Pomeroy Ratings (thing)
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A symphony of predictive power, the Pomeroy ratings are currently my favorite ratings system for [college basketball].
The root of Pomeroy's system is the [Pythagorean expectation], a value invented by [Sabermetrics|Sabermetricians] to predict the winning percentage of a [baseball] team based on its number of runs scored and runs allowed.
Win% = RS2 / (RS2 + RA2)
How does this formula translate into [basketball] terms? Simply using points scored and points allowed won't cut the mustard, because comparing point amounts across teams means almost nothing. For one thing, basketball is a timed game, and [time of possession] varies from team to team regardless of skill level. Time of possession is more or less irrelevant to how good a team is at winning basketball games, but it does affect point totals. "But wait," you say, "surely a defense that lets the other team hold onto the ball forever is worse than one that doesn't!" To which I reply, "indeed, unless the other team plays its best basketball in a [half-court set], and every time they settle in against that fast-paced defense they score. Or if their defense is awesome but their offense kinda sucks. Or if the other team's defense sucks." In truth, points scored and points allowed are often correlated (independent of skill level) because teams often play to the level of their competition. A better way to look at how good a team is at playing basketball than absolute points is to average their number of points scored per possession. Pomeroy, to give his numbers a little extra punch, uses points scored per 100 possessions, a value he calls "[offensive efficiency]." [Defensive efficiency] is defined similarly, as a team's number of points allowed per 100 possessions.
To account for fluctuations in the entire basketball landscape over the years, Pomeroy adjusts offensive and defensive efficiencies based on the national average. The adjustment also takes into account opponents' efficiencies, to account for [strength of schedule]. A team receives efficiency values for each game played, and these values are weight-averaged (with greater weight given to more recent games) to give overall offensive and defensive efficiencies. These are plugged into the Pythagorean formula above, using an exponent of 11.5 rather than 2 (for predictive reasons), to give the team's overall Pythagorean value, which is not quite its predicted win percentage.
The predicted win percentage is actually closer to .500 than the raw Pythagorean value by an amount related to the team's "Consistency" value, the standard deviation of the team's efficiency differentials for all games played. A higher Consistency value means the team is less consistent. More inconsistent teams, the logic goes, will have win percentages more close to .500 due to their wild but equally up and down fluctuations in play. Interestingly, last year [Kentucky] was the 19th most inconsistent team in college basketball, with a nauseating differential standard deviation of 26.1! And sure enough, their actual win percentage (58%) was much closer to .500 than their adjusted Pythagorean at the end of the season (87%).
One of the great advantages of Pomeroy's system is that predicting the winner of any given basketball game, even across years, is quite easy. A [quick-and-dirty] comparison of [offense|offensive] and [defense|defensive] efficiencies is illuminating, but he computes a variety of other predictive parameters as well. His "[Luck]" value is simply the difference between a team's predicted win percentage and its actual win percentage. "[Tempo]" is simply the number of possessions a team gets per 40 minutes, and figures into predictions of how many points a team will score in an upcoming game. He even correlates efficiency values with more real-life stats like effective [field-goal percentage] (a three-pointer counts as 1.5 FG's) and [turnover] percentage (TO's per possession), in order to show what happens to a team in real life as its efficiencies vary.
And best of all, all of these stats are available for all 344 NCAA Div-I teams! Conference ratings are also available.