnesota 17
7. Minnesota 25, Penn State 16
8. Penn State 22, Purdue 20
9. Purdue 32, Michigan 31
10. Michigan 13, Wisconsin 10
11. Wisconsin 27, Oregon 23
12. Oregon 23, Washington 16
13. Washington 34, Miami 29
14. Miami 27, Florida State 24

The obvious conclusion here is that when a game is close, the only information gained is that the winner might be better than the loser, but nearly as likely they are not. Thus, the idea that teams can "settle it on the field" is inherently flawed.

We can add a few more links to this chain. At the top place Ball State 44, Buffalo 35; and at the bottom add Florida State 30, Florida 7. Ball State appears 119 points better than Florida. Oh, and guess what - Florida and Ball State played in 2001. The score? Florida 40, Ball State 19.

From 2001:

1. Rice 45, Boise State 14
2. Boise state 35, Fresno State 30
3. Fresno State 24, Colorado 22
4. Colorado 62, Nebraska 36

This chain of only four games makes it appear that Rice is 64 points better than Nebraska, but Nebraska beat Rice 48-3! The Nebraska vs. Rice game contradicts transitive logic by 109 points (64+45), suggesting games decided by less than 21.8 points (109 points ÷ 5 transitive links from Rice back to Rice) do not definitely prove which is the "better" team!

An amazing chain from 2003:

1. Marshall 27, Kansas State 20
2. Kansas State 41, Troy State 5
3. Troy State 33, Marshall 24

Almost as dumbfounding is...

1. Notre Dame 26, Washington State 19
2. Washington State 55, Oregon 16
3. Oregon 31, Michigan 27
4. Michigan 38, Notre Dame 0

An 88-point contradiction in 4 links = 22 points/link.

Finally, the ultimate proof that transitivity is almost meaningless is the fact that we can find teams who played twice in the same season, with each team winning a game and one or both games being a blow-out. An example from 2001:

1. Colorado 7, Texas 41 (in Austin)
2. Colorado 39, Texas 37 (neutral field)

The home field advantage is not 36 points! These two games paint vastly different pictures. Who's the better team? In the strange world of college football, even a 41-7 score should not convince anyone of much... (Other examples I know of are Florida-Florida State 1996, Nebraska-Oklahoma 1978)

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