Ratings Percentage Index
Encyclopedia
The Rating Percentage Index, commonly known as the RPI, is a quantity used to rank sports teams based upon a team's wins and losses and its strength of schedule
. It is one of the systems by which NCAA
basketball
and baseball
teams are ranked. This system has been in use in college basketball since 1981 to aid in the selecting and seeding of teams appearing in the 68-team men's playoffs (see March Madness
), and for the 64-team women's tournament since its inception in 1982. In its current formulation, the index comprises a team's winning percentage (25%), its opponents' winning percentage (50%), and the winning percentage of those opponents' opponents (25%). The opponents' winning percentage and the winning percentage of those opponents' opponents both comprise the strength of schedule (SOS). Thus, the SOS accounts for 75% of the RPI calculation and is 2/3 its opponents' winning percentage and 1/3 times its opponents' opponents' winning percentage.
The RPI lacks theoretical justification from a statistical standpoint. Other ranking systems which include the margin of victory of games played or other statistics in addition to the win/loss results have been shown to be a better predictor of the outcomes of future games. Because the margin of victory has been manipulated in the past by teams or individuals in the context of gambling, the RPI can be used to mitigate motivation for such manipulation.
Some feel that the heavy emphasis upon strength of schedule gives an unfair advantage to teams from major conferences. Teams from "majors" are allowed to pick many of their non-conference opponents (oftentimes blatantly weaker teams). Teams from minor conferences, however, may only get one or two such opponents in their schedules. Also, some mid-major
conferences regularly compel their member teams to schedule opponents ranked in the top half of the RPI, which could boost the strength of that conference and/or its tougher-scheduling teams. In basketball, the Missouri Valley Conference
has successfully done this: It has become one of the top-rated RPI conferences, despite having very few of its teams ranked in the two national Top 25 polls. http://www.cstv.com/sports/m-baskbl/stories/103006aad.html In 2006, the NCAA began to release their RPI calculations weekly starting in January. Independent sources, such as ESPN
or CNN/SI, also publish their own RPI calculations, which are updated more frequently.
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 Duke 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 Duke has played one other game and lost, while Cincinnati has played two other teams and won. The team in question has played Duke twice and therefore must be counted twice. Thus the OWP of the team is (0/1 + 0/1 + 2/2)/ 3 (number of opponents - Duke, Duke, 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 Duke twice and Cincinnati once. Duke 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 (Duke's OWP + Duke's OWP + Cincinnati's OWP ) / 3.
Duke has played and beat the team in question (which, excluding the games against Duke, only lost to Cincinnati), lost to the team in question (excluding Duke, only lost to Cincinnati, and lost one other game (excluding Duke, this team has no WP). Duke's OWP is (0/1 + 0/1) / 2 = 0.0000.
Cincinnati has played the team in question (excluding Cincinnati, they went 1-1 vs. Duke) 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
Here is the calculation of the WPs, OWPs, and OOWPs for each team:
WP
OWP
OOWP
These are then combined via the formula
resulting in the following ratings:
This weighting replaces the current system of bonuses or penalties that teams receive. Bonus points are awarded for beating top-75 non-conference opponents on the road and penalty points are given for losing to bottom-75 non-conference opponents at home. Bonuses and penalties are on a sliding scale, separated into groups of 25, with the top bonus for a road win against a top-25 team and the worst penalty for a home loss to a bottom-25 opponent.
Strength of schedule
In sports, strength of schedule refers to the difficulty or ease of a team's/person's opponent as compared to other teams/persons. This is especially important if teams in a league do not play each other the same number of times.-Computation:...
. It is one of the systems by which NCAA
National Collegiate Athletic Association
The National Collegiate Athletic Association is a semi-voluntary association of 1,281 institutions, conferences, organizations and individuals that organizes the athletic programs of many colleges and universities in the United States...
basketball
Basketball
Basketball is a team sport in which two teams of five players try to score points by throwing or "shooting" a ball through the top of a basketball hoop while following a set of rules...
and baseball
Baseball
Baseball is a bat-and-ball sport played between two teams of nine players each. The aim is to score runs by hitting a thrown ball with a bat and touching a series of four bases arranged at the corners of a ninety-foot diamond...
teams are ranked. This system has been in use in college basketball since 1981 to aid in the selecting and seeding of teams appearing in the 68-team men's playoffs (see March Madness
NCAA Men's Division I Basketball Championship
The NCAA Men's Division I Basketball Championship is a single-elimination tournament held each spring in the United States, featuring 68 college basketball teams, to determine the national championship in the top tier of college basketball...
