RPI: Formula

Updated September 2025

WHAT IS THE RPI?

The Rating Percentage Index is a mathematical system for rating sports teams.  The NCAA began developing the RPI in the late 1970s for use in selecting teams to participate in the NCAA Division I Men's Basketball Tournament.  The first actual use of the RPI for men's basketball was in 1982.  Over time, the NCAA has expanded use of the RPI to other sports, with the following Division I sports now using it: men's and women's soccer, men's and women's volleyball, women's field hockey, men's ice hockey, men's and women's lacrosse, baseball, softball, and women's water polo.  The NCAA used the RPI for women's ice hockey for a time, but recently has changed to the NCI, which is different. Interestingly, the NCAA stopped using the RPI for men's basketball beginning with the 2018-19 season, replacing it with the  NET system.  In addition, it now uses that system for women's basketball.  I do not know whether the NCAA will make a comparable change for other sports at some point in the future.

The NCAA first used the RPI for Division I women's soccer in 1997.

The way in which the NCAA computes the RPI varies some from sport to sport.  The central structure of the RPI, however, is the same for all sports.

This website deals only with the RPI as used for Division I women's soccer.

COMPUTING THE RPI

The RPI consists of three Elements, plus bonus and penalty adjustments.  It considers only games against Division I opponents.  Below, "Team A" refers to the team whose RPI is being computed.

Element 1:  Team's Winning Percentage

Element 1 of the RPI compares the number of games Team A has won and tied to the total games Team A has played.  For purposes of this Element, the formula through 2023 treated a tie as half a win and half a loss.  In 2024, however, the Women's Soccer Committee changed this to one-third of a win and two-thirds of a loss.  The current formula for Element 1 is:

(W + 1/3T)/((W + 1/2T) + (L + 1/2T))

which simplifies to

(W + 1/2T)/(W + L + T)

In this formula, W is Team A's wins; T is Team A's ties; and L is Team A's losses.  Games determined by penalty kicks are considered ties.

So, if Team A has a record of 8 wins, 8 losses, and 4 ties, Element 1 of its RPI is

(8 + (1/3 x 4))/(8 + 8 + 4) = (8 + 1 1/3)/20 = 9 1/3/20 = .4867

Element 1 tells only Team A's wins and ties compared to its games played.  It tells nothing about the strength of Team A's opponents.  Thus, as an example, Element 1 for a team with an 8-8-4 record against the top 20 Division I teams will be .4867 and Element 1 for a team with an identical record against the bottom 20 Division I teams also will be .4867.

Element 2: Opponents' Average Winning Percentage (Against Other Teams)

Element 2 measures a team's opponents'  average winning percentage (against teams other than Team A).  The NCAA's stated purpose of Element 2, combined with Element 3, is to measure the strength of schedule against which Team A achieved its Element 1 Winning Percentage.

To determine Team A's opponents' average winning percentage, the NCAA first computes, for each of Team A's opponents, the opponent's wins and ties as compared to the opponent's total games played, in the same way it does the calculation for Team A's Element 1, except that an opponents' winning percentage values ties as half of a win rather than a third.  The only other difference is that the NCAA excludes the opponent's games against Team A itself.

So, if Team A played an opponent once and won the game, the portion of Element 2 of Team A's RPI attributable to that opponent is determined by the following formula, in which O stands for "Opponent's":

(OW + 1/2OT)/(OW + (OL - 1) + OT)

Note that in the denominator, 1 is subtracted from the Opponent's losses.  This is because the Opponent lost to Team A, and by rule the result of the Opponent against Team A is not to be considered in determining that Opponent's contribution to Element 2 of Team A's RPI.

Likewise, if Team A tied the Opponent, the portion of Element 2 attributable to that Opponent is determined by the following formula:

(OW + 1/2(OT - 1))/(OW + OL + (OT - 1))

And, if Team A lost to the Opponent, the portion of Element 2 attributable to that Opponent is:

((OW - 1) + 1/2OT)/((OW - 1) + OL + OT)

Once the NCAA does this calculation for each opponent, it then computes the average of the numbers so computed for all of Team A's opponents.  This average is Element 2 of Team A's RPI.

