Introduction
Most chess players are infatuated with their Elo rating and constantly monitor their rating after each chess game, but what exactly is an Elo rating and what is its significance in chess? The Elo rating system in chess is a fundamental component of competitive chess which is useful for many reasons but mainly because it allows chess players to measure their strength and progress in chess and it also allows chess players to easily find opponents that are closely matched in experience. The history and evolution of the Elo rating system as well as the calculations used to determine a chess players Elo rating in chess are some of the most interesting aspects of chess which will intrigue regular chess players as well as non-chess players. In this article I will cover everything you need to know about the Elo rating system in chess including its origins, evolution, how it is measured and much more.
The Origins And The Evolution Of The Elo Rating System In Chess
The Elo rating system in chess was initially developed in the 1960’s by a Hungarian American physics professor, Arpad Elo which is where the term Elo comes from and is the successor of the previously used Harkness rating system which was created by Kenneth Harkness. The Elo rating system is an improved version of the Harkness rating system which utilises a sophisticated mathematical framework for determining a chess players skill based on probabilities and a dynamically adjusting performance metric.
The Elo rating system in chess is the successor of the Harkness rating system that was developed by Kenneth Harkness during the 1950’s and later adopted by the USCF (united states chess federation). Kenneth Harkness was a chess organiser and former executive director and business manager of the USCF (united states chess federation) from 1952 to 1960. The Harkness rating system was initially developed to assess and assign a numerical value to chess players skills during rated chess games however the system had some limitations which impacted its ability to accurately determine the true skill level of chess players. Some of the main factors that contributed to the Harkness rating system’s inefficiencies as a rating system includes infrequent updates to chess players ratings due to the fact that it updated chess player ratings annually instead of after each chess game which is standard in the Elo rating system, sensitivity to the outcome of individual chess games which resulted in significant changes to chess player ratings and a complex mathematical method of measuring chess player ratings that had to be manually calculated after each chess game which ultimately resulted in an inability to accurately determine a chess players current skill level in real time. The Harkness rating system was also used primarily in the United States and lacked the adoption from the international chess community.
The Elo rating system was developed by Arpad Elo, who was a Hungarian American physics professor, highly skilled chess player and active participant in the USCF (united states chess federation) since its founding in 1939. The Elo rating system was introduced into mainstream chess and adopted by the USCF (united states chess federation) ten years after the release of the Harkness rating system during the 1960’s and was created using an even more sophisticated mathematical framework than was previously utilised in the Harkness rating system. Although the Elo rating systems method of calculating the rating of chess players was much more sophisticated than the Harkness rating systems it was also much more efficient and reliable. Elo ratings are calculated by incorporating mathematical formulas and algorithms which allows chess players to receive ratings that are much more accurate and up to date. One of the main characteristics of the Elo rating system is that much like the beliefs of its creator Arpad Elo, it assumes that a chess players true and current skill level is the sum of that chess players past performance and their current performance in rated chess games. For example, if a chess player has been consistently successful throughout their career in chess but goes through a period of playing chess at a level that is beneath their anticipated levels of success, their rating will drop by a set amount for each chess game depending on the rating of their opponent and the expected outcome of the game which makes it much easier to accurately determine an estimation of their true and current skill level. The Elo rating system was considered to be much fairer and accurate than the Harkness rating system and was later adopted by the world chess federation, FIDE, in 1970.
The Calculations Behind The Elo Rating System
Elo ratings are calculated by issuing chess players an initial rating and an expected score before a chess game. After the chess game chess players are then given an actual score and their Elo ratings are updated accordingly. There are numerous variations to how Elo ratings are calculated in chess depending on the criteria that needs to be met by each chess governing organisation, the most common Elo rating system is based on FIDE’s calculations however other chess governing organisations calculate Elo ratings differently and do not follow Arpad Elo’s methods exactly.
Before a chess game chess players are given a random Elo rating however in most cases, they are given an Elo rating of a thousand and an expected score based on their current estimated skill level which are essential for calculating their final Elo rating. The mathematical formula that’s used for working out a chess players expected score is as follows: E = 1 / 1 + 10(Rb – Ra) / 400 this formula is used to calculate the expected score of the example player A and switching the placement of the rating of player B with the rating of player A in the equation can be used to calculate the expected score of the example player B. The E represents the expected score of the player, Rb represents the initial given rating of player B and Ra represents the initial given rating of player A. The second formula which calculates the updating of each players rating is as follows: NR= Current Rating + K (actual score-expected score), the NR represents the new or updated rating of the player, and the K represents the K factor which is a constant that’s used to determine the impact of the result of the game on each chess players ratings. Each chess governing organisation uses a different number to represent the K factor, but it generally ranges from 10 to 32. A higher K factor results in a much more significant increase or decrease in ratings and is typically used in the chess games of less established chess players whereas a lower K factor results in a less significant increase or decrease in ratings and is typically used in the chess games of more established chess players.
