Sports rating system
Encyclopedia
A sports rating system is a system that analyzes the results of sports competitions to provide objective
ratings for each team or player. Ranking
s are then derived by sorting each team's ratings and assigning an ordinal
rank to each team starting with the highest rated team earning the #1 rank. Ratings systems provide an alternative to traditional sports standings which are based on win-loss-tie ratios, or to polls
which are a subjective
rating of the teams in a league.
In the United States, the biggest use of sports ratings systems is to rate NCAA
Division I-A Football
teams towards choosing two teams to play in the BCS
championship game. Sports ratings systems are also used to help determine the field for the NCAA Men's and Women's Basketball
tournaments, men's professional golf
tournaments, Pro Tennis
, and NASCAR
. They are often mentioned in discussions about the teams that could or should receive "at large" invitations to participate in certain contests ("bubble teams").
systems, the NY Times system, and the Dunkel Index, which dates back to 1929.
s in a given data set due to game outcomes. For example, if A defeats B and B defeats C, then one can safely say that A>B>C.
There are obvious problems with basing a system solely on wins and losses. For example, if C defeats A, then an intransitive
relation is established (A>B>C>A) and a ranking violation will occur if this is the only data available. Scenarios such as this happen fairly regularly in sports -- for example, in the 2005 NCAA Division I-A football season
, Penn State
beat Ohio State
, Ohio State beat Michigan
, and Michigan beat Penn State. To address these logical breakdowns, rating systems usually consider other criteria such as the game's score and where the match was held (for example, to assess a home field advantage
). In most cases though, each team plays a sufficient amount of other games during a given season, which lessens the overall effect of such violations.
From an academic perspective, the use of linear algebra
and statistics
are popular among many of the systems' authors to determine their ratings. They are obvious choices for providing a solution to such a problem, however to effectively use these fields typically requires education
in them at a collegiate
level. Not surprising then is the fact that many of the systems' authors have backgrounds in these areas, such as Jeff Sagarin
, who received a Bachelor of Science
in Mathematics
from MIT in 1970.
Objectivity (science)
Objectivity in science is a value that informs how science is practiced and how scientific truths are created. It is the idea that scientists, in attempting to uncover truths about the natural world, must aspire to eliminate personal biases, a priori commitments, emotional involvement, etc...
ratings for each team or player. Ranking
Ranking
A ranking is a relationship between a set of items such that, for any two items, the first is either 'ranked higher than', 'ranked lower than' or 'ranked equal to' the second....
s are then derived by sorting each team's ratings and assigning an ordinal
Ordinal
Ordinal may refer to:* Ordinal number , a word representing the rank of a number* Ordinal scale, ranking things that are not necessarily numbers* Ordinal indicator, the sign adjacent to a numeral denoting that it is an ordinal number...
rank to each team starting with the highest rated team earning the #1 rank. Ratings systems provide an alternative to traditional sports standings which are based on win-loss-tie ratios, or to polls
Opinion poll
An opinion poll, sometimes simply referred to as a poll is a survey of public opinion from a particular sample. Opinion polls are usually designed to represent the opinions of a population by conducting a series of questions and then extrapolating generalities in ratio or within confidence...
which are a subjective
Subjectivity
Subjectivity refers to the subject and his or her perspective, feelings, beliefs, and desires. In philosophy, the term is usually contrasted with objectivity.-Qualia:...
rating of the teams in a league.
In the United States, the biggest use of sports ratings systems is to rate 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...
Division I-A Football
College football
College football refers to American football played by teams of student athletes fielded by American universities, colleges, and military academies, or Canadian football played by teams of student athletes fielded by Canadian universities...
teams towards choosing two teams to play in the BCS
Bowl Championship Series
The Bowl Championship Series is a selection system that creates five bowl match-ups involving ten of the top ranked teams in the NCAA Division I Football Bowl Subdivision , including an opportunity for the top two to compete in the BCS National Championship Game.The BCS relies on a combination of...
championship game. Sports ratings systems are also used to help determine the field for the NCAA Men's and Women's Basketball
College basketball
College 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....
tournaments, men's professional golf
Golf
Golf is a precision club and ball sport, in which competing players use many types of clubs to hit balls into a series of holes on a golf course using the fewest number of strokes....
tournaments, Pro Tennis
Tennis
Tennis is a sport usually played between two players or between two teams of two players each . Each player uses a racket that is strung to strike a hollow rubber ball covered with felt over a net into the opponent's court. Tennis is an Olympic sport and is played at all levels of society at all...
