## Notes on My RPI Calculations

### The Basic Formula

A team's RPI is a sum of three values: 25% of the team's winning percentage, 50% of its
opponents' average winning percentage (strength of schedule), and 25% of its opponents'
opponents' average winning percentage (opponents' strength of schedule). Only results
against teams which are in NCAA Division I are counted in all of these winning percentages.
For example, say that a team has

- a winning percentage of 64%
- an opponents' winning percentage of 58%
- an opponents' opponents' winning percentage of 52%

Then its RPI is (.25 * .64) + (.5 * 58) + (.25 * .52) = .570 (a typical bubble team)
### Some Adjustments to the Basic Formula

In calculating a team's RPI, the win-loss records of its opponents (and hence their winning
percentages) do not include the games against the original team. For example, if a team is
2-0, and has played opponents who are 2-3 and 2-1, then the opponents' records are adjusted
to 2-2 and 2-0 in order to calculate their winning percentages.
If this were not done, teams that won a lot would suffer a penalty in a lower opponents' winning percentage.

A similar adjustment used to be made to remove each team's wins and losses from its opponents'
opponents' records before calculating its opponents' opponents' winning percentage. This adjustment has
been dropped beginning with the 2000-2001 season

### How I Calculate Opponents' Winning Percentages

(and Opponents' Opponents' Winning Percentages)

There are a couple of ways to calculate opponents' winning percentages. We can either (A)
add up the wins and losses of all opponents (after adjustments) and calculate the
percentage of wins, or (B) calculate each opponents' winning percentage separately and
then average the results.
To illustrate, I'll use the example above -- a 2-0 team with opponents who have 2-3
and 2-1 records (2-2 and 2-0 adjusted!). Then we get the following results:

- Method A: 4 total wins in 6 total games, so 4/6 = .667 opponents' winning pct.
- Method B: first team has .5 winning pct., second team 1.0, averaging we get (1.0 + 0.5) / 2 = .75 opponents' winning pct.

As you can see, it makes a difference (though with more games, it is not this dramatic).
Method A gives more influence to opponents who have played more games; Method B gives each
opponent equal weight. I use Method B, because I believe it makes sense for each opponent
to have equal weight in determining the opponents' winning percentage.
The same issue comes up in calculating opponents' opponents' winning percentages, and I
have resolved it in the same way.