FIDE uses a K factor of 10 for high rated chess players but they also utilise a tiered system depending on the rating of chess players to assign a K factor when calculating their rating increase or decrease. All chess players that are new to FIDE’s database until the completion of events with a total of 30 games under FIDE’s observation, and for chess players under the age of 18 that have maintained an Elo rating of under 2300 will have a K factor of 40 when calculating their new FIDE approved Elo rating, chess players that have consistently maintained an Elo rating of under 2400 will have a K factor of 20 when calculating their new FIDE approved Elo rating and chess players with any published rating of at least 2400 and at least 30 games played in previous events will have a K factor of 10 permanently applied to the calculation of their new FIDE approved Elo rating. The USCF (united states chess federation) used to implement a tiered system of assigning a K factor to calculate chess players ratings which were as follows: a K factor of 32 for chess players with a rating below 2100, a K factor of 24 for chess players with a rating between 2100 and 2400 and a K factor of 16 for chess players with a rating above 2400 however they now use a formula that calculates the K factor depending on the number of chess games played and the chess players rating whilst reducing the K factor for higher rated chess players in chess games with shorter time controls. Online chess gaming sites use various methods to calculate the rating of chess players whilst most use the Elo rating system, others consider it to be outdated and prefer to use more up to date rating systems such as Glicko-1 and Glicko-2 which is a rating system that was created by Mark Glickman.
What Are Performance ratings?
Performance ratings also known as special ratings are hypothetical ratings that are assigned to chess players based on the games played in a single event. For example, after competing in a chess tournament chess players can be assigned a specific performance rating based on the results of their performance during that tournament.
Some chess organisations use the following method to calculate the performance rating of chess players during official events: for each win add your opponent’s rating plus 400, for each loss add your opponent’s rating minus 400, lastly divide this sum by the number of games played during the event. For example, during an event consisting of 4 games played with 2 opponents with ratings of 2400 and 2300, with 2 wins and 2 losses from each player the following equations would be used for each player to determine their performance rating for the event, for the player with the rating of 2300: 2400+400+2400+400+2400-400+2400-400/4, for the player with the rating of 2400: 2300+400+2300+400+2300−400+2300−400/4. However formal and reputable organisations such as FIDE prefer to use a different formula to calculate the performance rating of chess players during events which is as follows: Performance rating= average of opponents’ rating + rating difference (dp). The rating difference in this formula is represented as (dp) and is based on a chess player’s percentage score (p) in an event which is used as a key in a lookup table. The (p) represents the number of points scored during the event divided by the number of games played. For example, a chess player competing in an event with three opponents with ratings of 2500, 2550 and 2600 would have an average opponents’ rating of 2500+2550+2600/3=2500, if the chess player won 3 out of 3 games and achieved 3 points the equation would be as follows: 3/3= 1, so therefore the chess players performance rating during the event would be 2550+1=2551.
What Are Ratings Inflation Vs Ratings Deflation In Chess?
The terms ratings inflation and ratings deflation are terms that express the increase and decrease of chess player ratings across the board. The term ratings deflation is used to express the fact that the average rating of chess players across the board are expected to increase over time whereas ratings inflation refers to the decrease of chess player ratings over time.
The average rating of chess players over time has been steadily increasing which means that we have been experiencing a period of ratings deflation and chess players are becoming more skilled as time progresses. The average playing strength of the most skilled chess players a hundred years ago is much lower than the playing strength of the most skilled chess players today which is a prime example of ratings deflation. However, the average playing strength of chess players can also decrease or show signs of stagnation, and both have occurred throughout history especially during the 33-year period from 1976 to 2009. The occurrence of ratings inflation and deflation in chess is one of the main reasons chess governing organisations implement different K factor constants for new and established chess players as a method of limiting the rapid increase or decrease of new chess player ratings after playing a certain amount of chess games and the rapid increase or decrease of established chess players ratings over time. Newer chess players are usually given a higher K factor constant to calculate their ratings until they have played around 30 chess games and established a performance baseline after which point their K factor constant is typically decreased to prevent their ratings from rising or falling significantly. On the other hand, higher rated chess players are typically given a lower K factor constant which prevents their rating from rising or falling significantly after a chess game.