, and NASCAR
NASCAR
The National Association for Stock Car Auto Racing is a family-owned and -operated business venture that sanctions and governs multiple auto racing sports events. It was founded by Bill France Sr. in 1947–48. As of 2009, the CEO for the company is Brian France, grandson of the late Bill France Sr...
. They are often mentioned in discussions about the teams that could or should receive "at large" invitations to participate in certain contests ("bubble teams").
History
Sports ratings systems have been around for almost 80 years, when ratings were calculated on paper rather than by computer, as most are today. Some older computer systems still in use today include: Jeff Sagarin'sJeff Sagarin
Jeff Sagarin is an American sports statistician well-known for his development of a methodology for ranking and rating sports teams in a variety of sports...
systems, the NY Times system, and the Dunkel Index, which dates back to 1929.
Theory
Sports ratings systems use a variety of methods for rating teams, but the most prevalent method is called a power rating. The power rating of a team is a calculation of the team's strength relative to other teams in the same league or division. The basic idea is to maximize the amount of transitive relationTransitive relation
In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c....
s in a given data set due to game outcomes. For example, if A defeats B and B defeats C, then one can safely say that A>B>C.
There are obvious problems with basing a system solely on wins and losses. For example, if C defeats A, then an intransitive
Intransitivity
In mathematics, the term intransitivity is used for related, but different, properties of binary relations:- Intransitivity :A relation is transitive if, whenever it relates some A to some B, and that B to some C, it also relates that A to that C...
relation is established (A>B>C>A) and a ranking violation will occur if this is the only data available. Scenarios such as this happen fairly regularly in sports -- for example, in the 2005 NCAA Division I-A football season
2005 NCAA Division I-A football season
The 2005 NCAA Division I-A football season ended with the least amount of controversy surrounding the Bowl Championship Series title game in many years.To an extent it was a return to classic football...
, Penn State
Pennsylvania State University
The Pennsylvania State University, commonly referred to as Penn State or PSU, is a public research university with campuses and facilities throughout the state of Pennsylvania, United States. Founded in 1855, the university has a threefold mission of teaching, research, and public service...
beat Ohio State
Ohio State University
The Ohio State University, commonly referred to as Ohio State, is a public research university located in Columbus, Ohio. It was originally founded in 1870 as a land-grant university and is currently the third largest university campus in the United States...
, Ohio State beat Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
, and Michigan beat Penn State. To address these logical breakdowns, rating systems usually consider other criteria such as the game's score and where the match was held (for example, to assess a home field advantage
Home Field Advantage
Home Field Advantage is a 2000 independent film starring Tony Award-winning actor Dan Fogler in the role of Charlie....
). In most cases though, each team plays a sufficient amount of other games during a given season, which lessens the overall effect of such violations.
From an academic perspective, the use of linear algebra
Linear algebra
Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
and statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
are popular among many of the systems' authors to determine their ratings. They are obvious choices for providing a solution to such a problem, however to effectively use these fields typically requires education
Education
Education in its broadest, general sense is the means through which the aims and habits of a group of people lives on from one generation to the next. Generally, it occurs through any experience that has a formative effect on the way one thinks, feels, or acts...
in them at a collegiate
College athletics
College athletics refers primarily to sports and athletic competition organized and funded by institutions of tertiary education . In the United States, college athletics is a two-tiered system. The first tier includes the sports that are sanctioned by one of the collegiate sport governing bodies...
level. Not surprising then is the fact that many of the systems' authors have backgrounds in these areas, such as Jeff Sagarin
Jeff Sagarin
Jeff Sagarin is an American sports statistician well-known for his development of a methodology for ranking and rating sports teams in a variety of sports...
