Change to the formula

posted Sep 29, 2016, 7:44 PM by Ted P   [ updated Sep 29, 2016, 7:57 PM ]
While the fundamentals will remain the same, I think this will be my most significant change in the formula since 2010, which is when I implemented a comprehensive system for FCS/I-AA opponents.  This will be implemented with my first ratings of the season, which should be posted in the early morning hours on Sunday the 2nd.

In short, I'm going to give more credit for quality wins so teams can more easily overcome losses.  In last season's final ratings for instance, Appalachian St. was in the top 25, and Arkansas was not.  When I made the change to emphasize quality wins more than avoiding losses, the two teams roughly switched spots.  I will show the top 25 under the new formula for last year below, but first I wanted to explain more how we got to this point.

The formula in the current form as represented on this site was not the first formula I used.  I had started with a fairly simple formula that was more similar to an RPI.  Whereas RPI formulas usually add things like winning percentage and opponents' winning percentage together, I found a way to make a strength of schedule based on opponents and opponents' opponents.  I then took that number and multiplied it by the team's winning percentage.  I thought this was preferable since if you don't actually beat anyone, you don't get any credit.  

When I began the ratings posted here, I took a further step as I realized that provided a team has a win, their score can be unfairly increased by losing to a good opponent with a good schedule.  This especially dawned on me after one of the games Troy played against an SEC opponent.  I'm not going to look up the game or the stats for that season, but a comparable example took place last season when Georgia played Georgia Southern.  Under the old formula, Georgia Southern would have improved from a rating of about 3.00 to about 3.36 despite losing.  That doesn't make any sense, obviously.

So my solution to this problem was to add another step in the process.  The number I had been using changed from an overall rating to an opponent rating.  So now when you lose, you have a number subtracted no matter what; and when you win, you have a number added no matter what.  Georgia Southern's rating as an opponent still improved, but things like this balance out when you play 12 games or more.  The teams that beat Georgia Southern got a boost of 0.012.  For context, the two closest top-10 teams in the final ratings last season were Houston and Oklahoma.  They were separated by 0.021.  As for Georgia Southern itself, their rating fell from about 0.046 to about 0.040, so the problem of a team like that improving with a loss was eliminated.

I'm not completely sure why this doesn't make a bigger difference, but the change I decided to make was instead of dividing the opponent scores by 30 in the event of a win, I'll only divide them by 10.  1/(opponent score x 2) is still what I subtracted for losses.  I guess the main reason is, since everyone has roughly the same number of games, every win you have is a loss you've avoided.  So if the formula is 80% based on rewarding teams for wins or 80% based on punishing teams for losses, the order of most teams will not change.

So this was the top 30 in the 2015 final ratings.  I'll show the changes below that.  Somehow, only a few teams experienced much movement.  I italicized the teams that moved up more than a single spot.  They were all teams with good schedules.  Arkansas was #1 in strength of schedule, USC was #9, Mississippi St. was #10, and Florida was #26.  North Carolina and Utah did not have amazing strengths of schedule, but North Carolina had a loss to #93 South Carolina and Utah had two losses outside the top 40 (#44 UCLA and #63 Arizona).  So this allows the wins by North Carolina and Utah (double digits in both cases) to overcome the bad losses.

1Alabama1.788745
2Clemson1.340525
3Michigan St.1.154173
4Ohio St.1.123617
5Stanford1.086094
6Oklahoma0.933149
7Houston0.912188
8Iowa0.830925
9Ole Miss0.790432
10TCU0.727804
11LSU0.696757
12Western Kentucky0.685069
13Michigan0.672603
14Notre Dame0.645402
15Northwestern0.632768
16Navy0.629937
17Utah0.618819
18Florida0.580560
19Toledo0.548158
20Oklahoma St.0.512307
21Appalachian St.0.469065
22Mississippi St.0.454009
23Baylor0.448700
24Georgia0.446010
25Wisconsin0.434243
26Oregon0.429406
27Tennessee0.406242
28North Carolina0.367099
29Florida St.0.312854
30Arkansas0.307026

New formula:
1 Alabama 1.835621
2 Clemson 1.381007
3 Michigan St. 1.298501
4 Stanford 1.222672
5 Ohio St. 1.182743
6 Oklahoma 1.110108
7 Houston 1.021402
8 Ole Miss 1.006611
9 Iowa 0.934286
10 Utah 0.887724
11 LSU 0.886032
12 Western Kentucky 0.864322
13 Michigan 0.859931
14 TCU 0.848495
15 Florida 0.829168
16 Northwestern 0.820768
17 Notre Dame 0.805415
18 Navy 0.748729
19 Toledo 0.743622
20 Mississippi St. 0.707822
21 Oklahoma St. 0.696839
22 Oregon 0.692704
23 Baylor 0.686210
24 North Carolina 0.670169
25 Arkansas 0.667304
26 Tennessee 0.647179
27 Florida St. 0.643034
28 Southern California 0.631457
29 Georgia 0.627629
30 Washington St. 0.622407
31 Appalachian St. 0.616337
32 Wisconsin 0.610187

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