# Elo System

## Das ELO-System

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Chess Ratings: A Deep DiveOn Chess. He reached an impressive classical rating of in As of June , Carlsen is the highest-rated player for classical and rapid time controls and second in blitz behind GM Hikaru Nakamura.

Each player's Elo rating is represented by a number that reflects that person's results in previous rated games.

After each rated game, their ratings are adjusted according to the outcome of the encounter. While people usually think of the Elo rating system as a way of measuring a player's absolute strength, you should note that this is not the case.

This system calculates the probable outcome of a person's games against other players. Calculating the probable outcome of chess games is one of the fascinating aspects of this rating system: it takes into consideration the fluctuations in a player's performance.

From time to time, we all have bad days when we play poorly. Even when we are at our best, we can still slip up and make a game-losing blunder.

Lower-rated players can still beat someone who is rated higher than them, and the Elo system calculates the probability of that happening.

However, if both players face each other in a match of multiple games, the player with the higher rating probably wins most of the games.

Another feature of this system is that the rating gap between the players dictates how many points they can win or lose.

Since a much higher rated player is expected to win, they do not receive a lot of points for a victory against a player rated much lower.

Their opponent also does not lose a significant amount of points for the defeat. In turn, when the lower-rated player wins, this achievement is considered much more significant, and that player's reward is more points added to their rating.

The higher-rated player, though, is penalized accordingly. To determine the exact amount of points a player would win or lose after a game, several complex mathematical calculations are needed.

Do not worry, though, because Chess. After every rated game, your rating is updated instantly. Almost all chess federations and websites around the world use the Elo rating system or a variation of it, such as the Glicko system.

This measurement of a player's strength has become the standard in the chess world, so it is the easiest way to assess someone's level of play. In addition, the Elo system is a statistical model that operates solely based on the outcomes of the games played.

An example may help to clarify. Suppose Player A has a rating of and plays in a five-round tournament. He loses to a player rated , draws with a player rated , defeats a player rated , defeats a player rated , and loses to a player rated The expected score, calculated according to the formula above, was 0.

Note that while two wins, two losses, and one draw may seem like a par score, it is worse than expected for Player A because their opponents were lower rated on average.

Therefore, Player A is slightly penalized. New players are assigned provisional ratings, which are adjusted more drastically than established ratings.

The principles used in these rating systems can be used for rating other competitions—for instance, international football matches.

See Go rating with Elo for more. The first mathematical concern addressed by the USCF was the use of the normal distribution. They found that this did not accurately represent the actual results achieved, particularly by the lower rated players.

Instead they switched to a logistic distribution model, which the USCF found provided a better fit for the actual results achieved.

The second major concern is the correct "K-factor" used. If the K-factor coefficient is set too large, there will be too much sensitivity to just a few, recent events, in terms of a large number of points exchanged in each game.

And if the K-value is too low, the sensitivity will be minimal, and the system will not respond quickly enough to changes in a player's actual level of performance.

Elo's original K-factor estimation was made without the benefit of huge databases and statistical evidence. Sonas indicates that a K-factor of 24 for players rated above may be more accurate both as a predictive tool of future performance, and also more sensitive to performance.

Certain Internet chess sites seem to avoid a three-level K-factor staggering based on rating range. The USCF which makes use of a logistic distribution as opposed to a normal distribution formerly staggered the K-factor according to three main rating ranges of:.

Currently, the USCF uses a formula that calculates the K-factor based on factors including the number of games played and the player's rating.

The K-factor is also reduced for high rated players if the event has shorter time controls. FIDE uses the following ranges: [20].

FIDE used the following ranges before July [21]. The gradation of the K-factor reduces ratings changes at the top end of the rating spectrum, reducing the possibility for rapid ratings inflation or deflation for those with a low K-factor.

This might in theory apply equally to an online chess site or over-the-board players, since it is more difficult for players to get much higher ratings when their K-factor is reduced.

In some cases the rating system can discourage game activity for players who wish to protect their rating. Beyond the chess world, concerns over players avoiding competitive play to protect their ratings caused Wizards of the Coast to abandon the Elo system for Magic: the Gathering tournaments in favour of a system of their own devising called "Planeswalker Points".

A more subtle issue is related to pairing. When players can choose their own opponents, they can choose opponents with minimal risk of losing, and maximum reward for winning.

In the category of choosing overrated opponents, new entrants to the rating system who have played fewer than 50 games are in theory a convenient target as they may be overrated in their provisional rating.