During the late 1970’s Anatoly Karpov was the only active chess player with a rating as high as 2700 however as time has progressed this ceiling has decreased and during the early 1990’s eight chess players had achieved a rating of 2700 which includes Garry Kasparov, Anatoly Karpov, Nigel Short, Jan Timman, Vassily Ivanchuk, Boris Gelfand, Artur Yusupov, and Viswanathan Anand. The concept of ratings inflation and deflation in chess however seemingly only applies to humans as our computer counterparts have demonstrated their ability to beat even the highest rated chess players which was brought to the attention of the global chess community during the late 1990’s with the infamous DeepBlue vs Garry Kasparov chess match. The ratings of computers have continuously increased throughout history and are currently unbeatable to many of the highest rated chess players. The phenomenon of performance deflation can be seen in a range of sports as well as in many other occupational fields such as science, mathematics, and technology. For instance, before Roger Bannister ran a mile in under 4 minutes it was considered an impossible feat to achieve however after Roger Bannister broke this record more athletes began to demonstrate the ability to run faster. Technology is advancing at an unprecedented rate as was predicted by Gorden Moore which led to the introduction of the term Moore’s Law, much like the capabilities of athletes and the playing strength of chess players over time.
What Is The Normal Distribution Model Vs The Logistic Distribution Model And How Are They Used In Chess?
Normal and logistic distribution models are statistical tools that use data and mathematical calculations to map the distribution probability of possible outcomes based on a set of data which can be applied to an event such as a chess game. These models analyse the likelihood of a range of different outcomes taking place. Normal and logistic distribution models can be applied to a variety of studies.
In chess the normal and logistic distribution models are used in conjunction with the Elo rating system to calculate how much a chess players rating will increase or decrease after a chess game. Normal and logistic distribution models can be used to determine the probability of a chess player winning or losing a game based on the data collected about their playing strength using their previous performance in chess games or their estimated Elo rating and can be used to determine their expected score against future opponents. The Elo rating of a chess player is partly determined by comparing their expected score before a chess game and their actual score after the chess game has finished, if a chess player performs better than initially expected their Elo rating will increase much more than it would if they performed according to the expectations that the distribution models predicted. The normal distribution model is similar to the logistic distribution model as they both create similar patterns when charted on a graph, the only major difference between the two models is that the logistic distribution model can produce longer tails than the normal distribution model as the logistic distribution model is able to account for greater variances when measuring the probability of a range of outcomes.
In chess the logistic distribution model is preferred over the normal distribution model because the logistic distribution model is much better able to consider the unpredictable nature of a chess game as there are often instances where weaker chess players perform better than expected and stronger chess players perform worse than expected. Utilising the logistic distribution model in chess ensures that chess player ratings can increase in proportion to their performance especially in the event of an unexpected outcome. The logistic distribution model ensures that when updating chess player ratings, the expected scores of chess players have more room for variations and take into account anomalies that can and do frequently occur during chess games. In comparison the normal distribution model is less sensitive to anomalies that can occur during chess games which can result in smaller rating increases and decreases in the event of a chess player performing extremely well or extremely worse than expected. An accurate system of rating chess players is essential in chess because it limits the rate of both ratings inflation and deflation that’s unjustified by ensuring that chess players can establish an accurate performance baseline much faster and reduce as much overestimation or underestimation of chess players abilities as possible.
The Significance Of Elo Ratings In Professional Chess
Elo ratings are crucial in professional chess for many reasons which includes ensuring competitions are fair by pairing chess players with similar skill levels to compete against each other, to create distinctions between chess players of various skill levels which is essential for the awarding of titles, to provide a historical record of all chess players level of skill throughout history and much more.
Elo ratings are useful in professional chess for numerous reasons, some of the main reasons Elo ratings are used in professional chess games includes: they ensure that professional chess competitions are fair by pairing chess players of similar levels of skill to compete against each other, they provide chess players with a method of measuring their strength in chess and allow chess players to track their progress, Elo ratings can be used to create distinctions between chess players of various skill levels which is especially useful for awarding chess players with titles and they can be used to provide a historical record of all chess players level of skill throughout history which is essential for tasks such as measuring ratings inflation and deflation. Organisers of chess tournaments often use Elo ratings to create a structured event by pairing higher rated chess players against lower rated chess players during the starting rounds of a tournament to provide lower rated chess players with a chance to demonstrate their strength and potentially surprise their opponents and the tournament organisers with an unexpected score and to provide higher rated chess players with a chance to win points early in the event. Elo ratings also provide a global benchmark which can be used definitively to compare chess players from different countries around the world objectively.
