# Explanation of Wobus RPI Calculation

 In 2006 I read online that the NCAA some time ago begain incorporating home/away information into their calculations, counting "away wins" more than "home wins" and "away losses" less than "home losses". I have not adjusted my calculations to follow. If this is true, then in yet another respect, this calculation differs from the NCAA's. These calculations match most closely the RPI used by the NCAA some years ago.

This is my calculation of ratings using methods publicized on the Internet about the NCAA's RPI and SOS formulas. While my goal is to reproduce the formula, it is not to reproduce the NCAA's calculations and definitely not to predict whom the NCAA will choose for tournaments based upon their RPI calculations. Rather it is to see what the RPI formula produces, for comparison with other rating and ranking methods and efforts. For example, I continue calculating and posting what this formula produces even including the NCAA tournament games, whereas my understanding of the NCAA's use of their formula is as input regarding their selection of teams for their tournament, a purpose which is achieved when the tournament commences.

My calculations will undoubtedly diverge from what the NCAA produces and uses. Among the reasons are: (1) I cannot vouch for the game wins/losses data that I use to perform the calculations. While my goal is to use correct data, I do not check newspapers, etc. and verify it; (2) I do not know all the calculations and adjustments the NCAA uses, only what I've been able to find mentioned online; (3) While my goal is to do the calculations as described below, I may have made mistakes.

The RPI ("Rating Percentage Index" or "Ratings Percentage Index") assigns a numerical rating to each of a group of competing teams. A ranking can be derived from the rating by ranking the team with the highest RPI first, the next highest second, and so forth. The NCAA uses the RPI to help select and seed teams for post-season play in a number of sports, but not Division I-A football. The formula as used by the NCAA probably varies somewhat between sports.

I use a formula reputed to be used for basketball. The basic formula for a team is the sum of

• Its winning percentage (as a decimal) times .25
• Its opponents' winning percentage times .50
• Its opponents' opponents' winning percentage times .25.
The result is a decimal fraction between 0 and 1, the higher the number, the stronger the team is rated. In all cases, only the games and opponents within the group being rated are counted. This is the publicized formula but the NCAA is reputed to make a private adjustment to the results.

As I tried these calculations I ran into questions as to how the averaging of opponents' winning percentage is done. I looked for answers on the Internet and use those that appear most informed but have found nothing official. Here is what I do--I believe it matches the NCAA's calculations (other than their secret adjustments) but I am not certain. When rating a team:

• Each opponent's winning percentage is calculated without including that opponent's game(s) with the team being rated.
• The opponents' winning percentages are averaged and the result comprises the second item of the basic formula.
• If the team plays the opponent two or more times, then that opponent's winning percentage is included in the average the same as the number of games they played the team.
• The opponents' opponents' winning percentage is calculated in exactly as above, but from the opponent's point of view. One such number (as described above) is produced for each of the initial team's opponents, and the resulting numbers are averaged. (In this case, it is the original team's opponents that are "skipped"; games with the original team are included in the calculations.)
• Once again, as the average of these opponents' opponents' average winning percentages is calculated, if the team in question plays that opponent two or more times, then that opponents "average opponents' winning percentage" is included in the team's average that number of times.

My calculations are not an attempt to duplicate the NCAA's efforts. Instead I provide them to offer the chance to compare the formula's evaluation with other rating and ranking systems. To this end, I continue calculating them as the post season progresses and I apply them to football.