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Friday, November 9, 2012

More fun with the transitive property, the SEC is good at football, some other conferences are not

The problem with using the transitive property (e.g., if A>B & B>C then A>C) in college football is that a team's performance can vary a lot from game to game. Texas can lose to West Virginia, almost lose to Kansas, and then own Texas Tech after Tech destroys West Virginia. But, with 124 teams and 12 to 14 game schedules, the transitive property is essential.

Freakishly Symmetric
To make the most of it, then, I've tracked every connection between each college football team and Alabama, using up to 6 different games to make the connection. I added up the point differentials of the connecting games and averaged them together (weighting cases for the error introduced when you use additional steps to make the connection).

For example, Texas A&M lost to LSU by 5. LSU lost to Alabama by 4. So Texas A&M would get a -9 for that connection. Then, Texas A&M beat Mississippi State by 25 after Alabama beat them by 31, so Texas A&M gets a -6. But also Alabama played Western Kentucky, who played Kentucky, who played Arkansas, who played Ole Miss who played Texas A&M.

The result is what I call the Transitive Gap (TG). Alabama comes out on top, beating its opponents on average by the exact same average that its opponents get beaten by the Tide. Coming in at #2 is Texas A&M, meaning that no one else comes as close to beating the same teams (or teams that played teams) as badly as Alabama does than the Aggies. Texas A&M is followed by Kansas State, Oklahoma and Oregon. (In case you're wondering, the results do depend somewhat on the team used for comparison - Alabama in this case. That being said, Alabama is consistently on top with Oregon and Texas A&M usually in the top 3. Kansas State, Oklahoma, South Carolina and Georgia are often in the top 5.)



One interpretation of these results is that there is not a team out there in college football that is better suited to beat Alabama. Another interpretation is that Alabama and A&M play many of the same opponents, or opponents' opponents, and A&M scores fast and in large numbers. The latter is a more reasonable interpretation, but the former is a lot funner.

In other transitive news, LSU gets Mississippi State this weekend. If the transitive property tells us anything it tells us that LSU should win this by between 27 and 30 points. The model says 13 and Vegas say 14.5. If you add those together you get 27.5. This means something. This is important.

South Carolina is favored by 13 over Arkansas. The model likes South Carolina by 18. The model has had a real good handle on the Gamecocks this season but it has a really hard time adjusting to injuries, especially major injuries. In other words, if we abandon all scientific rigor, this gap allows us to estimate the contribution from Lattimore at more than 5 and probably around 7 points per game. That's huge and the whole situation just makes me sad.

In other news, Akron gets Massachusetts this weekend. Seeing as how UMass has been sending out the equestrian team to play football, this gives Akron a great opportunity to get a win, top last years win total and double last years win total at the same time. This is the same Akron team that scored 26 on Tennessee and kept it interesting way too long. Then again, Towson did the same to LSU, and LSU was one act of insanity short of getting back in the national title hunt. Speaking of Tennessee, with four wins and Vanderbilt, Missouri and Kentucky left on the schedule, Tennessee has a 73% chance of getting to a bowl game. If Dooley needs to win out to stay employed, his chances fall to 22%.

Finally, Tulane and Memphis play this weekend. Tulane, with the 120th more efficient offense, has become an offensive powerhouse compared to Memphis (124th by the same measure). Fortunately for all involved, the defenses are porous and points will be scored - Vegas says 56.5, the model say 54. Both are calling this game a pick'em, and I pick awesome.




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