, who received a Bachelor of Science
Bachelor of Science
A Bachelor of Science is an undergraduate academic degree awarded for completed courses that generally last three to five years .-Australia:In Australia, the BSc is a 3 year degree, offered from 1st year on...
in Mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
from MIT in 1970.
Pros
- Ratings are objectiveObjectivity (science)Objectivity in science is a value that informs how science is practiced and how scientific truths are created. It is the idea that scientists, in attempting to uncover truths about the natural world, must aspire to eliminate personal biases, a priori commitments, emotional involvement, etc...
, without specific player, team, regional, or style bias - Ratings are verifiable and repeatable
- Ratings are comprehensive, requiring assessment of all selected criteria
- Ratings do not "forget old games" (although some are designed to diminish their overall weight as a season progresses)
Cons
- Formulae criteria are subjective (some use just scores, some use margin of victory, some include auxiliary game data, such as hits, interceptions, lead changes, shot percentage) with no consensus among authors on which to include, even minimally
- Most ignore qualitative criteria such as weather, participation (or lack thereof due to injuries or "throw-away" games -- see below), and individual efforts
- Some assume parityParity (sports)Parity in sports is defined as attempting to make an equal playing field for all participants, specifically with regard to financial issues. When parity in a sports league is achieved, all participating teams enjoy roughly equivalent levels of talent. In such a league, the "best" team is not...
among all members of the league, such as each team being built from an equitable pool of players via a draftDraft (sports)A draft is a process used in the United States, Canada, Japan, Australia, Russia and the Philippines to allocate certain players to sports teams. In a draft, teams take turns selecting from a pool of eligible players...
or free agencyFree agentIn professional sports, a free agent is a player whose contract with a team has expired and who is thus eligible to sign with another club or franchise....
system as is done in many major league sports such as the NFLNational Football LeagueThe National Football League is the highest level of professional American football in the United States, and is considered the top professional American football league in the world. It was formed by eleven teams in 1920 as the American Professional Football Association, with the league changing...
, MLBMajor League BaseballMajor League Baseball is the highest level of professional baseball in the United States and Canada, consisting of teams that play in the National League and the American League...
, NBANational Basketball AssociationThe National Basketball Association is the pre-eminent men's professional basketball league in North America. It consists of thirty franchised member clubs, of which twenty-nine are located in the United States and one in Canada...
, and NHLNational Hockey LeagueThe National Hockey League is an unincorporated not-for-profit association which operates a major professional ice hockey league of 30 franchised member clubs, of which 7 are currently located in Canada and 23 in the United States...
. This is certainly not the case in collegiate leagues such as Division I-A football or men's and women's basketball. - If sufficient "inter-divisional" league play is not accomplished, teams in an isolated division may be artificially propped up or down in the overall ratings due to a lack of correlation to other teams in the overall league. This phenomenon is evident in systems that analyze historical college football seasons, such as when the top Ivy LeagueIvy LeagueThe Ivy League is an athletic conference comprising eight private institutions of higher education in the Northeastern United States. The conference name is also commonly used to refer to those eight schools as a group...
teams of the 1970s, like DartmouthDartmouth CollegeDartmouth College is a private, Ivy League university in Hanover, New Hampshire, United States. The institution comprises a liberal arts college, Dartmouth Medical School, Thayer School of Engineering, and the Tuck School of Business, as well as 19 graduate programs in the arts and sciences...
, were calculated by some rating systems to be comparable with accomplished powerhouse teams of that era such as Nebraska, USCUniversity of Southern CaliforniaThe University of Southern California is a private, not-for-profit, nonsectarian, research university located in Los Angeles, California, United States. USC was founded in 1880, making it California's oldest private research university...
, and Ohio StateOhio State UniversityThe Ohio State University, commonly referred to as Ohio State, is a public research university located in Columbus, Ohio. It was originally founded in 1870 as a land-grant university and is currently the third largest university campus in the United States...