Note that the NCAA does not simply add up the different opponents' wins, losses, and ties and then do a single calculation of wins and ties in relation to games played.  Rather, it does a calculation for each opponent and then averages the results.  The NCAA uses this averaging method to take into account the fact that different opponents play different numbers of games: By averaging, the NCAA assures that each opponent's contribution to Team A's Element 2 is weighted the same as each other opponent's contribution.

Also, if Team A plays multiple games against an opponent, then the opponent's winning percentage against teams other than Team A is counted multiple times in determining Team A's opponents' average winning percentage.

Element 3:  Team A's Opponents' Opponents' Average Winning Percentage

Element 3 of the RPI measures a team's opponents' opponents' average winning percentage using, for each Team A opponent, the same method to determine that opponent's opponents' winning percentage as used in computing Team A's Element 2.  Thus another way to describe Team A's Element 3 is to say it is the average of Team A's opponents' Element 2s.

Calculation of RPI

Once the NCAA has calculated each of these Elements, it combines them to determine the variously called "basic" or "normal" or "original" or "unadjusted" RPI.  The formula for determining the unadjusted RPI is:

(Element 1 + (2 x Element 2) + Element 3)/4

At first glance, this looks like the RPI formula gives Team A's strength of schedule (Elements 2 and 3) three times the impact on the RPI that Team A's winning record (Element 1) has, since Element 1 counts for 25% of the formula's apparent weight, Element 2 counts for 50%, and Element 3 counts for 25%.  In effect, however, this is not true.  The following table shows why:

The table shows, for each year, the high and low of each of the three RPI elements.  It then shows the difference (spread) between the high and low for each element.  And, based on the spread for each element, it shows the effective weight of each element as a result of using the 1-2-1 (25%-50%-25%) RPI formula.  The bottom row of the table shows the averages for the element highs and lows, the element spreads, and the element effective weights.  

As the table shows, the spreads for the three elements grow smaller when progressing from Element 1 to Element 3.  The reason for the diminishing spreads is obvious, if one thinks about it.  The computation of Element 1 looks at one team's record.  Individual team records reasonably can range from undefeated (an RPI Element 1 of 1.0000) to all losses (an RPI Element 1 of 0.0000), for a maximum reasonable (though not average) spread of 1.0000.  Teams on average play about 17 games in a season, so for Element 2, the computation looks at about 17 teams' records and averages them out.  With this many teams' records being used for Element 2, nearly all of the teams are going to have some wins and some losses, so the high Element 2 is going to be less than 1.0000 and the low is going to be higher than 0.0000.  Similarly, for Element 3 the computation looks at about 289 (17 x 17) teams' records.  This inclusion of a very large number of teams' records produces Element 3 numbers that are even less at the extremes than for Element 2, making Element 3's maximum reasonable (and average) spread smaller than for Element 2 and much smaller than for Element 1.

At the bottom right of the table, the green highlighted numbers show the average effective weights of the three elements covered by the table, when the three elements are incorporated into the RPI formula using the 25%-50%-25% ratios:

Element 1: 51.2 % -- roughly 50%

Element 2:  38.0% -- roughly 40%

Element 3:  10,9% -- roughly 10%

If you are having trouble grasping this, think of fruit salad.  I want my fruit salad to consist of 50% cantaloupe (Element 1), 40% oranges (Element 2), and 10% kiwi fruit (Element 3).  To do that, I compare the fruit sizes and figure out that the right ratio of ingredients is 1 cantaloupe to 2 oranges to 1 kiwi fruit.  In this analogy, 1 canteloupe = 1 x RPI Element 1; 2 oranges = 2 x RPI Element 2; and 1 kiwi fruit = 1 x RPI Element 3.

