Resume Rankings

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:

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:

MOV

WS: Winner's score
LS: 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).

Bonus

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

Meta
Rank ƒ(ranks) Rank Team Rec Conf Best
Win Other
Wins Over Worst
Loss Other
Losses To

1 944 2 Alabama 5-0 SEC 16 20 30 102 106 –

2 700.4 8 Clemson 5-0 ACC 20 24 35 76 121 –

3 698.2 4 LSU 5-0 SEC 13 22 60 84 121 –

4 679 4 Oklahoma 4-0 B12 35 42 55 73 –

5 676.5 6 Boise State 4-0 MW 34 55 62 64 –

6 608.25 6 Oklahoma State 4-0 B12 28 55 59 73 –

7 558 8 Michigan 5-0 B10 22 40 50 90 107 –

8 540.75 10 Texas 4-0 B12 38 58 65 94 –

9 437.4 7 Wisconsin 5-0 B10 17 87 102 103 121 –

10 393.75 6 Stanford 4-0 P12 65 70 73 91 –

11 360.4 22 Notre Dame 3-2 ND 31 41 88 29 8

12 334.2 23 Arizona State 4-1 P12 32 42 103 121 16

13 325.4 17 South Carolina 4-1 SEC 34 49 67 90 20

14 300.8 17 Nebraska 4-1 B10 26 71 88 121 7

15 268.8 32 Southern California 4-1 P12 47 60 73 107 23

16 263.4 26 Washington 4-1 P12 45 47 68 121 17

17 262.8 16 Illinois 5-0 B10 23 50 76 76 121 –

18 258.6 41 Pittsburgh 3-2 BigE 29 110 121 38 22

19 238.75 28 Texas A&M 2-2 B12 42 110 20 6

20 234.25 13 Oregon 3-1 P12 64 73 121 4

21 229.6 16 Florida 4-1 SEC 33 84 108 116 2

22 225.25 33 Tennessee 3-1 SEC 46 110 121 16

23 215.4 14 Georgia Tech 5-0 ACC 28 76 82 104 121 –

24 205.5 40 San Diego State 3-1 MW 56 88 121 8

25 193.25 21 Kansas State 4-0 B12 33 52 102 121 –

Meta Rank	ƒ(ranks)	Rank	Team	Rec	Conf	Best Win	Other Wins Over	Worst Loss	Other Losses To
1	944	2	Alabama	5-0	SEC	16	20 30 102 106	–
2	700.4	8	Clemson	5-0	ACC	20	24 35 76 121	–
3	698.2	4	LSU	5-0	SEC	13	22 60 84 121	–
4	679	4	Oklahoma	4-0	B12	35	42 55 73	–
5	676.5	6	Boise State	4-0	MW	34	55 62 64	–
6	608.25	6	Oklahoma State	4-0	B12	28	55 59 73	–
7	558	8	Michigan	5-0	B10	22	40 50 90 107	–
8	540.75	10	Texas	4-0	B12	38	58 65 94	–
9	437.4	7	Wisconsin	5-0	B10	17	87 102 103 121	–
10	393.75	6	Stanford	4-0	P12	65	70 73 91	–
11	360.4	22	Notre Dame	3-2	ND	31	41 88	29	8
12	334.2	23	Arizona State	4-1	P12	32	42 103 121	16
13	325.4	17	South Carolina	4-1	SEC	34	49 67 90	20
14	300.8	17	Nebraska	4-1	B10	26	71 88 121	7
15	268.8	32	Southern California	4-1	P12	47	60 73 107	23
16	263.4	26	Washington	4-1	P12	45	47 68 121	17
17	262.8	16	Illinois	5-0	B10	23	50 76 76 121	–
18	258.6	41	Pittsburgh	3-2	BigE	29	110 121	38	22
19	238.75	28	Texas A&M	2-2	B12	42	110	20	6
20	234.25	13	Oregon	3-1	P12	64	73 121	4
21	229.6	16	Florida	4-1	SEC	33	84 108 116	2
22	225.25	33	Tennessee	3-1	SEC	46	110 121	16
23	215.4	14	Georgia Tech	5-0	ACC	28	76 82 104 121	–
24	205.5	40	San Diego State	3-1	MW	56	88 121	8
25	193.25	21	Kansas State	4-0	B12	33	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 Rank→Meta-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.