Better losses? Worse wins?

© Copyright 2011, Paul Kislanko

Does one "bad win" make a team better than a team with a "good loss?" What is a "good loss/win" or "bad win/loss?" Everyone is free to decide for themselves, but it can help to present the relevant data in a way that makes it easy to compare team-pairs based upon their resumes.

I am fond of inventing meta-rankings ("ratings" whose inputs are other rankings instead of game results) not because they have any intrinsic value, but because they make visible characteristics of the input rankings that aren't otherwise obvious. I'm especially fond of meta-rankings that turn ordinal ranking data into a rating value, because good variations of those can show that the difference between #1 and #10 is a lot greater than that between #56 and #64.

In fact, the meta-rating described below has a larger difference between #1 and #2 than between #40 and #80, as you can see from the graph:

opponents ranks and mov
The horizontal axis is meta-rank, the vertical is the meta-rating.
And consider: the difference between #1 and #10 is larger than the difference between #10 and #83!

The Formula

This meta-rating uses game-scores and opponents' ranks, so it's not really a "pure" meta-ranking. The algorithm assigns a value to each win by a team and a value to each loss based upon MOV and opponent's rank with o-rank being used two different ways:
Winner's score
Loser's score
⌈ (WS - LS)÷8 ⌉ = the margin of victory in number of scores
(⌈x⌉ is the least integer ≥ x)
For example, a 37-7 score is 30÷8 and for our purposes that is 4, since 30/8 = 3+a fraction, and 4 is the least integer higher than that.
Opponents' Ranks
For each game, the winning team gets a factor = (121-opponent's rank) and the losing team gets a factor = −(opponent's rank).
Teams that beat top 20, top 40, etc. opponents get an extra "boost" for those games they win. Likewise teams that lose to the bottom 20, 40 ... etc; get an opposite of "boost." Winning over a non-FBS team doesn't help at all, but losing to one hurts a lot.

For winning teams, the MOV factor is capped at three scores - we don't learn more about the winner as the margin goes up past that. The negative MOV factor for the losing team is not capped because we do get more information about a team that loses by 10 scores than one that loses by three.

For each game, multiply the three factors, then take the average over all games to form the "rating."

Now, this isn't more of a good "rating" than any other meta-rating, but it is useful in the same way I think the baseball RPI is. I don't think it is a great measure of team performance, but it's as reasonable as any as a sort sequence. Here's a sample:

Better win - Worse loss meta ranking

Wins Over
Losses To
19442 Alabama 5-0SEC16 20 30 102 106
2700.48 Clemson 5-0ACC20 24 35 76 121
3698.24 LSU 5-0SEC13 22 60 84 121
46794 Oklahoma 4-0B1235 42 55 73
5676.56 Boise State 4-0MW34 55 62 64
6608.256 Oklahoma State 4-0B1228 55 59 73
75588 Michigan 5-0B1022 40 50 90 107
8540.7510 Texas 4-0B1238 58 65 94
9437.47 Wisconsin 5-0B1017 87 102 103 121
10393.756 Stanford 4-0P1265 70 73 91
11360.422 Notre Dame 3-2ND31 41 8829 8
12334.223 Arizona State 4-1P1232 42 103 12116
13325.417 South Carolina 4-1SEC34 49 67 9020
14300.817 Nebraska 4-1B1026 71 88 1217
15268.832 Southern California 4-1P1247 60 73 10723
16263.426 Washington 4-1P1245 47 68 12117
17262.816 Illinois 5-0B1023 50 76 76 121
18258.641 Pittsburgh 3-2BigE29 110 12138 22
19238.7528 Texas A&M 2-2B1242 11020 6
20234.2513 Oregon 3-1P1264 73 1214
21229.616 Florida 4-1SEC33 84 108 1162
22225.2533 Tennessee 3-1SEC46 110 12116
23215.414 Georgia Tech 5-0ACC28 76 82 104 121
24205.540 San Diego State 3-1MW56 88 1218
25193.2521 Kansas State 4-0B1233 52 102 121

Here the input Rank is itself a meta-rank: it is the best rank for which >50% of the computer rankings tracked by Dr. Massey rank the team at least that highly. It's kind of interesting to look at the RankMeta-Rank changes for each team, and the presentation makes it easier to see why one team's results against their schedule give it a different result than another's against their schedule (for this input Rank.)

The team-names link to the better-wins/worse losses tables for each of the teams. The "Valu" column combines the opponent's rank and MOV (but not the bonus.)

One of the things I like about the report is that the opponents' names do not appear. It's easier for us humans to be objective when we see only the opponents' rankings, not their names. Here's the full report.