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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 sports rating systems by which NCAA basketball, baseball, softball, hockey, soccer, lacrosse, and volleyball 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 men's playoffs (see March Madness), and for the 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 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. However, 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 (often 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. ==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 the 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 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Rating Percentage Index」の詳細全文を読む スポンサード リンク
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