Q: What are the most important factors in rating sports teams?

A: Who they play and how well they perform.

These are the only factors I use in my rankings, of which there are two types.
Power Rankings assign numbers to teams in such a way that subtracting two numbers gives an estimate of the outcome of a game between the two teams.
These numbers are calculated using a recursive form of regression, with a particular team's ranking based on the rankings of teams it has played in the past and the margins of victory in each of those games. Since the opponents' rankings are also being calculated at the same time (using a matrix method), recursion is needed, with the calculations being done a certain number of steps until the difference between successive calculations falls below a chosen threshold. To help decrease the effects of large margins of victory, what is actually used is a "tranquilized" value that is close to the margin of victory when small, then only slowly increasing for larger values. These values are also adjusted using home/away factors, which are also calculated based on past performance. Finally, a weighting method is used so that recent games are more heavily weighted than earlier games (thus I refer to this method as regression with a fading memory).
Since power rankings are computed using past game outcomes, the result is these numbers can then also be used to predict future game outcomes. Thus, my power rankings are both predictive and retroactive. However, when posting these rankings I receive numerous complaints, because they do not always reward teams who have performed solidly without any huge victories over teams regarded as more powerful.
Thus, a few years ago I began computing Merit Rankings, which are based solely on win/loss percentages.
These are calculated in an RPI fashion, with different weights given to a team's W/L record, the records of that team's opponents, and the records of the opponents' opponents. Again, a fading memory is used so that more recent games count more than earlier games. Merit rankings are obviously non-predictive in nature, since margin of victory is not used in their calculation.
One final thing to note is that another weight factor is needed to distinguish between games played against I-A teams, I-AA teams, and lower division teams. This type of weighting method is used in both types of rankings.

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