March 9, 2011 - by David Hess
[This post is the first in a four part series on our ratings and models. Today we present a brief introduction to the ideas that form the basic foundation of our ratings. Part 2 contains more detailed descriptions of the differences between the various power ratings that we publish. Part 3 examines strengths and weaknesses of the system. And, Part 4 covers our statistical models that combine the ratings with outside information in order to make game winner, spread, totals, and money line predictions.]
The Intro Blurb
Our power ratings measure the relative performance of teams using nothing but objective, unbiased, quantitative data. Like the systems built by Ken Pomeroy and Jeff Sagarin, our ratings are 100% algorithmic and have no human bias inherent in their results. The only factors considered are win/loss results, margins of victory, game locations and dates, and schedule strength.
Now that that’s out of the way …
Several different versions of our college basketball power ratings appear on the site, but there are two basic ideas underpinning all of them.
The first is that in every game, teams are competing for a share of one “win credit.” In real life, only one team gets credit for a win; the other walks away with nothing. In most of our ratings, though, we effectively divide up a win so that the winner gets some or most of the credit for it, and the loser gets the remainder, with the exact portion depending on margin of victory.
We use various formulas to convert that final victory margin into win credits, which enables us to construct multiple ratings, each designed to analyze different aspects of team performance.
The second idea, common to many rating systems, is that we can take the ratings of two teams and subtract them to get a predicted margin of victory for a game. This predicted margin can then be converted into a win credit, just as the actual margin of victory is.
Combining the two above ideas, we calculate numerical ratings for all teams so that each team’s predicted number of win credits (considering the ratings of a team and adjusting for schedule strength) equals its actual earned win credits. How do we do this, you ask? Didn’t you read the section heading?
Actually, a computer program takes all of the results from the season, and our specified margin-of-victory-to-win-credits conversion formula, and assigns each team a rating. It then checks to see if the assigned ratings lead to predictions that match the actual results, in terms of win credits. If not, it adjusts the ratings slightly and checks again. It repeats this process until the predicted and actual results match as closely as possible.
Of course, there are a couple additional tweaks. We adjust for home court advantage, as any system worth a second look must do, by adding a few points to the rating of the home team. And we give slightly more weight to games that occurred recently, to get a better picture of how a team is playing right now. But the basic idea remains the same.
Different Strokes For Different Folks
One of the benefits of our rating system is its flexibility. The Predictive power ratings, Wins power ratings, and Overall power ratings are all built on the exact same framework; the only difference between them is the formula used to convert margin of victory into win credits.
The Wins power rating is winner-take-all: the winner gets 1 win credit, and the loser 0. In the Predictive power rating, the win credit is determined largely by what a final game score tells us about likely results of a rematch: a narrow win is worth barely more than 0.5 credits, while a large win is worth nearly a full credit. The Overall power rating strikes a balance by using values halfway between those of the Wins and Predictive ratings.
Which one you should look at depends on your intended purpose. Want to find a more advanced (and fair) replacement for the RPI, which rewards a team for winning games, but can’t be gamed by scheduling quirks? Check out the Wins rating. Want to know which team would be favored in a hypothetical matchup, and by how many? Check out the Predictive rating, and just subtract.
To Be Continued
A more in depth discussion of the differences between our various ratings will follow tomorrow. [Edit: Here it is: Defining Each Rating] In the meantime, please feel free to ask questions about win credits, the process of calculating the ratings, or any other general topics in the comments section below.
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