# Ratings Percentage Index

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RPI (ratings percentage index) is a rating that applies to a team's record and schedule such that the stronger the opponents,
the higher the RPI rating. Conversely, the weaker the opponents, the lower the RPI rating. In order to tabulate an RPI rating,
each opponent's strength has to be evaluated by examining its W-L record as well as the W-L record of its opponents.

RPI =  (1/4 * team's record) + (1/2 * opponents' record) + (1/4 * opponents' opponents' record)

Records are in the usual form of a win proportion: wins / (wins + losses). Ties are treated as 1/2 win +
1/2 loss. Here is an example of the computation:

A team has played 8 of its 12 games through the season. The team's record is 7 wins and 1 loss or 0.875.

The records for the opponents are as follows:

Team A        5   3   .625
Team B        4   3   .571
Team C        2   5   .286
Team D        3   4   .428
Team E        7   1   .875
Team F        2   5   .286
Team G        2   5   .286
Team H        9   0  1.000
--  --
34  26   .545

Note that the .545 is not based on 34/60 (.567) but on the average of each opponent's percentage in the
right-hand column.

The records for each opponent's opponents are

Team A       42  18   .750  - based on average of all of a team's opponents
Team B       22  24   .502    and not based on total wins / total games
Team C       18  18   .483
Team D       32  22   .600
Team E       30  31   .530

Team F       29  15   .624
Team G       37  16   .645
Team H       39  27   .615
---  --
249 171   .594

Note that the .594 opponent-opponent figure above is not based on 249/(249+171) but rather is the average
of the percentages in the last column.

The RPI for our example team is then computed as follows:

RPI = (0.25 * 0.875) + (0.50 * 0.545) + (0.25 * 0.594) = 0.600

```