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College soccer Polls Soccer Buzz (W only) collegesoccernews (M only) Ratings Percentage Index Dissecting the RPI National teams FIFA Rankings Ron Kessler's Rankings for other sports
Heal Points System as used by the Maine Principle's Assn. College Hockey Chess (mostly Elo ratings) FIDE (Int'l Chess Fed.) Tennis |
Rankings and Ratings
Rankings and ratings are estimates of either team performance or strength. A ranking is simply an ordered list of teams. A rating is a number or descriptive term assigned to a specific team. A ranking can be derived from ratings but ratings can be more meaningful. In addition to indicating which team is supposedly better, a rating can also indicate how much better. Performance vs. strength - A performance-based rating or ranking (sometimes called "merit-based" or earned) is determined entirely by past results. Strength-based ratings (including predictive statistical models and power ratings) are based on other factors in addition to past performance, such as injuries, changes in personnel and fitness. Although past performance and strength are often related, they are not necessarily so. For a variety of reasons, a strong team may have done poorly in the past and, conversly, a weak team may have done well. A merit-based system is based on actual accomplisments while a strength based system is based on the potential for future accomplishments. A dynamic rating system counts recent results more than earlier results. A static system counts early season and late season results the same. Many feel that merit-based or 'earned' systems should be static. Most rating systems intended to be predictive are dynamic. Polls use the votes of poll participants to arrive at rankings. Accuracy depends on the knowledge of the voters (who are usually either coaches or journalists). In theory, polls should be sensitive to short-term phenomena such as injuries but, in practice, they usually aren't. Polls are based on opinion and tend to be highly volatile. They almost invariably over-react to the most recent result. The main reason most polls exist is their entertainment value. Polls are used to stimulate interest, either in the webpage or magazine that conducts the poll or in the sport. Some polls are little more than beauty contests that have little to do with qualifications for post-season play. Standings are calculated directly from results of round-robin play. Standings work well for small groups of teams (leagues, conferences, etc.) where each team plays every other team and all teams play essentially the same schedule. The method works less well when different teams play different schedules. Standing are usually based on either accumulated points or winning percentage. In soccer, round-robin accumulated points (AP) is calculated by awarding three points for a win, one point for a tie and no points for a loss. In some leagues bonus points are added for goals scored. Adjusted results account, in some way or another, for differences in strength of schedule. These systems (sometimes called 'merit-based' or 'earned') usually count early-season results the same as late-season results and are therefore called 'static'. The goal is not to identify the strongest teams but, rather, to identify the teams that have the best records over a given period of time. Systems intended to be merit-based include: Soccer: the Rating Percentage Index (RPI) (used by the NCAA) Longo ratings (used by the NAIA) FIFA National Team Rankings Other sports Heal points system (Maine high schools) FIDE ratings (chess) WTA ratings (women's tennis) ATP ratings (men's tennis)
Predictive ratings are based on a statistical model of some kind (such as Bradley-Terry or Elo). Models vary considerably. Some consider home field advantage and/or opponent strength; others do not. Some consider score (usually score difference or score ratio); others do not. Some recalculate opponent strength every time the opponent plays; others do not. Some require a recursive calculation; others do not. Power ratings are intended to be predictive and are similar to statistical models. The difference is that power ratings consider subjective factors. Most predictive models and power rating systems count recent results more than earlier results, and are therefore dynamic. Examples of predictive and/or power ratings include: Albyn Jones ratings for college soccer KRACH ratings for college hockey Sagarin ratings for various sports Massey ratings for various sports Elo ratings for world football Ron Kessler International Soccer ratings
An arbitrary or preferential rating or ranking is based on factors that have little to do with performance or strength. For example, the NCAA seeds its national tournaments by committee and considers factors that are arbitrary and preferential. A meta rating (or ranking) is a combination (sometimes an average) of ratings or rankings derived by different methods. The Bowl Championship Series (BCS) in college football uses a meta ranking. Pairwise rankings (under construction) Tournaments seedings / qualification for post-season play The selection and seeding of post-season tournaments can be done in a wide variety of ways. A seeding is a ranking, and it can be based on almost any of the ranking method described above. An interesting example of a system created specifically to seed tournaments is the HEAL rating system used in various high school sports in Maine. Many conferences and small leagues simply use standings, combined with tiebreakers such as head to head record and goal differential are often used. Seeding of the NAIA tournaments in soccer heavily on adjusted results (Longo ratings) although other factors are considered in the case of teams with similar ratings. The NCAA uses a complex system. Ultimately, selecting and seeding is done by committtee based, at least in part, on the following criteria (not listed in preferential order): Primary factors
> Won-loss record. > Strength of schedule/RPI. > Head-to-head competition. > Results against common opponents. > Results against teams already selected to participate in the championship. > Results against teams under consideration. Secondary factors: > Late-season performance. > Eligibility or availability of student-athletes. It is unclear exactly how the various factors are weighed. What is clear is that NCAA selection committees are not bound by any objective criteria or process. Ultimately, selection and seeding is done by committee on a basis known only to the committee. |
is an attribute associated with individual i.|
(Used by the US Chess Federation, among others.) Elo ratings change according to whether a team or player performs better or worse than expected. A new rating is calculated from an old rating according to the formula:
The win expectancy is given by:
The preceeding only works if a player already has a rating. A new player's
rating is given by:
Elo ratings were developed in 1959 by Arped Elo, a professor of physics at Marquette University and a former president of the American Chess Federation. They are based on the assumption of a bell-shaped curve (normal distribution) of ratings. |
is the sum of win expectancies
for each match
is the difference
in ratings:A comparison of selected rating systems
| rating system | type of system |
game result function |
calculation | other factors | |||||
| type | recursive? | dynamic? | HFA | OS | other | ||||
| RPI | merit | WP+OS | addition | no | no | no | yes | no | |
| Longo rating | merit | WP+TGS | table | no | no | yes | yes | no | |
| Albyn Jones rating | predictive | WL | formula | yes | yes | yes | yes | no | |
| Tennis (ATP, WTA) | merit | WL | addition | no | no | no | yes | yes | |
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FIDE Rating system international chess FIDE uses a relatively simple numerical system with an arbitrary scale. Results (percentage scores) are converted to rating differences by means of a simple table look-up. Table values are based on Elo-type calculations. The change in a player's rating due to a tournament result is given
by:
The development coefficient, k, stabilizes the ratings for established players. When K is 10 it takes about 75 games for a rating to change completely. When k is 25, it only takes about 30 games. |
TENNIS
| WTA Rankings women's tennis
WTA Rankings are a 52-week cumulative point system (published weekly), in which ranking points are the sum of round points and quality points. Round points are awarded depending upon how far a player advances in a tournament, as well as the level of the tournament and the prize money. Quality points are awarded for each victory and depend on the ranking of the opponent at the time the game is played. Only a player's 17 best tournaments are counted (for singles). Some examples of round points are shown in the abbreviated table below. Round Points (examples)
In addition, quality points are awarded for each win in a tournament
over a player ranked in the top 500 at the time of the game. The number
of quality points awarded depends on the loser's rank. Quality point examples
are shown below. Quality points are doubled for grand slam events.
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| ATP rankings men's tennis
ATP rankings are "merit-based", and award points depending on how far
a player advances in a tournament and the level of the tournament. The
ATP
Champions Race ranks players on a calendar-year basis. The ATP Entry
Ranking determines seeding in all tournaments. Both rankings are published
about 45 times a year.
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