How the Rimbot Works

Basically, the Rimbot computes the allowed-factors and scored-factors for each team, along with allowed-per-game and scored-per-games.

The allowed-factor is that percentage of what a team's opponents typically score, that the team typically allows. Thus if a team's opponents scored on average 25 points per game, and the team allowed 20 points per game to each of them, its allowed-factor is 0.8. Scored factor is the same thing in reverse.

Thus, to compute the number of points you expect Team A to score on Team B, you take Team A's scored-per-game and multiply it by Team B's allowed-factor and average it with Team B's allowed-per-game multiplied by Team A's scored-factor.

You do the reverse for Team B, and you have a predicted score.

The weighted-average Rimbot ("WARimbot", NFL only) adds weights to individual games, so that more recent games are more valuable.

Now the key to the accuracy is the std. dev. If the std. dev. is high for any factor, it means that the team has been very inconsistent. What I've found is that as time goes by, this tends to normalize to about the 35%-40% range for NFL games. A lot of this is because the scoring in football is so coarse-grained. On the other hand, focusing purely on scoring focuses purely on what matters -- yards, rushing yards, defense, turnovers is all accounted for properly.

There are several valuable lessons from the whole thing:

1. Football is a sucker's bet. If you add the std. dev. to a predicted loser's allowed-factor and subtract the corresponding std. dev. from its opponents' scored-factor, representing a bad day for one team and a good day for the other, then you get an entirely likely and yet completely different outcome than what the Rimbot says should be typical.
2. The factors are great ways of measuring how good a team's offense and defense are, regardless of the opponent's quality. They are somewhat misleading in that defensive/special teams touchdowns are credited to the other factor -- e.g., both the allowed-factor and scored-factor for UT-Austin (in the NCAA Rimbot, for 2009) are getting a boost due to the offense giving up about half of the points the team has allowed all year and the defense and special teams scoring a significant percentage of the points all year. But ultimately, since the goal is focused on what the score is and NOT on how it's generated, this is exactly how it should be.
3. The NFL Rimbot works well to an extent because of parity in the league, the 16-game season, and the small total number of teams. There's a difference between the Saints and the Rams, to be sure, but generally they're not nearly as vast as the difference between, say, FBS and Division-III teams in the NCAA. In the NCAA, an FBS team that beats up on FCS patsies in its first few weeks will artificially improve its factors in a way that won't be accounted for, because the FCS teams will be mostly playing other FCS teams. This improves over time as the graph of who-played-whom gets bigger, but there are just too many teams and too few games for it to get really well-connected.
4. The Rimbot doesn't account for injured players at all, because the essential philosophy behind it is that there is no one player so key to the game of football that he can substantively alter the outcome of games. If Tennessee is 0-6 with Kerry Collins (as they are as of this writing) and if Vince Young starts for the rest of the season, even if he were the God-given miracle of football we Longhorn fans think he is, he is not going to magically lead the Titans to a 10-6 record. It simply won't happen. For one thing, he doesn't play defense...