. This conflicts with the subjective opinion that claims that while good in their own right, they were not nearly as good as those top programs. However, this may be considered a "pro" by non-BCSBowl Championship SeriesThe Bowl Championship Series is a selection system that creates five bowl match-ups involving ten of the top ranked teams in the NCAA Division I Football Bowl Subdivision , including an opportunity for the top two to compete in the BCS National Championship Game.The BCS relies on a combination of...
teams in Division I-A college football who point out that ratings systems have proven that their top teams belong in the same strata as the BCS teams. This is evidenced by the 2004 UtahUniversity of UtahThe University of Utah, also known as the U or the U of U, is a public, coeducational research university in Salt Lake City, Utah, United States. The university was established in 1850 as the University of Deseret by the General Assembly of the provisional State of Deseret, making it Utah's oldest...
team that went undefeated in the regular season and earned a BCS bowl bid due to the bump in their overall BCS ratings via the computer ratings component. They went on to play and defeat the Big East ConferenceBig East ConferenceThe Big East Conference is a collegiate athletics conference consisting of sixteen universities in the eastern half of the United States. The conference's 17 members participate in 24 NCAA sports...
champion PittsburghUniversity of PittsburghThe University of Pittsburgh, commonly referred to as Pitt, is a state-related research university located in Pittsburgh, Pennsylvania, United States. Founded as Pittsburgh Academy in 1787 on what was then the American frontier, Pitt is one of the oldest continuously chartered institutions of...
in the 2005 Fiesta BowlFiesta BowlThe Fiesta Bowl, now sponsored by Frito-Lay and named with their Tostitos brand, is a United States college football bowl game played annually at the University of Phoenix Stadium in Glendale, Arizona. Between its origination in 1971 and 2006, the game was hosted in Tempe, Arizona at Sun Devil...
by a score of 35-7. A related example occurred during the 2006 NCAA Men's Basketball TournamentNCAA 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...
where George MasonGeorge Mason UniversityGeorge Mason University is a public university based in unincorporated Fairfax County, Virginia, United States, south of and adjacent to the city of Fairfax. Additional campuses are located nearby in Arlington County, Prince William County, and Loudoun County...
were awarded an at-large tournament bid due to their regular season record and their RPI ratingRatings Percentage IndexThe 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...
and rode that opportunity all the way to the Final FourNCAA 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...
. - Goals of some rating systems differ from one another. For example, systems may be crafted to provide a perfect retrodictive analysis of the games played to-date, while others are predictive and give more weight to future trends rather than past results. This results in the potential for misinterpretation of rating system results by people unfamiliar with these goals; for example, a rating system designed to give accurate point spread predictions for gamblers might be ill-suited for use in selecting teams most deserving to play in a championship game or tournament. Additionally, this issue limits the use of ratings in combination with each other as part of an overall consensus rating, such as the BCS computer component is supposed to provide, as the results may be skewed and exhibit unacceptably large deviations from the overall average ranking per team.
- Rating systems can not ignore "throw-away" games. These are games where teams have already earned a post-season bid and have secured their playoff seeding before the end of the regular season, and want to rest/protect their starters by benching them for those remaining regular season games. This usually results in unpredictable outcomes, but without a mechanism to ignore such games (which runs counter to the goals of such systems), this will unintentionally skew the outcomes of rating systems.
International
- ATP rankings - men's tennis
- IRB World RankingsIRB World RankingsThe IRB World Rankings is a ranking system for men's national teams in rugby union, managed by the International Rugby Board , the sport's governing body. The teams of the IRB's member nations are ranked based on their game results, with the most successful teams being ranked highest...
- men's rugby - FIFA World RankingsFIFA World RankingsThe FIFA World Rankings is a ranking system for men's national teams in association football, currently led by Spain. The teams of the member nations of FIFA , football's world governing body, are ranked based on their game results with the most successful teams being ranked highest...
- men's international football (soccer) - FIFA Women's World RankingsFIFA Women's World RankingsThe FIFA Women's World Rankings for football were introduced in 2003, with the first rankings published in March of that year, as a follow-on to the existing FIFA World Rankings for men...
- women's international football (soccer) - WPBF Computerized World Rankings - world professional boxing (boxing)
- ICC Player Rankings - men's international cricket (ranks individual players rather than teams)
- Official World Golf RankingsOfficial World Golf RankingsThe Official World Golf Ranking is a system for rating the performance level of male professional golfers...