The significance of Elo ratings in professional chess can also be attributed to the fact that it can positively impact the success of a chess players career. Higher Elo ratings tends to attract opportunities for sponsorship deals, brand commercials and advertisement deals, chances to participate in lucrative events, opportunities to teach chess online via streaming platforms such as YouTube and Twitch and the opportunity to win cash prizes in tournaments. In terms of creating legacy Elo ratings are crucial for establishing a historical record of a chess players achievements in chess which can also be useful when comparing chess players from different eras. Although the skill level of chess players throughout history has been steadily increasing having a historical record of a chess players ratings and skills during their career as a chess player can still be useful for educational purposes such as tracking the evolution of chess through time, studying the playing styles and strategies of different chess players from different eras and as a means of documenting the overall progression of chess for the global chess community as well as journalists and chess enthusiasts. The introduction of the Elo rating system in chess has significantly improved the functioning of the game which has resulted in a fairer and more efficient method of classifying and ranking chess players than was previously possible with older rating systems.
How The Elo Rating System Works In Different Chess Variants
The Elo rating system is used in numerous chess variants such as chess960, bullet chess, blitz chess, three check, bughouse chess, crazyhouse chess and atomic chess to assess the level of skill of players. The Elo rating system in each chess variant is similar but there are slight differences in how they are implemented in each chess variant as there are different winning criteria in each variant.
The Elo rating system was initially designed for standard chess games but has been adapted to accommodate the rules of numerous chess variants. Although many of the characteristics of the Elo rating system are used in chess variants there are slight alterations in the way that the Elo rating system is implemented in variants of chess which is mainly because the rules that govern many chess variants differs significantly from the rules that govern standard chess. Chess variants that have shorter time controls such as bullet, blitz and rapid chess typically use a higher K factor constant to update chess player ratings since there is a higher chance that blunders and mistakes will be made during the game, chess player ratings can rise or fall dramatically because of this. Chess variants such as three check chess, king of the hill chess, and atomic chess that have unique winning criteria will usually have an alternative method of calculating the expected score of chess players to accommodate for the unique and often challenging winning criteria that is required within these chess variants. The Elo rating system’s formula for updating chess player ratings differs the most in chess variants with unique win conditions such as three check chess, king of the hill chess and atomic chess and tends to result in much more dramatic rating increase and decreases much like the chess variants with shorter time controls because of the unpredictable nature of these games.
Chess variants that require a team to play such as Bughouse chess and business chess utilise the Elo rating system on an individual as well as on a collective basis. Teams and individual players performance are assessed and assigned an Elo rating in multi-player chess variants which is based on the sum of the standard or other chess variant rating of the players within a team. For instance, a team that consists of a group of players that each have high Elo ratings in standard or other variants of chess will result in a higher Elo rating for that team and a team that consists of a group of players that each have low Elo ratings in standard or other variants of chess will result in a lower Elo rating for that team. The Elo rating system in chess variants that require a team works similarly to how it works in single player chess in the sense that if a lower rated team defeats a team that has a higher Elo rating, the Elo rating of the lower rated team will increase in proportion to the significance of the win and the Elo rating of the team with a higher Elo rating will decrease in the same proportion.
How The Elo Rating System Is Used In Different Sports
The Elo rating system is used in various sports and competitive games due to its effectiveness, simplicity, and its ability to objectively assess the strength of players based on specific criteria and their players performance during games. The Elo rating system has been adopted by various sports outside of chess such as baseball, basketball, tennis, soccer/football, table tennis/ping-pong, Go as well as a range of E-sports and card games.
Although the Elo rating system was originally designed for chess it is used in numerous chess variants, and it has also been adopted by numerous other sports such as baseball, basketball, tennis, soccer/football, table tennis/ping pong, hockey, rugby, pool, handball, Go and a range of E-sports and card games. The Elo rating system is the rating system of choice for many zero-sum competitive sports because of its effectiveness, simplicity, and its ability to objectively measure and assess the strength of players based on specific criteria and players performance during games. The Elo rating system in many team-oriented sports is implemented in the same way that it is implemented in team-oriented chess variants such as Bughouse chess and business chess in the sense that the rating of teams will increase or decrease based on the outcome of matches. Factors such as the number of goals scored in team sports such as football/soccer, American football, and basketball will also impact the rating increase or decrease of the team. In single player sports such as tennis and table tennis/ping pong the rating system is implemented in the same way it is implemented in standard chess where the rating of players is determined by factors such as the outcome of the match and players performance during the game. Factors such as the rating difference between players will have a significant impact on the rating increase or decrease of the player much like in standard chess.