), and for the 64-team women's tournament since its inception in 1982. In its current formulation, the index comprises a team's winning percentage (25%), its opponents' winning percentage (50%), and the winning percentage of those opponents' opponents (25%). The opponents' winning percentage and the winning percentage of those opponents' opponents both comprise the strength of schedule (SOS). Thus, the SOS accounts for 75% of the RPI calculation and is 2/3 its opponents' winning percentage and 1/3 times its opponents' opponents' winning percentage.
The RPI lacks theoretical justification from a statistical standpoint. Other ranking systems which include the margin of victory of games played or other statistics in addition to the win/loss results have been shown to be a better predictor of the outcomes of future games. Because the margin of victory has been manipulated in the past by teams or individuals in the context of gambling, the RPI can be used to mitigate motivation for such manipulation.
Some feel that the heavy emphasis upon strength of schedule gives an unfair advantage to teams from major conferences. Teams from "majors" are allowed to pick many of their non-conference opponents (oftentimes blatantly weaker teams). Teams from minor conferences, however, may only get one or two such opponents in their schedules. Also, some mid-major
Mid-major
Mid-major is a term used in American Division I college sports, to refer to athletic conferences that are not among the major six conferences...
conferences regularly compel their member teams to schedule opponents ranked in the top half of the RPI, which could boost the strength of that conference and/or its tougher-scheduling teams. In basketball, the Missouri Valley Conference
Missouri Valley Conference
The Missouri Valley Conference is a college athletic conference whose members are located in the midwestern United States...
has successfully done this: It has become one of the top-rated RPI conferences, despite having very few of its teams ranked in the two national Top 25 polls. http://www.cstv.com/sports/m-baskbl/stories/103006aad.html In 2006, the NCAA began to release their RPI calculations weekly starting in January. Independent sources, such as ESPN
ESPN
Entertainment and Sports Programming Network, commonly known as ESPN, is an American global cable television network focusing on sports-related programming including live and pre-taped event telecasts, sports talk shows, and other original programming....
or CNN/SI, also publish their own RPI calculations, which are updated more frequently.
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 Duke 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 Duke has played one other game and lost, while Cincinnati has played two other teams and won. The team in question has played Duke twice and therefore must be counted twice. Thus the OWP of the team is (0/1 + 0/1 + 2/2)/ 3 (number of opponents - Duke, Duke, 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 Duke twice and Cincinnati once. Duke 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 (Duke's OWP + Duke's OWP + Cincinnati's OWP ) / 3.
Duke has played and beat the team in question (which, excluding the games against Duke, only lost to Cincinnati), lost to the team in question (excluding Duke, only lost to Cincinnati, and lost one other game (excluding Duke, this team has no WP). Duke's OWP is (0/1 + 0/1) / 2 = 0.0000.