- men's professional golf - Women's World Golf RankingsWomen's World Golf RankingsThe Women's World Golf Rankings, also known for sponsorship reasons as the Rolex Rankings, were introduced in February 2006. They are sanctioned by the five main women's golf tours and the organisations behind them: Ladies Professional Golf Association , Ladies European Tour, Ladies Professional...
- women's professional golf - WTA rankings - women's tennis
United States
- Advanced NFL StatsAdvanced NFL StatsAdvanced NFL Stats is a website dedicated to the analysis of the National Football League using advanced mathematical and statistical methods. The site's lead author is noted football researcher and analyst Brian Burke...
- Albrecht Matrix HybridAlbrecht Matrix HybridThe Matrix Hybrid is a college football rating system that was developed by Scott Albrecht in 2006, and has been revised several times since. The hybrid rating is a compilation of the Matrix-Performance and Matrix-Elo ratings. The Performance rating uses location and point margin to rate teams, and...
- Anderson & Hester
- ARGH Power RatingsARGH Power RatingsThe ARGH Power Ratings are a sports rating system created by Stewart Huckaby in 1990 and designed to identify the best team from within a closed system. They are most closely identified with NCAA football...
- AtomicFootball
- Richard Billingsley
- Wesley Colley
- Dunkel Index
- James Howell
- Herman MatthewsHerman MatthewsHerman Matthews is an American drummer and composer.Matthews works as a session and touring musician, most notably for Tower of Power, Kenny Loggins and being on tour with Tom Jones for more than 7 years....
- Omni Rankings
- Jeff SagarinJeff SagarinJeff Sagarin is an American sports statistician well-known for his development of a methodology for ranking and rating sports teams in a variety of sports...
- Kenneth MasseyKenneth MasseyKenneth Massey is an American sports statistician known for his development of a methodology for ranking and rating sports teams in a variety of sports...
- Sonny Moore Power RatingsSonny Moore Power RatingsSonny Moore's Power Ratings are a sports rating system that was devised in 1974. This is a hobby that began so a comparison could be made of any two teams in a given sport, so as to get an indication on which team would win and by how many points if a game were played between them...
- Laxpower
- RPIRatings Percentage IndexThe 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...
- Peter WolfePeter Wolfe (Sports Rankings)Peter R. Wolfe is the owner of a computer system that is used by the Bowl Championship Series to rank collegiate football teams.-External links:*...
- VHSL-Reference
- CS SportsRank
Ratings of other contests
- Elo rating systemElo rating systemThe Elo rating system is a method for calculating the relative skill levels of players in two-player games such as chess. It is named after its creator Arpad Elo, a Hungarian-born American physics professor....
— Chess - Chess rating systemsChess rating systemsA chess rating system is a system used in chess to calculate an estimate of the strength of the player, based on his performance versus other players. They are used by organizations such as FIDE, the US Chess Federation , International Correspondence Chess Federation, and the English Chess Federation...
- Capello IndexCapello IndexThe Capello Index is an on-line player rating system for footballers. It was devised by a gaming firm, Football Cap Index, to which England manager Fabio Capello sold his name. The Index uses a statistical system, created by Capello, to analyse each player's performance, marking them out of 100...
— Association Football
External links
- Bettify Football Data
- System-Bet.com - Goal Rating System
- Anderson & Hester
- ARGH Power Ratings
- AtomicFootball
- Kenneth Massey's College Football Ranking Comparison
- CollegeTOP25.com Rankings
- Link Power Ratings
- Dunkel Index
- Jeff Sagarin's ratings
- Steve Pugh's Compughter Ratings
- Richard Billingsley
- Colley Matrix
- Omni Rankings
- Sonny Moore Power Ratings
- Laxpower Lacrosse rating system
- Albrecht Matrix Hybrid
- VHSL-Reference website
- Sportheory
- SciBet.com - Time-Dependent Ranking of Soccer Teams
- Alternative tennis ranking system - Based on bookmaker's odds
- SRI Rankings (Men's and Women's Tennis)