Team-Pairwise Conference Comparisons

© Copyright 2010, Paul Kislanko

Defining Conference Strength in terms of Computer Ratings

I've devised various measurements that account for extremes, or at least make them visible, but all of them require some interpretation. And whether one thinks the criterion should be highest-rated team(s) or lower-rated teams should be discounted, eventually the argument boils down to some version of how "deep" the conference is.

Folks making that argument use vague definitions (sometimes based upon some of my reports) but if we must compare conferences based upon team ratings, there is a way to compare conferences based upon their constituent teams' ratings.

If there are n teams t1 in conference C1 and and m teams t2 in conference C2, define a Team-Pairwise Comparison of C1 and C2 by:

TPC(C1,C2) = [	n	m
	∑	∑	R(t1i) − R(t2j)	] ÷ (n×m)
	i=1	j=1

Then the conferences can be directly compared in a table that has TPC(C_i,C_j) in row i column j, and the conferences ordered 1,2,3,... by summing the row values.

TPC(C1,C2) can be thought of as the expected value for the difference in ratings when one selects a team from conference C1 and a team from conference C2 at random. A positive number means conference C1 is "deeper", "stronger at the top" or both. And of course TPC(C2,C1) = −TPC(C1,C2) and TPC(C,C) = 0.

Now, if settling (or starting!) barroom arguments were the only use for a measure that aggregates ratings by conference I'd consider it a waste of time. The value in such a measurement is that it allows us to compare conference records for teams in different conferences. This is especially important in FBS football, since there are so few data points fot interconference comparisions. Here's such a report based upon Chris Breisch's version of MLE:

ix Sort Comps Conf P10 SEC B12 B10 ACC BigE WAC MW CUSA MAC SBC 1 0.1368 1160 P10   0.0235 0.0370 0.0810 0.0923 0.1220 0.1535 0.1573 0.2317 0.2856 0.3193 2 0.1131 1392 SEC -0.0235   0.0136 0.0575 0.0688 0.0986 0.1300 0.1338 0.2082 0.2621 0.2958 3 0.0994 1392 B12 -0.0370 -0.0136   0.0440 0.0552 0.0850 0.1164 0.1202 0.1947 0.2485 0.2822 4 0.0551 1276 B10 -0.0810 -0.0575 -0.0440   0.0113 0.0410 0.0725 0.0763 0.1507 0.2046 0.2383 5 0.0437 1392 ACC -0.0923 -0.0688 -0.0552 -0.0113   0.0298 0.0612 0.0650 0.1394 0.1933 0.2270 6 0.0137 928 BigE -0.1220 -0.0986 -0.0850 -0.0410 -0.0298   0.0314 0.0352 0.1097 0.1635 0.1972 7 -0.0180 1044 WAC -0.1535 -0.1300 -0.1164 -0.0725 -0.0612 -0.0314   0.0038 0.0782 0.1321 0.1658 8 -0.0219 1044 MW -0.1573 -0.1338 -0.1202 -0.0763 -0.0650 -0.0352 -0.0038   0.0744 0.1283 0.1620 9 -0.0969 1392 CUSA -0.2317 -0.2082 -0.1947 -0.1507 -0.1394 -0.1097 -0.0782 -0.0744   0.0539 0.0876 10 -0.1513 1508 MAC -0.2856 -0.2621 -0.2485 -0.2046 -0.1933 -0.1635 -0.1321 -0.1283 -0.0539   0.0337 11 -0.1853 1044 SBC -0.3193 -0.2958 -0.2822 -0.2383 -0.2270 -0.1972 -0.1658 -0.1620 -0.0876 -0.0337

Lagniappe

For each team t and each team tC in conference C, count a "rating win" (Rw) for team t over tC if R(t) ≥ R(tC) and a "rating loss" (Rl) otherwise. Then Rw ÷ ( Rw + Rl ) is the "expected conference winning percentage" for team t were they to be in conference C. Multiply that by the number of conference games played in conference C and you get the "expected" conference record were team to play in conference C.

Of course the higher-rated team doesn't win every game, and may not even be favored. Nonetheless, it's a more objective way to play the "if team X were in a different conference their record would like be..." game. That game is more fun if the ratings used are "predictive" ones. Here's how the team conference comparison looks for Chris Bresisch's version of MLE (for the team's own conference the "Record" is just the number of higher and lower-rated teams in the same conference):

Team Comparison to Conference Strength
Based upon MLE through games of 6 November 2010