# The Ideas Behind My Ratings

I have been using this system since 1998 to rate college football teams. My goal is to objectively rank the Division I-A football teams based only on their performance thus far this year. Since I only use wins and losses from the current season, early ratings are pretty erratic, but as more games get played they soon settle down and start making more sense. At no point are these ratings meant to predict the outcome of future games. And mid season results are not intended to predict where the teams will end up. It simply rates every team's performance so far.

Special thanks to Peter R. Wolfe for collecting and posting the results of all the college football games. This is where I get my raw data from.

## My Philosophy

I wanted to create a totally objective way of rating college football teams. This meant that I didn't want to allow any arbitrary personal opinions about how good a team is, how strong a conference is, what constitutes a "big" win, or what counts as a strong schedule. Since I believe that every team is a new team at the beginning of the season I didn't want my formula to include any weight for last year's performance, a school's overall history, or a coach's past performance. Objectivity is important because no personal rankings, however well intentioned, can be perfectly fair. This is especially true in college football where most fans (myself in the extreme) are partial to their school and conference.

I also don't believe that running up the score proves a damn thing. So this is another "A win is a win is a win" rating. Scores don't go into the formula at all, just a 1 for a win and a 0 for a loss.

But a school's record alone doesn't tell the whole story. The strength of the schedule that they've played must be counted as well. I think pretty much everybody agrees with this. The trick is just how to figure out the strength of a schedule and how to count it into a rating. I've played around with all sorts of ideas but most of them turned out to have some glaring deficiency until I came up with...

## The Formula

I like this formula because it is really simple but has produced excellent results. Every team receives a rating between 0 and 1 (1 being perfect). It is simply a weighted average of their record and their strength of schedule. A team's record is expressed as win percent (games won divided by games played). Their strength of schedule is computed by taking the average win percent of the school's opponents and the average win percent of the school's opponents' opponents.

I wanted strength of schedule to be two parts opponents' win percent and one part opponents' opponents' win percent. But I found that the range of numbers that appeared for opponents' records was much more spread out than the range of numbers for opponents' opponents' records (opponents' opponents' records tended to be closer to 50%). Specifically, in studying the numbers from past seasons I found that the standard deviation of opponents' win percent was about twice that for opponents' opponents' win percent. So it turns out that these numbers naturally form a 2:1 ratio in their significance and I can just average the two numbers to get strength of schedule.

To balance record and strength of schedule I settled on a formula of three parts record to one part schedule strength. Records obviously range all the way from 1.0 (perfect season) to 0.0 (winless record), but there tends to be a lot less variation in schedule strength. Again looking at the numbers from past seasons I found that record had six times the standard deviation of schedule strength. So to get the 3:1 ratio I want I give strength of schedule twice the weight of record. Remember, the strength of schedule numbers don't vary nearly as much as the records do, so the result is that record accounts for about 75% of a school's rating and schedule strength for about 25%.

So the formula goes like this, let W be team A's win%, OW be A's opponents'
average win%, and OOW be A's opponents' opponents' average win%. The rating for
team A is:

(W + 2*( schedule strength ) ) /3

or

(W + 2*( (OW + OOW)/2 ) ) /3

which is the same as

(W + OW + OOW) /3

It is important to note that I am using the average of win percents not the count of all the opponents' wins divided by the count of all their games. For example, imagine team A has played both team B and team C. B's record is 1-0 and C's record is 1-4. I do not add up the wins (2) divide by the games played (6) and come up with 1/3. I do average 1.00 and 0.20 and come up with 60%.

Teams are ranked according to their rating, highest to lowest.

I've compiled a step by step example of calculating my ratings if you'd like further explanation.

If you're still reading at this point you might be thinking, "But wait a minute, if you just add in the strength of schedule you are rewarding a team for playing tough opponents even if they never win a game." This is true. In the extreme case a school could play the mother of all schedules, lose all of their games, and still have a rating of 61%. However, since opponent record will show less deviation than record, and opponents' opponent record even less, the impact of that part of the rating is somewhat diminished. The result is that a school's record is clearly the dominant factor in determining their rating. The strength of schedule factor very effectively serves to elevate teams who have played an especially tough schedule and lower teams that have played an especially weak one, as well as sort out teams with the same record.

If you're really paying attention you will notice that, as a rule, every team is it's own opponents' opponent. It sill makes sense to count it, though, because if A plays B and you are figuring out A's strength of schedule you want to determine how good a team B is. To do that you need to know who B has played, so you end up looking back at A. Besides, it adds a little extra weight to a team's own record which I think is OK.

I rate only the Division I-A schools. Games played against Division I-AA opponents are counted as a generic I-AA team with a record of 3-7 and an opponents' average record of 4-6. These numbers are chosen to lower the strength of schedule of a team playing below its division, but not drastically. The numbers represent a strength of schedule just lower than the worst numbers from last year. If a Division I-A team plays a Division II team they should be ashamed of themselves, and it will count against them as a team with a record of 0 and an opponents' record of 0.

Please understand that early in the season the rating for a team can move wildly up and down. But as the season progresses it should settle down and become more accurate (hopefully).

Here's the standard disclaimer: These ratings are not meant to predict the winners of future games, just rate team's performances so far. It is certainly not meant to predict the spread or scores of a game. I know of no correlation whatsoever between my rating and scores of individual games, especially since I don't even count scores in my formula. I do not recommend or condone using these ratings for the purpose of gambling. Sports betting is evil. Blah blah blah.