The 50-40-10 percentages suggest that the NCAA adopted the 1:2:1 weights in the formula for the three Elements in order to have a team's winning percentage count for approximately half the team's RPI (Element 1's roughly 50% effective impact) and the team's strength of schedule count for the other half of the team's RPI (Element 2's roughly 40% effective impact plus Element 3's roughly 10% effective impact).  In a January 23, 2009 Memorandum from the NCAA's Associate Director of Statistics to the Division I Men's Basketball Committee, the NCAA confirmed that this is its intention:  "About half of the rating is based on winning percentage and the other half on strength of schedule.  Winning percentage (Factor I) only receives a 25 percent weighting although its real strength is larger.  There always is a far wider gap in the rankings between the top and bottom teams in this category than between the first and last in Factors II and III."

Bonus and Penalty Adjustments

The formula described above produces Team A's unadjusted (or "basic" or "normal" or "original") RPI.  Once the NCAA has calculated teams' unadjusted RPIs, it then adjusts them by adding bonuses for "good" wins and ties and subtracting penalties for "poor" losses and ties, to produce the adjusted RPI (or "NCAA RPI").  On this website, when I refer to the NCAA RPI, I am referring to the adjusted RPI.

The bonus and penalty structures and amounts vary from sport to sport.  The committee for a particular sport sets the basic structure  for that sport.  In setting it, the committee, among other things, typically tells the staff how many positions it wants a team to rise in the rankings for a good result or fall in the rankings for a poor result.  The staff then identifies the adjustment amount that will achieve the intended rise or fall.  Since the unadjusted RPI ratings evolve over time, especially as additional schools sponsor a sport, the staff periodically, between seasons, can re-calibrate the bonus and penalty amounts to reflect changes needed in order for the bonus and penalty amounts to reflect the number of positions the committee decided it wants teams to rise or fall.  The staff's re-calibration revisions ordinarily are in the range of an 0.0001 to 0.0002 change in bonus and/or penalty amounts.  These are the only changes the staff is allowed to make on its own.  The committee must approve all other changes.

In 2024, the Women's Soccer Committee revised the bonus and penalty structure and amounts.  Below are the 2024 structure amounts.  The bonuses and penalties are only for non-conference games.   And, there are no bonuses or penalties for non-Division I games.

The Women's Soccer Committee has not disclosed publicly the number of positions it wants teams to rise or descend based on bonuses or penalties.  The following table, however, may shed some light on this:

This table shows the average rating gap between teams each year, for the 2024 NCAA RPI with No Overtimes applied retroactively from 2010 through 2021.  At the bottom are the average  gap for all years and the average for the last 5 years.  Looking at the 2024 bonus and penalty amounts in the earlier table, it seems possible that the Committee wanted the basic structure to reflect maximum bonus and penalty amount adjustments equivalent to 2 rank positions -- 0.0026.  This would match the penalty structure, which has a maximum penalty of 0.0026.  For the bonuses, however, the maximum bonus is 0.0032.  It is possible this is because the Committee wanted to have three bonus tiers of opponents ranked 1-25, 26-50, and 51-100.  In order to fit in the 51-100 tier while otherwise mirroring the penalty amounts, it then became necessary to increase the maximum bonus to 0.0032.

This table shows the impacts on teams' ranks of the 2024 bonuses and penalties, for all teams (green highlighting) and for the Top 75 teams (salmon highighting).   As you can see,  the impacts are small, especially for the Top 75.  I use the Top 75 since for practical purposes those  are the teams -- plus some -- that matter for NCAA Tournament seeding and at large selection purposes.  Given the inherent limitations of rating systems, in my opinion the impacts shown -- especially for the Top 75 -- have at best a minimal meaning.

How Has the Bonus and Penalty Structure Changed Over Time?

From 2007 to 2009 (and perhaps earlier), the bonus and penalty structure was as follows, apparently considering 0.0016 as a 1 rank position difference.  The bonuses and penalties applied to both conference and non-conference games.