Many card games also use the Elo rating system or a modified version of the Elo rating system to rank players based on their skill level and performance as well as to match opponents of similar skill levels to create games that are both challenging and balanced. Some card games also implement ratings decay which is similar to ratings inflation in chess to ensure that players ratings are accurately assigned. The main difference between ratings inflation in chess and ratings decay in card games is that ratings inflation in chess is a natural by-product of a decrease in the average skill of chess players that are actively competing against each other in FIDE approved and other officially recognised games and events whereas ratings decay is an internal mechanism that automatically reduces a player’s ratings after a certain period of inactivity. Players that are inactive for extended periods of time will experience a decrease in their ratings to ensure that player ratings are a true reflection of their current skill level. The Elo rating system that is used in card games is in some instances modified to accommodate for special rules and winning criteria similar to how the Elo rating system may be altered in certain variants of chess.
How Technology Such As Online Chess And AI Is Reshaping The Elo Rating System
The introduction of online chess gaming sites and artificial intelligence have played a significant role in reshaping many of the components that make up the Elo rating system such as the expected scores and outcome of chess games, the frequency of rating updates, the K factor constants that are used to increase or decrease player ratings and much more. Online chess gaming sites have made chess much more accessible which has increased the number of chess players that are competing against each other and therefore Elo ratings have become reflective of a diverse and global pool of chess players.
Technology and artificial intelligence have had a significant impact on the way chess is played, the training resources available to chess players and the accessibility of chess that is reshaping many of the components that make up the Elo rating system such as the expected scores and outcome of chess games, the frequency of rating updates, the K factor constants that are used to increase or decrease the rating of chess players as well as the educational resources that are available to chess players around the world. Many of the components that play a key role in determining how a chess player will be rated such as the K factor constant, the frequency of rating updates and the expected score and outcome of chess games have been impacted because of the increase in the number of people that have access to chess. Online chess gaming sites have become extremely popular over time which has led to a larger, and more diverse pool of chess players that other chess players around the world are able to compete against. In the past Elo ratings were the result of a localised pool of chess players whereas nowadays Elo ratings are the result of a much larger and diverse pool of chess players. The rate of ratings deflation is a byproduct of a larger and more diverse pool of chess players and has increased in line with the availability of online chess gaming sites.
Most online chess gaming sites that utilise the Elo rating system assign higher K factor constants for newer chess players that impact the chess games sensitivity to wins and losses which leads to significant rating increase and decreases for players and lower K factor constants for higher rated chess players that are less sensitive to wins and losses during chess games. Chess player ratings are also updated much more frequently on online chess gaming sites and chess games are typically between chess players from different countries around the world as a result the rating of chess players online are a much more accurate representation of a chess players current playing strength worldwide. The playing strength of artificial intelligence has also improved dramatically over the years which is partly due to artificial intelligence having access to the global chess community in addition to AI’s self-learning capabilities. Online chess gaming sites have become a rich training ground for artificial intelligence which can also benefit chess players that are willing to play against the computer. Artificial intelligence has demonstrated immense skill in chess since the 90’s with the most notable example being the infamous match in 1996 and 1997 between DeepBlue and the former world chess champion Garry Kasparov. Chess players that have attained extremely high Elo ratings such as Magnus Carlsen can benefit immensely by playing against artificial intelligence as there is much more to gain and less to lose in terms of Elo rating increases and decreases from playing against higher rated chess players even if they are non-human.
Conclusion
The Elo rating system is a fundamental component of chess and has been instrumental in the evolution of chess since its introduction into chess by Arpad Elo in 1960. The effectiveness and simplicity of the Elo rating system has led to it being adopted in numerous sports such as tennis, table tennis/ping pong, baseball, basketball, football/soccer, rugby, hockey, pool and Go as well as chess variants such as chess960, three check chess, bughouse chess, crazyhouse chess, business chess, king of the hill chess and atomic chess. The Elo rating system is used by many chess organisations to rank players based on their performance during chess games based on criteria such as the difference in the level of skill of opponents, the expected outcome of the game and the actual outcome of the game. The formulas that are used by each chess governing organisation differs slightly depending on factors such as the K factor constant that’s assigned to players and the method used to measure the expected outcome of the game as some may use the normal distribution model and others may use the logistic distribution model. The Elo rating system however has been fundamental in professional as well as casual chess because it has allowed chess players to tracking their progress and it has also provided a way of objectively measuring their performance during chess games.
