I've gotten a lot of hits on my percentage-to-win projections I posted for various teams, so I thought I should explain how they work. It's an interesting system, I think, though it's definitely meant to be used to look at a cumulative *range* of games, moreso than individual games. To put the numbers in perspective (and explain why home field advantage seems to carry so much weight), here's how it works:

First step: involves the creation of a score-margin-based power rating, such as this one.

Then, when two teams are compared, each game by each team is assigned a score, using the power rating. For example, if USC's rating is, say, 20, and you beat USC by 7, the rating for that game is 27.

That gives two teams, each with a series of rated games. Now each combination of games is compared. If for example, Team A has 7 games and Team B has 8 games, that gives 56 pair-comparisons.

The percentage-to-win reflects the number of comparisons in which Team A's performance rates higher than Team B's. What the game performance ratings reflect is that team on a given day; with 7 or 8 games, that represents the full span of quality we've seen from that team to date. We assume that next game, any version of Team A might show up, and any version we've seen from Team B might also show up. By comparing all the possible combinations, we come up with percentage odds that one team will beat the other.

This of course doesn't account for the possibility that a team may do the best it's done all year...or the worst. It's based solely on what they've shown so far, the range that has existed. Therefore, it's possible to score 100%, or 0%, over another team. If every game Hawaii has played rates better than every game New Mexico State has played, then the system will yield a result of 100% for the odds. Clearly this is never the case, but it makes sense within this system, and only happens to team pairings with which most people would say, yes, that team is certain to win.

Home field advantage is programmed in by adding to each of the home team's games the home field advantage determined by the power rating's converged scores (normally around 3 points). The reason it seemed overdone on my previous results is because...it was. I had previously also subtracted HFA from the visiting team, so it was being double-counted. This is called "what happens when you get an idea at 3am and program it right then." The feedback I got about it here and on message boards made me look at it again with awake eyes and see the mistake.

Now, when I update the numbers, HFA should look like less of a factor. It still will be important, however, since this system produces results that are "flatter", i.e. less bell-curved or distributed around 50%, than most would assign to a series of A or B choices. Bumping the ratings around slightly can shift several game comparisons over to a win or loss pretty easily.

I've used this system for college basketball before, and just adapted it for football, even though it's more suited to basketball than football for a number of reasons.

One, there are far more games in the basketball season; more games = more comparisons. For example, at this point in the basketball season, the average team would have played 20 games or so, meaning roughly 400 pairwise comparisons rather than 64 average for two football teams. More comparisons equals more exact projections.

Two, there would still be 10 games left per team in basketball, which lends itself to this kind of analysis better. When there are only a few football games left, you might as well look at each one separately, make a judgement and forget the numbers. So with this system, just at the point where there are enough comparisons available to make some reliable forecasts, the number of games left isn't enough to make the forecast meaningful. Who wants to hear that their team is projected to be 2.5-0.5 in their last 3 games?

**UPDATE**: Lately I've been using an improved system for football, one that separates out a team's offensive and defensive performances. These are then re-combined to make X-squared game performance possibilities. So if a team has played 8 games, instead of 8 game-performances there are 64 possible game-performances that a team is deemed capable of. If two teams have each played 8 games, then instead of 64 possible outcomes, there are 64x64 or 4,096 possible game outcomes that are used to form the percentages.

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