Win v RPI 1 to 40:  0.0032 (away),   0.0030 (neutral),   0.0028 (home)

Tie v RPI 1 to 40:  0.0016 (away),   0.0014 (neutral),   0.0012 (home)

Win v RPI 41 to 80:  0.0018 (away),   0.0016 (neutral),   0.0014 (home)

Tie v RPI 41 to 80:  0.0012 (away),   0.0010 (neutral),   0.0008 (home)

Tie v RPI 135 to 205: -0.0008 (away), -0.0010 (neutral), -0.0012 (home)

Loss v RPI 135 to 205: -0.0014 (away), -0.0016 (neutral), -0.0018 (home)

Tie v RPI 206 and poorer: -0.0012 (away), -0.0014 (neutral), -0.0016 (home)

Loss v RPI 206 and poorer: -0.0028 (away), -0.0030 (neutral), -0.0032 (home)

In 2010, there was a change to the following structure, apparently using 0.0012 as a 1 rank position difference.  The bonuses and penalties applied to both conference and non-conference games.

Win v RPI 1 to 40:  0.0024 (away),   0.0022 (neutral),   0.0020 (home)

Tie v RPI 1 to 40:  0.0012 (away),   0.0010 (neutral),   0.0008 (home)

Win v RPI 41 to 80:  0.0018 (away),   0.0016 (neutral),   0.0014 (home)

Tie v RPI 41 to 80:  0.0006 (away),   0.0004 (neutral),   0.0002 (home)

Tie v RPI 135 to 205: -0.0002 (away), -0.004 (neutral), -0.0006 (home)

Loss v RPI 135 to 205: -0.0014 (away), -0.0016 (neutral), -0.0018 (home)

Tie v RPI 206 and poorer: -0.0008 (away), -0.0010 (neutral), -0.0012 (home)

Loss v RPI 206 and poorer: -0.0020 (away), -0.0022 (neutral), -0.0024 (home)

In 2012, the Committee made two changes in the structure, but not the amounts.  It eliminated bonuses and penalties for conference games.  And, it changed the penalty tiers to the teams ranked 41 to 80 positions from the bottom of the rankings and the bottom 40 teams in the rankings.

In 2015, the staff changed the amounts, apparently based on 0.0013 as equivalent to a 1 rank position change.

Win v RPI 1 to 40:  0.0026 (away),   0.0024 (neutral),   0.0022 (home)

Tie v RPI 1 to 40:  0.0013 (away),   0.0011 (neutral),   0.0009 (home)

Win v RPI 41 to 80:  0.0020 (away),   0.0017 (neutral),   0.0015 (home)

Tie v RPI 41 to 80:  0.0007 (away),   0.0004 (neutral),   0.0002 (home)

Tie v RPI 41 to 80 from bottom: -0.0002 (away), -0.004 (neutral), -0.0007 (home)

Loss v RPI 41 to 80 from bottom: -0.0015 (away), -0.0017 (neutral), -0.0020 (home)

Tie v RPI 0 to 40 from bottom: -0.0009 (away), -0.0011 (neutral), -0.0013 (home)

Loss v RPI 0 to 40 from bottomr: -0.0022 (away), -0.0024 (neutral), -0.0026 (home)

RELATIVE SIGNIFICANCE OF THE COMMITTEE'S 2022 TO 2024 CHANGES

Effects on Team Ranks

Which Committee RPI-related decisions  have really mattered for team ranks?  The following table addresses this question:

This table considers data from the years 2010 through 2021, in other words the years in which there were regular season overtime games for which data are available showing which games went to overtime.  Using only these years allows  a good comparison of the ranking effects of the change from having overtimes to not having overtimes.

The first data row is based on the actual RPI ranks of teams using the bonus and penalty system in effect when games were played, with overtimes.  The row summarizes how teams' unadjusted RPI ranks compare to their ranks after making the bonus and penalty adjustments.  As you can see, the maximum rank position change for any team over those years is 17 positions.  The average rank change is 2 positions and the median is 1, meaning at least half of all teams have a rank change of 1 or fewer positions.

The second data row is based on teams' actual unadjusted RPI ranks as compared to what their unadjusted RPI ranks would have been if the No Overtime rule had been in effect.  This roughly doubles the number of games ending in ties.  This row thus shows the impact of the Committee's change to the No Overtime rule.  As you can see, the change has a significant effect.  The largest rank position change for a team is 75 positions.  The average change in teams' ranks is 11.3 positions and the median is 8.