Cincinnati has played the team in question (excluding Cincinnati, they went 1-1 vs. Duke) 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
Extended Example
Assume the following game results:| Home | Score | Away | Score |
|---|---|---|---|
| Duke | 78 | North Carolina | 72 |
| Duke | 82 | Maryland | 68 |
| Wake Forest | 71 | Duke | 72 |
| North Carolina | 93 | Duke | 68 |
| Maryland | 81 | Wake Forest | 72 |
| Wake Forest | 52 | North Carolina | 68 |
Here is the calculation of the WPs, OWPs, and OOWPs for each team:
WP
- Duke: (0.6 + 0.6 + 1.4 + 0) / (0.6 + 0.6 + 1.4 + 1.4) = 0.6500
- North Carolina: (0 + 0.6 + 1.4) / (1.4 + 0.6 + 1.4) = 0.5882
- Maryland: (0 + 0.6) / (1.4 + 0.6) = 0.3000
- Wake Forest: (0 + 0 + 0) / (1.4 + 0.6 + 1.4) = 0.0000
OWP
- Duke: ((North Carolina 1.0) + (North Carolina 1.0) + (Maryland 1.0) + (Wake 0)) / (4 games) = 0.7500
- North Carolina: ((Duke 1.0) + (Duke 1.0) + (Wake 0.0)) / (3 games) = 0.6667
- Maryland: ((Duke 0.6667) + (Wake 0.0)) / (2 games) = 0.3333
- Wake: ((Duke 0.6667) + (Maryland 0.0) + (North Carolina 0.5)) / (3 games) = 0.3889
OOWP
- Duke: ((North Carolina 0.6667) + (North Carolina 0.6667) + (Maryland 0.3333) + (Wake 0.3889)) / (4 games) = 0.5139
- North Carolina: ((Duke 0.7500) + (Duke 0.7500) + (Wake 0.3889)) / (3 games) = 0.6296
- Maryland: ((Duke 0.7500) + (Wake 0.3889)) / (2 games) = 0.5694
- Wake: ((Duke 0.7500) + (Maryland 0.3333) + (North Carolina 0.6667)) / (3 games) = 0.5833
These are then combined via the formula
- RPI = (WP * 0.25) + (OWP * 0.50) + (OOWP * 0.25)
resulting in the following ratings:
- Duke: 0.6660
- North Carolina: 0.6378
- Maryland: 0.3840
- Wake Forest: 0.3403
Baseball Formula
The formula used in NCAA baseball is the same as that used in basketball except for the weighting of home and road records. Starting in 2013, college baseball "RPI formula will value each road victory as 1.3 instead of 1.0. Each home win will be valued at 0.7 instead of 1.0. Conversely, each home loss will count 1.3 against a team’s RPI and each road loss will count 0.7 against a team’s RPI. Neutral-site games will retain the same value of 1.0, but the committee is studying how to determine if a game should be considered a neutral-site contest. The weighting is based on data showing that home teams win about 62 percent of the time in Division I baseball." The change was made because of the discrepancy in the number of home games teams play. Some schools are able to play 35-40 of their 56 allowable games at home, while other teams, due to factors such as weather, may play only 20 home games.This weighting replaces the current system of bonuses or penalties that teams receive. Bonus points are awarded for beating top-75 non-conference opponents on the road and penalty points are given for losing to bottom-75 non-conference opponents at home. Bonuses and penalties are on a sliding scale, separated into groups of 25, with the top bonus for a road win against a top-25 team and the worst penalty for a home loss to a bottom-25 opponent.
Finding the RPI Online
College basketball RPI ratings can be found at a number of locations. The NCAA releases their official ratings weekly.- CollegeRPI.com
- Live-RPI.com provides free up-to-the-minute RPI updates.
- RealTimeRPI.com is a service providing both daily (free) and real-time (paid) men's and women's RPI updates.
- RPIForecast.com provides free predictions of end of season RPI on a daily basis.
- TeamRankings.com provides free RPI calculations, including the schedule strength component.
- WarrenNolan.com provides free RPI calculations updated several times each hour and a predicted RPI calculation updated each hour.
See also
- NCAA Men's Division I Basketball ChampionshipNCAA Men's Division I Basketball ChampionshipThe NCAA Men's Division I Basketball Championship is a single-elimination tournament held each spring in the United States, featuring 68 college basketball teams, to determine the national championship in the top tier of college basketball...
- BracketologyBracketologyBracketology is the process of predicting the field of the NCAA Basketball Tournament, named as such because it is commonly used to fill in tournament brackets for the postseason...
- Final FourFinal fourFinal Four isa sports term that is commonly applied to the last four teams remaining in a playoff tournament, most notably NCAA Division I college basketball tournaments. The term usually refers to the four teams who compete in the two games of a single-elimination tournament's semi-final round...
- College basketballCollege basketballCollege basketball most often refers to the USA basketball competitive governance structure established by the National Collegiate Athletic Association . Basketball in the NCAA is divided into three divisions: Division I, Division II and Division III....