The ICC compensates for this issue by assigning a lower K-factor to the established player if they do win against a new rating entrant.

The K-factor is actually a function of the number of rated games played by the new entrant. Therefore, Elo ratings online still provide a useful mechanism for providing a rating based on the opponent's rating.

Its overall credibility, however, needs to be seen in the context of at least the above two major issues described — engine abuse, and selective pairing of opponents.

The ICC has also recently introduced "auto-pairing" ratings which are based on random pairings, but with each win in a row ensuring a statistically much harder opponent who has also won x games in a row.

With potentially hundreds of players involved, this creates some of the challenges of a major large Swiss event which is being fiercely contested, with round winners meeting round winners.

This approach to pairing certainly maximizes the rating risk of the higher-rated participants, who may face very stiff opposition from players below , for example.

This is a separate rating in itself, and is under "1-minute" and "5-minute" rating categories. Maximum ratings achieved over are exceptionally rare.

An increase or decrease in the average rating over all players in the rating system is often referred to as rating inflation or rating deflation respectively.

For example, if there is inflation, a modern rating of means less than a historical rating of , while the reverse is true if there is deflation.

Using ratings to compare players between different eras is made more difficult when inflation or deflation are present.

See also Comparison of top chess players throughout history. It is commonly believed that, at least at the top level, modern ratings are inflated.

For instance Nigel Short said in September , "The recent ChessBase article on rating inflation by Jeff Sonas would suggest that my rating in the late s would be approximately equivalent to in today's much debauched currency".

By when he made this comment, would only have ranked him 65th, while would have ranked him equal 10th. It has been suggested that an overall increase in ratings reflects greater skill.

The advent of strong chess computers allows a somewhat objective evaluation of the absolute playing skill of past chess masters, based on their recorded games, but this is also a measure of how computerlike the players' moves are, not merely a measure of how strongly they have played.

The number of people with ratings over has increased. Around there was only one active player Anatoly Karpov with a rating this high.

In Viswanathan Anand was only the 8th player in chess history to reach the mark at that point of time.

The current benchmark for elite players lies beyond One possible cause for this inflation was the rating floor, which for a long time was at , and if a player dropped below this they were stricken from the rating list.

As a consequence, players at a skill level just below the floor would only be on the rating list if they were overrated, and this would cause them to feed points into the rating pool.

By July it had increased to In a pure Elo system, each game ends in an equal transaction of rating points. If the winner gains N rating points, the loser will drop by N rating points.

This prevents points from entering or leaving the system when games are played and rated. However, players tend to enter the system as novices with a low rating and retire from the system as experienced players with a high rating.

Therefore, in the long run a system with strictly equal transactions tends to result in rating deflation. In , the USCF acknowledged that several young scholastic players were improving faster than the rating system was able to track.

As a result, established players with stable ratings started to lose rating points to the young and underrated players.

Several of the older established players were frustrated over what they considered an unfair rating decline, and some even quit chess over it.

Because of the significant difference in timing of when inflation and deflation occur, and in order to combat deflation, most implementations of Elo ratings have a mechanism for injecting points into the system in order to maintain relative ratings over time.

FIDE has two inflationary mechanisms. First, performances below a "ratings floor" are not tracked, so a player with true skill below the floor can only be unrated or overrated, never correctly rated.

Second, established and higher-rated players have a lower K-factor. Rating floors in the United States work by guaranteeing that a player will never drop below a certain limit.

This also combats deflation, but the chairman of the USCF Ratings Committee has been critical of this method because it does not feed the extra points to the improving players.

A possible motive for these rating floors is to combat sandbagging, i. Human—computer chess matches between Deep Blue versus Garry Kasparov and demonstrated that chess computers are capable of defeating even the strongest human players.

However, chess engine ratings are difficult to quantify, due to variable factors such as the time control and the hardware the program runs on.

Published engine rating lists such as CCRL are based on engine-only games on standard hardware configurations and are not directly comparable to FIDE ratings.

The Elo rating system is used in the chess portion of chess boxing. In order to be eligible for professional chess boxing, one must have an Elo rating of at least , as well as competing in 50 or more matches of amateur boxing or martial arts.

American college football used the Elo method as a portion of its Bowl Championship Series rating systems from to after which the BCS was replaced by the College Football Playoff.

The use of rating systems was effectively scrapped with the creation of the College Football Playoff in ; participants in the CFP and its associated bowl games are chosen by a selection committee.