The third data row is based on the 2024 change the Committee made to how the NCAA computes RPI Element 1 -- from treating a tie as 1/2  of a win to treating it as 1/3 of a win.  This row compares teams' unadjusted RPI ranks with no overtimes but with RPI Element 1 treating ties as 1/2 a win to their unadjusted RPI ranks with no overtimess but with RPI Element 1 treating ties as 1/3 of a win.  In other words, it isolates the effect of the 1/2 to 1/3 change.  As you can see, this too is a significant change, but only about half the significance of the No Overtime rule change.

The fourth data row summarizes how teams' unadjusted RPI ranks under the 2024 formula, with no overtimes, compare to their adjusted RPI ranks under the 2024 formula, with no overtimes.  As you can see, the fourth data row is similar to the first data row, but indicating the 2024 bonus and penalty regime has a slightly larger impact than the actual regimes in effect from 2010 through 2021.

The bottom line of this is that the Committee's change to the No Overtime rule has a significant impact on teams' NCAA RPI ranks.  In addition, the Committee's change in the value of ties in the RPI Element 1 formula has a significant effect, although less of an effect than the No Overtime rule.  On the other hand, the bonus and penalty adjustment regimes have only small effects that, for practical purposes, are at best minimal.

Effects on NCAA Tournament Seeds and At Large Selections

The preceding discussion looks at how the Committee's recent decisions have affected teams' NCAA RPI ranks.  What about how those decisions have affected seeds and at large selections for the NCAA Tournament?

This table shows, for each Committee #1 through #4 seed and for at large selections, the poorest ranked team to receive the seed or selection over the time period from 2007 through the present.  The ranks are the ranks of teams under the rating system then in effect.  Thus, using at large selections as an example, the poorest ranked team to which the Committee has been willing to give an at large selection is #57, regardless of the exact details of the rating system the Committee was using.  In other words, each year the teams ranked #57 and better (that are not Automatic Qualifiers) are the candidate group for at large selections.

This table shows the number of teams over the 11 years from 2010 through 2021 (excluding Covid-affected 2020) that got a particular seed or an at large selection from the Committee but that would not have been in the seed or selection candidate group if there had been no overtimes and if the 2024 RPI formula changes had been in effect.

If you consider that each year there were 4 teams seeded in each of the #1 through #4 seed pods and either 33 or 34 at large selections you can see that the "mandatory" changes in seeds and at large selections are not large, although on average 1 to 2 teams that actually got at large selections each year would not have gotten theml under the current system.  It is important to bear in mind, however, that  these numbers represent numbers of changes that definitely would have occurred.

This table shows how the candidate pools would have changed from the actual pools for seeds and at large selections with the No Overtime rule and the 2024 RPI formula changes in effect.  The numbers represent the potential for changes in addition to the "mandatory" changes in the preceding table.

Regarding at large selections, from the preceding table you can see that over the 11 years from 2010 through 2021, a minimum of 18 teams that got at large selections would not have gotten them with the No Overtime rule and the 2024 RPI fromula changes in effect.  Using this additional table, if you subtract those 18 from the 45 total teams that no longer would be candidates, you can see that there are 27 teams that also drop out of the Top 57 but that did not get at large selections.  These 27 plus the 18 are replaced in the Top 57 by 39 new candidates for at large selections (plus 6 Automatic Qualifiers to bring the total to 45).  What we cannot know is whether some of these new candidates would have displaced teams that got at large selections.  What we do know, however, is that on average 1 to 2 teams per year definitely would have lost their at large selections and the maximum possible change in at large selections would be 3 to 4 positions (3.55 on average).

Bottom Line on Significance of Changes

The bottom line, on the significance of the No Overtime rule and 2024 RPI formula changes, is that they are significant in relation to teams' ranks.  They are not massively significant in relation to the Committee's NCAA Tournament seed and at large selection decisions, but they definitely will produce some decisions that will be different than what they would have been without the changes .  And, in relation to at large selections, on averagle they will produce 1 to 2 different at large selections per year and may produce as many as 3 to 4.