The Ratings Percentage Index (RPI) is a criterion commonly used by the NCAA to seed tournaments. It is a critical part of the Division I hockey selection critiera. It measures the strength of a team on the basis of its winning percentage and strength of schedule (determined by opponents' winning percentages).
The RPI is always calculated from three components: win percentage (winper), opponents' win percentage (oper), and opponents' opponents win percentage (ooper). For Division I college hockey, those components are weighted .25 * winper, .21 * oper%, and .54 * ooper%. (Note: until 2006 the weightings were .25/.5/.25; in 2006 new weightings were chosen that would have minimized the number of "negative" games, those in which a win hurts a team's RPI, over the previous two seasons).
Win percentage is ((wins + .5 * ties) / total games played), including only NCAA games.
Opponents' win percentage is the average winning percentage of a team's opponents. To calculate it, divide the sum of all opponents' win percentages, excluding those games played against the team for which RPI is being calculated, by the total number of opponents.
Opponents' opponents' win percentage is the average winning percentage of a team's opponents' opponents. To calculate it, divide the sum of the opponents' win percentage for each opponents (as calculated above) by the total number of opponents.
OK, three games have been played: Hobbits defeat Orcs, Elves defeat Hobbits, and Elves defeat Orcs.
|Elves (2-0)||Hobbits (1-1)||Orcs (0-2)|
In the example above, intuition tells you that each team should have the same "strength of schedule" measurement because they have played a full round-robin season. However, if you simply calculate the average opponents' winning percentage for each team, you get different results.
|Team||Opponents||Average Opponents' win percentage|
|Elves||Hobbits & Orcs||(0.500 + 0.000) / 2||0.250|
|Hobbits||Elves & Orcs||(1.000 + 0.000) / 2||0.500|
|Orcs||Elves & Hobbits||(1.000 + 0.500) / 2||0.750|
RPI addresses that problem by removing opponents' games against a team when calculating the RPI for that team. Excluding the game against the Elves, the Hobbits are 1-0 (1.000), having defeated the Orcs. Excluding the game against the Elves, the Orcs are 0-1 (0.000), having lost to the Hobbits. Therefore, the Elves' opponents' win percentage, as RPI calculates it, is 0.500 ((1.000 + 0.000) / 2).
Beginning in the 2002-03 season, the NCAA made an adjustment to RPI to try to reward "quality wins". A small bonus is added into the RPI score for a team for a win against a non-conference quality opponent (defined as currently being in the top 15 in RPI) at the opponent's home. (Until 2006, differing values of bonus points were also awarded for wins against non-conference quality opponents at home and at neutral sites).
Unfortunately, the NCAA has chosen not to reveal the exact bonuses given for quality wins, but the calculation of RPI on this site includes an assumption that fits closely with past seedings. Readers should keep in mind that the bonus can shift particularly closely rated teams a couple of positions in ranking, potentially affecting both what teams make the tournament and their seedings. US College Hockey Online has a "bonus guesser" tool that you can use to determine what changes would occur to the ranking given hypothetical bonus amounts
Beginning in the 2006-07 season, the NCAA made an adjustment to RPI to exclude from each team's RPI calculation any wins that negatively impact its RPI rating. RPI's dependence on strength of schedule (75% of the rating is derived from opponents' and opponents' opponents' win percentages) means that defeating lower-rated opponents could actually lower a team's RPI. This is an intentional feature of the rating -- a .500 team that has played no one other than top 10 opponents is likely better than a .900 team that has played only bottom 10 opponents.
In 2003-04, the NCAA began excluding wins in conference tournaments from harming teams' RPIs because participation in conference tournaments was mandatory and often forced top teams to play bottom teams. In 2006-07, simultaneous with reweighting RPI to dramatically reduce the number of "negative wins" in the regular season, the NCAA expanded that to exclude any win which would result in a lower RPI score.