In other sports, individuals maintain rankings based on the Elo algorithm. These are usually unofficial, not endorsed by the sport's governing body.

The World Football Elo Ratings is an example of the method applied to men's football. It is the official rating system of major organizations such as the Intercollegiate Tennis Association and World TeamTennis and is frequently used in segments on the Tennis Channel.

The algorithm analyzes more than 8 million match results from over , tennis players worldwide. On May 8, , Rafael Nadal — having won 46 consecutive sets in clay court matches — had a near-perfect clay UTR of One of the few Elo-based rankings endorsed by a sport's governing body is the FIFA Women's World Rankings , based on a simplified version of the Elo algorithm, which FIFA uses as its official ranking system for national teams in women's football.

In , Nate Silver, editor-in-chief of the statistical commentary website FiveThirtyEight , and Reuben Fischer-Baum produced Elo ratings for every National Basketball Association team and season through the season.

An Elo-based ranking of National Hockey League players has been developed. National Scrabble organizations compute normally distributed Elo ratings except in the United Kingdom , where a different system is used.

The North American Scrabble Players Association has the largest rated population of active members, numbering about 2, as of early Lexulous also uses the Elo system.

New players are assigned a rating of , with the best humans and bots rating over VogClub sets a new player's rating at Despite questions of the appropriateness of using the Elo system to rate games in which luck is a factor, trading-card game manufacturers often use Elo ratings for their organized play efforts.

However, the DCI abandoned this system in in favour of a new cumulative system of "Planeswalker Points", chiefly because of the above-noted concern that Elo encourages highly rated players to avoid playing to "protect their rating".

Similarly, Decipher, Inc. The Esports game Overwatch , the basis of the unique Overwatch League professional sports organization , uses a derivative of the Elo system to rank competitive players with various adjustments made between competitive seasons.

Nevertheless, it is common for players of ranked video games to refer to all ratings as an Elo. According to Lichess, the Elo system is outdated even by chess standards, with Glicko-2 now being used by a significant number of chess organisations.

Various online games use Elo ratings for player-versus-player rankings. Since , Golden Tee Live has rated players based on the Elo system. New players start at , with top players rating over The initial K-value was 30, but was changed to 5 in January , then changed to 15 in July Roblox introduced the Elo rating in The browser game Quidditch Manager uses the Elo rating to measure a team's performance.

RuneScape 3 was to use the Elo system for the rerelease of bounty hunter in In [55] [ circular reference ] an online gaming ladder called Clanbase [56] was launched, who used the Elo scoring system to rank teams.

The site later went offline in The Elo rating system has been used in soft biometrics , [59] which concerns the identification of individuals using human descriptions.

Comparative descriptions were utilized alongside the Elo rating system to provide robust and discriminative 'relative measurements', permitting accurate identification.

The Elo rating system has also been used in biology for assessing male dominance hierarchies, [60] and in automation and computer vision for fabric inspection.

Moreover, online judge sites are also using Elo rating system or its derivatives. For example, Topcoder is using a modified version based on normal distribution, [62] while Codeforces is using another version based on logistic distribution.

Elo rating system has also been noted in dating apps, such as in the matchmaking app Tinder , which uses a variant of the Elo rating system.

The Elo rating system was featured prominently in The Social Network during the algorithm scene where Mark Zuckerberg released Facemash. In the scene Eduardo Saverin writes mathematical formulas for the Elo rating system on Zuckerberg's dormitory room window.

Behind the scenes, the movie claims, the Elo system is employed to rank girls by their attractiveness. The equations driving the algorithm are shown briefly, written on the window; [67] however, they are slightly incorrect.

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After every game, the winning player takes points from the losing one. VogClub sets a new player's rating at If the game is a draw, the Gdax Verification players are assumed to have performed at nearly the same level. FIDE classifies tournaments into categories according to the average rating of the players. Although a player might perform significantly better or worse from one game to the next, Elo assumed that the mean value of the performances of any given player changes only slowly Stefan Raab Poker 2021 time. New players are assigned a Champions League Tipps of**Elo System**the best humans and bots rating over The Elo rating system was featured prominently in The Social Network during the algorithm scene where Mark Zuckerberg Gladiator Browsergame Facemash. Retrieved 3 July Both the average and the spread of ratings can be arbitrarily chosen. When players can choose their own opponents, they can choose opponents with minimal risk of losing, Wwe Aktuell maximum reward for winning.

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