Basketball Formula
The current and commonly used formula for determining the RPI of a college basketball team at any given time is as follows.
RPI = (WP * 0.25) + (OWP * 0.50) + (OOWP * 0.25)
where WP is Winning Percentage, OWP is Opponents' Winning Percentage and OOWP is Opponents' Opponents' Winning Percentage.
The WP is calculated by taking a team's wins divided by the number of games it has played (i.e. wins plus losses).
For Division 1 NCAA Men's basketball, the WP factor of the RPI was updated in 2004 to account for differences in home, away, and neutral games. A home win now counts as 0.6 win, while a road win counts as 1.4 wins. Inversely, a home loss equals 1.4 losses, while a road loss counts as 0.6 loss. A neutral game counts as 1 win or 1 loss. This change was based on statistical data that consistently showed home teams in Division I basketball winning about two-thirds of the time. Note that this location adjustment applies only to the WP factor and not the OWP and OOWP factors. Only games against Division 1 teams are included for all RPI factors. As an example, if a team loses to Syracuse at home, beats them away, and then loses to Cincinnati away, their record would be 1-2. Considering the weighted aspect of the WP, their winning percentage is 1.4 / (1.4 + 1.4 + 0.6) = 0.4117
The OWP is calculated by taking the average of the WP's for each of the team's opponents with the requirement that all games against the team in question are removed from the calculation. Continuing from the example above, assume Syracuse has played one other game and lost, while Cincinnati has played two other teams and won. The team in question has played Syracuse twice and therefore must be counted twice. Thus the OWP of the team is (0/1 + 0/1 + 2/2)/ 3 (number of opponents - Syracuse, Syracuse, Cincinnati). OWP = 0.3333
The OOWP is calculated by taking the average of each Opponent's OWP. Note that the team in question is part of the team's OOWP. In fact, the most re-occurring opponent of your opponents is team in question.
Continuing the example above, a team has played Syracuse twice and Cincinnati once. Syracuse has played one other game and lost, while Cincinnati has played two other games and won. Next, for simplicity, assume none of the unnamed teams has played any other games.
The OOWP is calculated as (Syracuse's OWP + Syracuse's OWP + Cincinnati's OWP ) / 3.
Syracuse has played and beat the team in question (which, excluding the games against Syracuse, only lost to Cincinnati), lost to the team in question (excluding Syracuse, only lost to Cincinnati, and lost one other game (excluding Syracuse, this team has no WP). Syracuse's OWP is (0/1 + 0/1) / 2 = 0.0000.
Cincinnati has played the team in question (excluding Cincinnati, they went 1-1 vs. Syracuse) and won versus two other opponents each of which have no WP when games versus Cincinnati are excluded. Cincinnati's OWP is (1/2) / 1 = 0.5000.
For the team in question, the OOWP is thus (0.0000 + 0.0000 + 0.5000) / 3 = 0.1667
For the team in question, the RPI can now be calculated:
RPI = (WP * 0.25) + (OWP * 0.50) + (OOWP * 0.25)
Plugging in numbers from the above example gives you
RPI = (0.4117 * 0.25) + (0.3333 * 0.50) + (0.1667 * 0.25) = 0.3113
Read more about this topic: Ratings Percentage Index
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