Unlike the other ratings on my site, the RPI formulas and hockey pairwise rankings are not my own. They are used in real-life tournament selection processes, and thus are important if inaccurate. The football RPI, improved RPI, and reinvented RPI, however, are my own inventions and credit must be given me if they are used.

Contents of this page:

RPI Formulas

A key rating used in all college sports is the RPI (ratings percentage index). The RPI consists of four factors:

   TWP = (wins + 1/2 ties) / (# games)
   OWP = the average of a team's opponents' TWP values
   OOWP = the average of a team's opponents' OWP values
   ADJ = adjustments for quality wins, bad losses, etc.

Note that the OWP average does not count games played between the team and its opponents. Also, if an opponent is played twice, its WP is averaged in twice. Only games against division I opponents are counted.

The first three components are combined into a single value with different weights depending on the sport:

   RPI = 0.25*TWP + 0.50*OWP + 0.25*OOWP (baseball, basketball, hockey)
   RPI = 0.334*TWP + 0.444*OWP + 0.222*OOWP (football)

Note that RPI isn't officially used in football; however the "loss", "schedule strength", and "quality win" portions of the BCS formaula map extremely well into the RPI formalism. In BCS terms, a team's football RPI ranking is about 1/7 as important as its ranking in the poll or computer averages, meaning that one can compute a "poor-man's BCS" by adding the poll average, computer average, and 1/7 of the RPI rank. The football RPI formula presented here is thus my own invention; the others are created by the NCAA.

The final element of the formula is adjustments that are added, which vary from sport to sport. The real adjustments used in college basketball and baseball are secret; the values I provide here are estimates.

Basketball:

Baseball:


Overall, the adjustment made to a baseball team's RPI is about twice that made to a basketball team's RPI. The larger bonuses are offset by the fact that bonuses are only given for road wins, but baseball teams play about twice as many games and thus have twice as many chances to pick up bonuses.

Football:


Again, the "football RPI" is my own invention. The adjustments here are the quality win component. It is clear why the quality win component is so controversial. A typical bonus of 0.01 points for beating a lower top-10 team would be the equivalent of a basketball team winning 11 games over a top-25 team at a neutral site. So while the bonus achievable in one football game is 25 times that achievable in one basketball game, the overall effect (considering that bonuses are only given out for top-10 wins and that the football season is 11 games instead of about 30) of the football quality win component is comparable to that in the other sports.

The Improved RPI

There are a few obvious shortcomings to the RPI. One is that it doesn't consider opponents' opponents' opponents or beyond. On the surface, this is a huge shortcoming since it appears to make the assumption that every team's opponents' opponents' opponents are of equal ability. This is not actually the case; one can statistically estimate the more distant relationships from just the opponents' opponents win percentage. Of course, it is better to actually compute the terms, which is what is done in my improved RPI.

The improved RPI is a self-consistent RPI-like rating scheme. There are two basic principles involved: (1) all games count equally [RPI-like] and (2) the rating of a team that goes 0.500 should equal the average of its opponents ratings [self-consistent]. I am thus looking for a solution where a team's rating is given by:

   Rating = (WP-0.5) + average of opponents' ratings.

Since the ratings are both input and output data in this system, the solution must run iteratively until convergence is reached (i.e. the result from one iteration is indistinguishable from that from the next).

In order to produce something resembling an RPI rating, the final team ratings should be multiplied by 0.25 (basketball and baseball), 0.35 (hockey), or 0.334 (football) and increased by 0.5.

A second problem is that, aside from the bonuses, the RPI makes no distinction between home and road games. Since many prominent college teams are known for playing most of their non-conference games at home, this unfairly boosts their RPI. The obvious and simple fix is to add another bonus to the RPI:

   HB = X * (#road games - #home games) / (# games),

where X is between 0.01 and 0.03, depending on the sport.

If you do not already have a home field advantage factor calculated, you should first calculate the team ratings with no home field advantage. Then, using all non-neutral site game, take the average of:

  (road team rating) - (home team rating) + (outcome),

where outcome is +0.5 for a home win, 0 for a tie, or -0.5 for a road win. Multiply this by either 0.25 (basketball or baseball), 0.334 (football), or 0.35 (hockey) to determine the home advantage factor.

A final problem in the RPI is that, in the computation of schedule strength, a team will be counted as a tougher opponent to somebody that beat it than it will to somebody that it beat because the games between the teams are subtracted. This isn't a huge "problem"; it just means that a team's record counts more than face value in the RPI. In football, where a team's games count about 1/11 of its opponents records, the team's record thus counts about 37.4% of its RPI instead of 33.4%. It does become problematic when the number of games played against each opponent is not constant, however. A football team that plays one opponent twice accounts for 2/12 of that opponents' record, which is of course added twice into the OWP component for an increase of a factor of four. In other words, a game played against a team that you play twice is more important than a game played against a team you play only once. If you play somebody three times, each game is even more important in your RPI. I'm sure that this is unintentional on the part of those who invented the BCS. The obvious solution is to not subtract head-to-head gams from the opponents' record; ironically this would greatly simplify the RPI calculation. At any rate, this problem is fixed by the improved RPI's use of a self-consistent solution.

The "improved" RPI rating is thus the best one can do with this sort of rating system. To summarize, it differs from the real RPI equations in five important ways: