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The 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.

The Elo system was invented as an improved chess rating system, but today it is also used in many other games. It is also used as a rating system for multiplayer competition in a number of video games,^[1] and has been adapted to team sports including association football, American college football, basketball, and Major League Baseball.

Each player has a rating, which is a number. A higher number indicates a better player, based on their results against other rated players. The winner of a contest between two players gains a certain number of points in his rating and the losing player loses the same amount. The number of points won or lost in a contest depends on the difference in the ratings of the players, so a player will gain more points by beating a higher-rated player than by beating a lower-rated player. In chess, for instance, if one player is rated 100 points higher than the other player, he is expected to win about five games out of eight, and the rating changes reflect that. Over a series of games, if a player does better than expected, based on the ratings (his compared to his opponents), his rating will go up.

History[link]

Arpad Elo was a master-level chess player and an active participant in the United States Chess Federation (USCF) from its founding in 1939.^[2] The USCF used a numerical ratings system, devised by Kenneth Harkness, to allow members to track their individual progress in terms other than tournament wins and losses. The Harkness system was reasonably fair, but in some circumstances gave rise to ratings which many observers considered inaccurate. On behalf of the USCF, Elo devised a new system with a more sound statistical basis.

Elo's system replaced earlier systems of competitive rewards with a system based on statistical estimation. Rating systems for many sports award points in accordance with subjective evaluations of the 'greatness' of certain achievements. For example, winning an important golf tournament might be worth an arbitrarily chosen five times as many points as winning a lesser tournament.

A statistical endeavor, by contrast, uses a model that relates the game results to underlying variables representing the ability of each player.

Elo's central assumption was that the chess performance of each player in each game is a normally distributed random variable. 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 over time. Elo thought of a player's true skill as the mean of that player's performance random variable.

A further assumption is necessary, because chess performance in the above sense is still not measurable. One cannot look at a sequence of moves and say, "That performance is 2039." Performance can only be inferred from wins, draws and losses. Therefore, if a player wins a game, he is assumed to have performed at a higher level than his opponent for that game. Conversely if he loses, he is assumed to have performed at a lower level. If the game is a draw, the two players are assumed to have performed at nearly the same level.

Elo did not specify exactly how close two performances ought to be to result in a draw as opposed to a win or loss. And while he thought it is likely that each player might have a different standard deviation to his performance, he made a simplifying assumption to the contrary.

To simplify computation even further, Elo proposed a straightforward method of estimating the variables in his model (i.e., the true skill of each player). One could calculate relatively easily, from tables, how many games a player is expected to win based on a comparison of his rating to the ratings of his opponents. If a player won more games than he was expected to win, his rating would be adjusted upward, while if he won fewer games than expected his rating would be adjusted downward. Moreover, that adjustment was to be in exact linear proportion to the number of wins by which the player had exceeded or fallen short of his expected number of wins.

From a modern perspective, Elo's simplifying assumptions are not necessary because computing power is inexpensive and widely available. Moreover, even within the simplified model, more efficient estimation techniques are well known. Several people, most notably Mark Glickman, have proposed using more sophisticated statistical machinery to estimate the same variables. On the other hand, the computational simplicity of the Elo system has proven to be one of its greatest assets. With the aid of a pocket calculator, an informed chess competitor can calculate to within one point what his next officially published rating will be, which helps promote a perception that the ratings are fair.

Implementing Elo's scheme[link]

The USCF implemented Elo's suggestions in 1960,^[3] and the system quickly gained recognition as being both more fair and accurate than the Harkness rating system. Elo's system was adopted by the World Chess Federation (FIDE) in 1970. Elo described his work in some detail in the book The Rating of Chessplayers, Past and Present, published in 1978.

Subsequent statistical tests have suggested that chess performance is almost certainly not distributed as a normal distribution, as weaker players have significantly (but not highly significantly) greater winning chances than Elo's model predicts. Therefore, the USCF and some chess sites use a formula based on the logistic distribution. Significant statistical anomalies have also been found when using the logistic distribution in chess.^[4] FIDE continues to use the normal distribution. The normal and logistic distribution points are, in a way, arbitrary points in a spectrum of distributions which would work well. In practice both of these distributions work very well for a number of different games.

Different ratings systems[link]

The phrase "Elo rating" is often used to mean a player's chess rating as calculated by FIDE. However, this usage is confusing and often misleading, because Elo's general ideas have been adopted by many different organizations, including the USCF (before FIDE), the Internet Chess Club (ICC), Yahoo! Games, and the now-defunct Professional Chess Association (PCA). Each organization has a unique implementation, and none of them precisely follows Elo's original suggestions. It would be more accurate to refer to all of the above ratings as Elo ratings, and none of them as the Elo rating.

Instead one may refer to the organization granting the rating, e.g. "As of August 2002, Gregory Kaidanov had a FIDE rating of 2638 and a USCF rating of 2742." It should be noted that the Elo ratings of these various organizations are not always directly comparable. For example, someone with a FIDE rating of 2500 will generally have a USCF rating near 2600 and an ICC rating in the range of 2500 to 3100.

FIDE ratings[link]

For top players, the most important rating is their FIDE rating. Since July 2009, FIDE issues a ratings list once every two months.

The following analysis of the November FIDE rating list gives a rough impression of what a given FIDE rating means:

• 5839 players had an active rating between 2200 and 2299, and are usually associated with the Candidate Master title.
• 2998 players had an active rating between 2300 and 2399, and are usually associated with the FIDE Master title.
• 1382 players had an active rating between 2400 and 2499, most of whom had either the International Master or the International Grandmaster title.
• 587 players had an active rating between 2500 and 2599, most of whom had the International Grandmaster title
• 178 players had an active rating between 2600 and 2699, all but one of whom had the International Grandmaster title
• 42 players had an active rating between 2700 and 2799
• 5 active players had a rating over 2800: Magnus Carlsen, Veselin Topalov, Viswanathan Anand, Vladimir Kramnik and Levon Aronian.

November 2011 marked the first time four players had a rating above 2800. The highest ever FIDE rating was 2851, which Garry Kasparov had on the July 1999 and January 2000 lists. A list of highest ever rated players is at Methods for comparing top chess players throughout history.

Performance rating[link]

Performance Rating is a hypothetical rating that would result from the games of a single event only. Some chess organizations use the "algorithm of 400" to calculate performance rating. According to this algorithm, performance rating for an event is calculated by taking (1) the rating of each player beaten and adding 400, (2) the rating of each player lost to and subtracting 400, (3) the rating of each player drawn, and (4) summing these figures and dividing by the number of games played. This can be expressed by the following formula:

Performance rating = [(Total of opponents' ratings + 400 * (Wins - Losses)) / Games].

This is a simplification because it doesn't take account of k-factors. But it offers an easy way to get an estimate of PR (Performance Rating).

FIDE, however, calculates performance rating by means of the formula: Opponents' Rating Average + Rating Difference. Rating Difference Failed to parse (Missing texvc executable; please see math/README to configure.): d_p

is based on a player's tournament percentage score Failed to parse (Missing texvc executable; please see math/README to configure.): p

, which is then used as the key in a lookup table where Failed to parse (Missing texvc executable; please see math/README to configure.): p

is simply the number of points scored divided by the number of games played. Note that, in case of a perfect or no score Failed to parse (Missing texvc executable; please see math/README to configure.): d_p
is indeterminate. The full table 

can be found in the FIDE handbook online. A simplified version of this table is on the right.

FIDE tournament categories[link]

FIDE classifies tournaments into categories according to the average rating of the players. Each category is 25 rating points wide. Category 1 is for an average rating of 2251 to 2275, category 2 is 2276 to 2300, etc. For women's tournaments, the categories are 200 rating points lower, so a Category 1 is an average rating of 2051 to 2075, etc.^[5] The highest rated tournaments have been category 22, with an average from 2776 to 2800. The top categories are in the table.

Live ratings[link]

FIDE updates its ratings list every two months. In contrast, the unofficial "Live ratings" calculate the change in players' ratings after every game. These Live ratings are based on the previously published FIDE ratings, so a player's Live rating is intended to correspond to what the FIDE rating would be if FIDE were to issue a new list that day.

Although Live ratings are unofficial, interest arose in Live ratings in August/September 2008 when five different players took the "Live" No. 1 ranking.^[6]

The unofficial live ratings were published and maintained by Hans Arild Runde at the Live Rating website until August 2011. Another website 2700.com has been maintained since May 2011 by Artiom Tsepotan. Both websites cover players over 2700 only.

Currently, the #1 spot in both the official FIDE rating list and the live rating list is taken by Magnus Carlsen.

United States Chess Federation ratings[link]

The United States Chess Federation (USCF) uses its own classification of players:^[7]

• 2400 and above: Senior Master
• 2200–2399 plus 300 games above 2200: Original Life Master^[8]
• 2200–2399: National Master
• 2000–2199: Expert
• 1800–1999: Class A
• 1600–1799: Class B
• 1400–1599: Class C
• 1200–1399: Class D
• 1000–1199: Class E
• 800–999: Class F
• 600–799: Class G
• 400–599: Class H
• 200–399: Class I
• 100–199: Class J

In general, 1000 is considered a bright beginner. In 2007, the median rating of all USCF members was 657.^[9]

The K factor, in the USCF rating system, can be estimated by dividing 800 by the effective number of games a player's rating is based on (Ne) plus the number of games the player completed in a tournament (m).^[10]

Failed to parse (Missing texvc executable; please see math/README to configure.): K = 800 / (Ne + m)\,

Rating floors[link]

The USCF maintains an absolute ratings floor of 100 for all ratings. Thus, no member can have a rating below 100, no matter their performance at USCF sanctioned events. However, players can have higher individual absolute ratings floors, calculated using the following formula:

Failed to parse (Missing texvc executable; please see math/README to configure.): AF = min(100+4N_W+2N_D+N_R , 150)

where Failed to parse (Missing texvc executable; please see math/README to configure.): N_W

is the number of rated games won, Failed to parse (Missing texvc executable; please see math/README to configure.): N_D
is the number of rated games drawn, and Failed to parse (Missing texvc executable; please see math/README to configure.): N_R
is the number of events in which the player completed three or more rated games.

Higher rating floors exist for experienced players who have achieved significant ratings. Such higher rating floors exist, starting at ratings of 1200 in 100 point increments up to 2100 (1200, 1300, 1400, ..., 2100). A player's rating floor is calculated by taking their peak rating, subtracting 200 points, and then rounding down to the nearest rating floor. For example, a player who has reached a peak rating of 1464 would have a rating floor of 1464 − 200 = 1264, which would be rounded down to 1200. Under this scheme, only Class C players and above are capable of having a higher rating floor than their absolute player rating. All other players would have a floor of at most 150.

There are two ways to achieve higher rating floors other than under the standard scheme presented above. If a player has achieved the rating of Original Life Master, his or her rating floor is set at 2200. The achievement of this title is unique in that no other recognized USCF title will result in a new floor. For players with ratings below 2000, winning a cash prize of $2,000 or more raises that player's rating floor to the closest 100-point level that would have disqualified the player for participation in the tournament. For example, if a player won $4,000 in a 1750 and under tournament, the player would now have a rating floor of 1800.

Ratings of computers[link]

Since 2005–2006, human-computer chess matches have demonstrated that chess computers are capable of defeating even the strongest human players (Deep Blue versus Garry Kasparov). However ratings of computers are difficult to quantify. There have been too few games under tournament conditions to give computers or software engines an accurate rating.^[11] Also, for chess engines, the rating is dependent on the machine a program runs on.

For some ratings estimates, see Chess Engine.

Theory[link]

Mathematical details[link]

Performance can't be measured absolutely; it can only be inferred from wins, losses, and draws against other players. A player's rating depends on the ratings of his or her opponents, and the results scored against them. The relative difference in rating between two players determines an estimate for the expected score between them. Both the average and the spread of ratings can be arbitrarily chosen. Elo suggested scaling ratings so that a difference of 200 rating points in chess would mean that the stronger player has an expected score (which basically is an expected average score) of approximately 0.75, and the USCF initially aimed for an average club player to have a rating of 1500.

A player's expected score is his probability of winning plus half his probability of drawing. Thus an expected score of 0.75 could represent a 75% chance of winning, 25% chance of losing, and 0% chance of drawing. On the other extreme it could represent a 50% chance of winning, 0% chance of losing, and 50% chance of drawing. The probability of drawing, as opposed to having a decisive result, is not specified in the Elo system. Instead a draw is considered half a win and half a loss.

If Player A has true strength Failed to parse (Missing texvc executable; please see math/README to configure.): R_A

and Player B has true strength Failed to parse (Missing texvc executable; please see math/README to configure.): R_B

, the exact formula (using the logistic curve) for the expected score of Player A is

Failed to parse (Missing texvc executable; please see math/README to configure.): E_A = \frac 1 {1 + 10^{(R_B - R_A)/400}}.

Similarly the expected score for Player B is

Failed to parse (Missing texvc executable; please see math/README to configure.): E_B = \frac 1 {1 + 10^{(R_A - R_B)/400}}.

This could also be expressed by

Failed to parse (Missing texvc executable; please see math/README to configure.): E_A = \frac{Q_A}{Q_A + Q_B}

and

Failed to parse (Missing texvc executable; please see math/README to configure.): E_B = \frac{Q_B}{Q_A + Q_B}

where Failed to parse (Missing texvc executable; please see math/README to configure.): Q_A = 10^{R_A/400}

and Failed to parse (Missing texvc executable; please see math/README to configure.): Q_B = 10^{R_B/400}

. Note that in the latter case, the same denominator applies to both expressions. This means that by studying only the numerators, we find out that the expected score for player A is Failed to parse (Missing texvc executable; please see math/README to configure.): Q_A/Q_B

times greater than the expected score for player B. It then follows that for each 400 rating points of advantage over the opponent, the chance of winning is magnified ten times in comparison to the opponent's chance of winning.

Also note that Failed to parse (Missing texvc executable; please see math/README to configure.): E_A + E_B = 1 . In practice, since the true strength of each player is unknown, the expected scores are calculated using the player's current ratings.

When a player's actual tournament scores exceed his expected scores, the Elo system takes this as evidence that player's rating is too low, and needs to be adjusted upward. Similarly when a player's actual tournament scores fall short of his expected scores, that player's rating is adjusted downward. Elo's original suggestion, which is still widely used, was a simple linear adjustment proportional to the amount by which a player overperformed or underperformed his expected score. The maximum possible adjustment per game (sometimes called the K-value) was set at K = 16 for masters and K = 32 for weaker players.

Supposing Player A was expected to score Failed to parse (Missing texvc executable; please see math/README to configure.): E_A

points but actually scored Failed to parse (Missing texvc executable; please see math/README to configure.): S_A
points. The formula for updating his rating is

Failed to parse (Missing texvc executable; please see math/README to configure.): R_A^\prime = R_A + K(S_A - E_A).

This update can be performed after each game or each tournament, or after any suitable rating period. An example may help clarify. Suppose Player A has a rating of 1613, and plays in a five-round tournament. He loses to a player rated 1609, draws with a player rated 1477, defeats a player rated 1388, defeats a player rated 1586, and loses to a player rated 1720. His actual score is (0 + 0.5 + 1 + 1 + 0) = 2.5. His expected score, calculated according to the formula above, was (0.506 + 0.686 + 0.785 + 0.539 + 0.351) = 2.867. Therefore his new rating is (1613 + 32· (2.5 − 2.867)) = 1601, assuming that a K factor of 32 is used.

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 his opponents were lower rated on average. Therefore he is slightly penalized. If he had scored two wins, one loss, and two draws, for a total score of three points, that would have been slightly better than expected, and his new rating would have been (1613 + 32· (3 − 2.867)) = 1617.

This updating procedure is at the core of the ratings used by FIDE, USCF, Yahoo! Games, the ICC, and FICS. However, each organization has taken a different route to deal with the uncertainty inherent in the ratings, particularly the ratings of newcomers, and to deal with the problem of ratings inflation/deflation. 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.

Elo ratings have also been applied to games without the possibility of draws, and to games in which the result can also have a quantity (small/big margin) in addition to the quality (win/loss). See go rating with Elo for more.

Mathematical issues[link]

There are three main mathematical concerns relating to the original work of Professor Elo, namely the correct curve, the correct K-factor, and the provisional period crude calculations.

Most accurate distribution model[link]

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 by particularly the lower rated players. Instead they switched to a logistical distribution model, which the USCF found provided a better fit for the actual results achieved. FIDE still uses the normal distribution as the basis for rating calculations as suggested by Elo himself.^[12]

Most accurate K-factor[link]

The second major concern is the correct "K-factor" used. The chess statistician Jeff Sonas believes that the original K=10 value (for players rated above 2400) is inaccurate in Elo's work. 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. Too low a K-value, and 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 2400) may be more accurate both as a predictive tool of future performance, and also more sensitive to performance.^[13]

Certain Internet chess sites seem to avoid a three-level K-factor staggering based on rating range. For example the ICC seems to adopt a global K=32 except when playing against provisionally rated players. The USCF (which makes use of a logistic distribution as opposed to a normal distribution) has staggered the K-factor according to three main rating ranges of:

• Players below 2100 -> K factor of 32 used
• Players between 2100 and 2400 -> K factor of 24 used
• Players above 2400 -> K factor of 16 used

FIDE uses the following ranges:^[14]

• K = 30 (was 25) for a player new to the rating list until s/he has completed events with a total of at least 30 games.^[15]
• K = 15 as long as a player's rating remains under 2400.
• K = 10 once a player's published rating has reached 2400, and s/he has also completed events with a total of at least 30 games. Thereafter it remains permanently at 10.

In over-the-board chess, the staggering of the K-factor is important to ensure minimal inflation at the top end of the rating spectrum. This assumption might in theory apply equally to an online chess server, as well as a standard over-the-board chess organisation such as FIDE or USCF. In theory, it would make it harder for players to get much higher ratings if their K-factor was reduced when they got over 2400 rating. However, the ICC's help on K-factors indicates^[16] that it may simply be the choosing of opponents that enables 2800+ players to further increase their rating quite easily. This would seem to hold true, for example, if one analysed the games of a grandmaster on the ICC: one can find a string of games of opponents who are all over 3100. In over-the-board chess, it would only be in very high level all-play-all events that this player would be able to find a steady stream of 2700+ opponents – in at least a category 15+ FIDE event. A category 10 FIDE event would mean players are restricted in rating between 2476 to 2500. However, if the player entered normal Swiss-paired open over-the-board chess tournaments, he would likely meet many opponents less than 2500 FIDE on a regular basis. A single loss or draw against a player rated less than 2500 would knock the GM's FIDE rating down significantly.

Even if the K-factor was 16, and the player defeated a 3100+ player several games in a row, his rating would still rise quite significantly in a short period of time, due to the speed of blitz games, and hence the ability to play many games within a few days. The K-factor would arguably only slow down the increases that the player achieves after each win. The evidence given in the ICC K-factor article relates to the auto-pairing system, where the maximum ratings achieved are seen to be only about 2500. So it seems that random-pairing as opposed to selective pairing is the key for combatting rating inflation at the top end of the rating spectrum, and possibly only to a much lesser extent, a slightly lower K-factor for a player >2400 rating.

Practical issues[link]

Game activity versus protecting one's rating[link]

This section has multiple issues. Please help improve it or discuss these issues on the talk page. It needs additional citations for verification. Tagged since March 2008. It may contain original research. Tagged since March 2008. It contains weasel words: vague phrasing that often accompanies biased or unverifiable information. Tagged since March 2008.

In general the Elo system has increased the competitive climate for chess and inspired players for further study and improvement of their game.^{[citation needed]} However, in some cases ratings can discourage game activity for players who wish to "protect their rating".

Examples:

1. Players may choose their events or opponents more carefully where possible.
2. If a player is in a Swiss tournament and loses a couple of games in a row, they may feel the need to abandon the tournament in order to avoid any further rating "damage".
3. Junior players who may have high provisional ratings might play less than they would because of rating concerns.

In these examples, the rating "agenda" can sometimes conflict with the agenda of promoting chess activity and rated games.^[17]

Interesting from the perspective of preserving high Elo ratings versus promoting rated game activity is a recent proposal by British Grandmaster John Nunn regarding qualifiers based on Elo rating for a World championship model.^[18] Nunn highlights in the section on "Selection of players", that players not only be selected by high Elo ratings, but also their rated game activity. Nunn clearly separates the "activity bonus" from the Elo rating, and only implies using it as a tie-breaking mechanism.

Outside the chess world, concerns over players avoiding competitive play to protect their ratings, often referred to as "sitting on rating", are the main reason Wizards of the Coast has given for abandoning the Elo system for Magic: the Gathering tournaments in favour of a system of their own devising called "Planeswalker Points".^[19][20]

Selective pairing[link]

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. Such a luxury of being able to hand-pick your opponents is not present in Over-the-Board Elo type calculations, and therefore this may account strongly for the ratings on the ICC using Elo which are well over 2800.

Particular examples of 2800+ rated players choosing opponents with minimal risk and maximum possibility of rating gain include: choosing computers that they know they can beat with a certain strategy; choosing opponents that they think are over-rated; or avoiding playing strong players who are rated several hundred points below them, but may hold chess titles such as IM or GM. In the category of choosing over-rated 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 3000, for example. This is a separate rating in itself, and is under "1-minute" and "5-minute" rating categories. Maximum ratings achieved over 2500 are exceptionally rare.

Ratings inflation and deflation[link]

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 2500 means less than a historical rating of 2500, while the reverse is true if there is deflation. Using ratings to compare players between different eras is made more difficult when inflation and deflation is present. (See also Greatest chess player of all time.)

It is commonly believed that, at least at the top level, modern ratings are inflated. For instance Nigel Short said in September 2009, "The recent ChessBase article on rating inflation by Jeff Sonas would suggest that my rating in the late 1980s would be approximately equivalent to 2750 in today's much debauched currency".^[21] (Short's highest rating in the 1980s was 2665 in July 1988, which was equal third in the world. When he made this comment, 2665 would have ranked him 65th, while 2750 would have ranked him equal 10th. In the March 2012 FIDE rating list, 2665 would have ranked him equal 83rd, while 2750 would have ranked him 14th.)

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.^[22]

The number of people with ratings over 2700 has increased. Around 1979 there was only one active player (Anatoly Karpov) with a rating this high. This increased to 15 players in 1994, while 33 players have this rating in 2009, which has made this top echelon of chess mastery less exclusive. One possible cause for this inflation was the rating floor, which for a long time was at 2200, 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.^[22] In the November 2011 FIDE rating list, there were 47 players with ratings over 2700. In July 2000 the average rating of the top 100 was 2644. By November 2011 it had increased to 2701.^[23]

In 1995, the USCF experienced that several young scholastic players were improving faster than what 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.^[24]

Combating deflation[link]

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. New players have a K=30, which drops to K=15 after 30 played games, and to K=10 when the player reaches 2400.^[25]

The current system in the United States includes a bonus point scheme which feeds rating points into the system in order to track improving players, and different K-values for different players.^[24] Some methods, used in Norway for example, differentiate between juniors and seniors, and use a larger K factor for the young players, even boosting the rating progress by 100% for when they score well above their predicted performance.^[26]

Rating floors in the USA 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.e. deliberate lowering of ratings to be eligible for lower rating class sections and prizes.^[24]

Other chess rating systems[link]

• Ingo system, designed by Anton Hoesslinger, used in Germany 1948-1992 (Harkness 1967:205–6).
• Harkness System, invented by Kenneth Harkness, who published it in 1956 (Harkness 1967:185–88).
• British Chess Federation Rating System, published in 1958, now termed the ECF grading system.
• Correspondence Chess League of America Rating System (now uses Elo).
• Glicko rating system
• Chessmetrics
• In November 2005, the Xbox Live online gaming service proposed the TrueSkill ranking system that is an extension of the Glicko rating system to multi-player and multi-team games.

Elo ratings in games other than chess[link]

American Collegiate Football uses the Elo method as a portion of its Bowl Championship Series rating systems. Jeff Sagarin of USA Today publishes team rankings for most American sports, including Elo system ratings for College Football. The NCAA uses his Elo ratings as part of a formula to determine the annual participants in the College Football National Championship Game.

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 2,000 as of early 2011. Lexulous also uses the Elo system.

The popular First Internet Backgammon Server calculates ratings based on a modified Elo system. New players are assigned a rating of 1500, with the best humans and bots rating over 2000. The same formula has been adopted by several other backgammon sites, such as Play65, DailyGammon, GoldToken and VogClub. VogClub sets a new player's rating at 1600.

The European Go Federation adopted an Elo based rating system initially pioneered by the Czech Go Federation. The Groshin's Score an Elo based game.

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 rank national teams in men's football. In 2006, Elo ratings were adapted for Major League Baseball teams by Nate Silver of Baseball Prospectus.^[27] Based on this adaptation, Baseball Prospectus also makes Elo-based Monte Carlo simulations of the odds of whether teams will make the playoffs.^[28] 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.

Sports-reference.com uses the Elo rating system to rate the best professional players in basketball, football, baseball (batters and pitchers rated separately), and hockey (goalies and skaters rated separately. The list changes constantly, but as of 30 August 2011 at 12:50 pm EDT, the number 1's are Michael Jordan, Barry Sanders (with Reggie White very close), Babe Ruth, Walter Johnson, Bobby Orr (with Wayne Gretzky very close), and Dominik Hasek.

The English Korfball Association rated teams based on Elo ratings, to determine handicaps for their cup competition for the 2011/12 season.

Rugbyleagueratings.com uses the Elo rating system to rank international and club rugby league teams. As of 29 March 2012, Manly are rated best in Australia's NRL; Warrington Wolves are rated best in Europe's Super League.

Various online games use Elo ratings for player-versus-player rankings. In Guild Wars, Elo ratings are used to record guild rating gained and lost through Guild versus Guild battles, which are two-team fights. The initial K-value was 30, but was changed to 5 in January 2007, then changed to 15 in July 2009.^[29] World of Warcraft formerly used the Elo Rating system when teaming up and comparing Arena players, but now uses a system similar to Microsoft's TrueSkill.^[30] The online action RTS game League of Legends uses an elo rating system as well.^[31] The game Puzzle Pirates uses the Elo rating system as well to determine the standings in the various puzzles. Also Roblox introduced the Elo rating in 2010.^[32] The upcoming title Counter-Strike: Global Offensive has also been confirmed to use the Elo rating.^[33]

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. The DCI (formerly Duelists' Convocation International) uses Elo ratings for tournaments of Magic: The Gathering and other Wizards of the Coast games. However, the DCI will be abandoning this system in 2012 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".^[19][20] Pokémon USA uses the Elo system to rank its TCG organized play competitors. Prizes for the top players in various regions include holidays and world championships invites. Similarly, Decipher, Inc. used the Elo system for its ranked games such as Star Trek Customizable Card Game and Star Wars Customizable Card Game.

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,^[34] while Codeforces is using another version based on logistic distribution.^[35][36][37]

Applications apart from gaming[link]

The Elo rating system has been used in a crowdsourcing application for determining best quality photographs. A company called Brilliant Arc has created the "Keep/Toss" game. Two photographs are presented and workers in Amazon's Mechanical Turk simply select which photograph they believe is the better photograph. Three votes are cast for each photograph and an Elo score is determined for all photographs. The photographs with a score above a certain threshold are then selected for further processing. The results have been well-received.

References in the media[link]

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 the mathematical formula for the Elo rating system on Zuckerberg's dorm room window.

See also[link]

• Chess rating systems
• FIDE World Rankings
• Sports rating system

Notes[link]

References[link]

• Elo, Arpad (1978). The Rating of Chessplayers, Past and Present. Arco. ISBN 0-668-04721-6. 
• Harkness, Kenneth (1967). Official Chess Handbook. McKay. 

External links[link]

• Official FIDE Rating List
• All Time Rankings - lists the top 10 from 1970 to 1997
• Live Chess Ratings - an unofficial live ratings list with daily updates
• GoBase.org: Introduction to the Elo Rating System
• Citations for Elo, A.E. 1978. The Ratings of Chess Players: Past and Present.
• Mark Glickman's research page, with a number of links to technical papers on chess rating systems
• PDF from Glickman's site explaining USCF ratings system
• Elo query with world ranking list and historical development since 1990
• Multiplayer Elo Calculator

Eduardo Saverin
Born	(1982-03-13) March 13, 1982 (age 30) São Paulo, Brazil
Residence	Singapore
Citizenship	Brazil[1][2]
Alma mater	Harvard University (B.S., Economics, 2006)
Known for	Co-founder of Facebook
Net worth	US $2 billion (March 2012)[3]

Eduardo Luiz Saverin^[4][5] (born March 13, 1982;^[6] Portuguese: [eduˈaɾdu ˈsaveɾĩ] or [saveˈɾĩˑ]) is a Brazilian internet entrepreneur and investor.^[7] Saverin is one of four co-founders of Facebook, along with Mark Zuckerberg, Dustin Moskovitz, and Chris Hughes.^[8] As of 2012, he owns less than 5% of Facebook's shares and has a net worth of $2 billion, according to Forbes. He has also invested in early-stage startups such as Qwiki^[9] and Jumio.^[10]

Personal life[link]

Eduardo Saverin was born in São Paulo, Brazil, to a wealthy Jewish Brazilian family,^{[11][12][13][14]} and was raised in Rio de Janeiro, Brazil and Miami, Florida. Eduardo's father was a Brazilian industrialist working in export, clothing, shipping, and real estate.^[15]

By 1993, Saverin's father had become wealthy, and in 1993 it was discovered that his son Eduardo´s name had been placed on a list of kidnapping victims by gangs specializing in kidnapping for ransom. As a result, the family moved to Miami to find a safer place to live. Saverin attended Gulliver Preparatory School in Miami, and went on to Harvard University, where he was a member of the Phoenix S.K. Club as well as president of the Harvard Investment Association. While an undergraduate at Harvard, Saverin took advantage of Brazil's lax insider trading regulations and made $300,000 via strategic investments in the oil industry.^[16][15][17] In 2006, Saverin graduated magna cum laude from Harvard University with a bachelor's degree in economics. He is a member of the Alpha Epsilon Pi Fraternity (Eta Psi chapter of Harvard University).

Saverin has lived in Singapore since 2009.^[18][19] In September 2011, he renounced his U.S. citizenship; the citizenship change may reduce the capital gains taxes Saverin pays after the Facebook IPO, although his taxes may increase initially.^[7][20] Saverin's renunciation of U.S. citizenship may result in his not being permitted to enter the U.S. in the future if the Ex-Patriot Act, which was proposed in response to Saverin's anouncement, becomes law.^[21][22]

Facebook[link]

During his junior year at Harvard University, Saverin met fellow Harvard undergraduate, sophomore Mark Zuckerberg. Noting the lack of a dedicated social networking website for Harvard students, the two worked together to launch The Facebook in 2004. As co-founder, Saverin held the role of chief financial officer and business manager.^[23] As Facebook rapidly expanded to universities across the US, internal conflicts and differences of opinion between Saverin and Zuckerberg regarding Facebook's direction resulted in Saverin's diminished involvement and influence in Facebook. The conflict peaked when Saverin's shares were diluted from the original 34.4%.

A lawsuit filed by Saverin against Facebook was settled out of court. Though terms of the settlement were not disclosed, the company affirmed Saverin's title as co-founder of Facebook. Saverin signed a non-disclosure contract after the settlement.^[24]

As of 2010, Saverin has liquidated at least $250 million worth of Facebook stock to later-stage investors such as Digital Sky Technologies ^[25][26], as well as via secondary exchanges like SharesPost.^[27]

Depictions in media[link]

In the 2010 film The Social Network, which depicts the relationship between Saverin and Mark Zuckerberg from the creation of Facebook to Saverin taking legal action against Zuckerberg, Saverin is played by actor Andrew Garfield. Garfield's portrayal of Saverin was met with critical acclaim and received nominations for the Golden Globe Award for Best Supporting Actor - Motion Picture, BAFTA Award for Best Actor in a Supporting Role,^[28] and the Broadcast Film Critics Association Award for Best Supporting Actor.

References[link]

Further reading[link]

• Saverin, Eduardo, "Facebook Co-Founder Speaks Publicly: What I Learned From Watching 'The Social Network'", CNBC, Friday, 15 Oct 2010.

External links[link]

• Eduardo Saverin on Facebook
• Profile at Forbes
• Works by or about Eduardo Saverin in libraries (WorldCat catalog)

Magnus Carlsen
Carlsen in 2010
Full name	Sven Magnus Øen Carlsen
Country	Norway
Born	(1990-11-30) 30 November 1990 (age 21) Tønsberg, Norway
Title	Grandmaster
FIDE rating	2835 (May 2012) (No. 1 in the March 2012 FIDE World Rankings)
Peak rating	2835 (January 2012, March 2012)

Sven Magnus Øen Carlsen (born 30 November 1990) is a Norwegian chess Grandmaster and chess prodigy who is currently the number-one ranked player in the world. In January 2010 he became the seventh player in history to be ranked number one in the world on the official FIDE rating list. His peak rating is 2835, the second highest in history, after Garry Kasparov.^[1]

On 26 April 2004 Carlsen became a Grandmaster at the age of &1000000000000001300000013 years, &10000000000000148000000148 days, making him the third-youngest Grandmaster in history. On 1 January 2010 the new FIDE rating list was published, and at the age of &1000000000000001900000019 years, &1000000000000003200000032 days, he became the youngest chess player in history to be ranked world number one, breaking the record previously held by Vladimir Kramnik.^[2] Carlsen was also the 2009 World blitz chess champion.

His performance at the September–October 2009 Nanjing Pearl Spring tournament has been described as one of the greatest in history^[3] and lifted him to an Elo rating of 2801, making him the fifth player to achieve a rating over 2800 – and aged 18 years 10 months at the time, by far the youngest to do so.

Based on his rating, Carlsen qualified for the Candidates Tournament which determined the challenger to World Champion Viswanathan Anand in the World Chess Championship 2012. In November 2010, however, he announced he was withdrawing from the Candidates tournament.^[4]

Childhood[link]

Carlsen playing simultaneous chess in Molde in July 2004

Born in Tønsberg, Vestfold, Carlsen currently lives in Haslum, Bærum, near Norway's capital, Oslo. He played his first chess tournament at the age of eight and was later coached at a Norwegian high school (for athletes) by the country's top player, Grandmaster (GM) Simen Agdestein. Agdestein introduced his civil worker Torbjørn Ringdal Hansen, currently an International Master, to Carlsen, and they had one training session every week, along with one of Carlsen's close friends. Becoming an International Master, Carlsen was given a year off from elementary school to participate in international chess tournaments during the fall season of 2003. In that same year, he finished third in the European Under-12 Boys Championship.

Chess career[link]

2004[link]

Carlsen was brought to the attention of the international chess world after his victory in the C group at the Corus chess tournament in Wijk aan Zee. Carlsen had a score of 10½/13, losing just one game (against the highest rated player of the C group, Dusko Pavasovic).^[5] As a result of the victory, he took his first Grandmaster norm and achieved a performance rating of 2702. Particularly notable was his win over Sipke Ernst in the penultimate round, when Carlsen sacrificed material to mate him in just 29 moves.^[6] Carlsen won the Audience Prize for that game, as the best game of the round (including the games played in the A and B groups). The first 23 moves in that game had already been played in another game Almagro Llanas-Gustafsson, Madrid 2003 (which ended in a draw), but Carlsen's over-the-board novelty immediately led to a winning position. Carlsen's victory in the C group qualified him to play in the B group in 2005, and it also led Lubomir Kavalek, writing for the Washington Post, to give him the title "Mozart of chess". Agdestein, who was once a young GM at 18, said in an interview that Carlsen was a significantly better player than he was himself at the same age. He also said that Carlsen had an excellent memory and played an unusually wide range of different openings. Carlsen's prowess caught the attention of Microsoft, who became his sponsor.^[7]

Carlsen obtained his second GM norm in the Moscow Aeroflot Open in February 2004. In a blitz chess tournament in Reykjavík, Iceland, Carlsen defeated former world champion Anatoly Karpov on 17 March 2004. The blitz tournament was a preliminary event leading up to a rapid knockout tournament beginning the next day, where Carlsen achieved one draw against Garry Kasparov, who was then the top-rated player in the world, before losing to Kasparov after 32 moves of the second game, thus being knocked out of the tournament.^[8]

In the sixth Dubai Open Chess Championship, held 18–28 April 2004, Carlsen obtained his third Grandmaster norm (enough for getting the GM title), after getting four wins and four draws before the last game was to be played. As a result of this, he was at the time the world's youngest Grandmaster and the second youngest person ever to hold GM status, after Sergey Karjakin of Ukraine who attained the feat at 12 years and 7 months of age in 2002.^[9]

Carlsen was the youngest player ever to participate in the FIDE World Chess Championship 2004, but was knocked out in the first round on tie breaks by Levon Aronian.

In July 2004, Carlsen and Berge Østenstad (then the reigning Norwegian champion) tied for first in the Norwegian Chess Championship, each scoring seven out of nine possible points. A two-game match between them was arranged to decide the title. Both games were drawn, which left Østenstad the champion because he had superior tiebreaks in the tournament.

2005[link]

Magnus Carlsen in 2008

In Smartfish Chess Masters at the Drammen chess festival 2004–05 (Norway) Carlsen defeated Alexei Shirov, ranked number 10^[10] in the world.^[11] In June 2005 in the Ciudad de Leon rapid chess tournament, Carlsen played a four-game semi-final against Viswanathan Anand, who was ranked second in the world at the time. Magnus lost 3–1. Carlsen was invited to the tournament as the most promising young chess player in 2005.

In the 2005 Norwegian Chess Championship, Carlsen again finished in a shared first place, this time with his mentor Simen Agdestein. A playoff between them was arranged between 7 November and 10 November. This time Carlsen had the better tiebreaks, but the rule giving the player with better tiebreaks scores the title in the event of a 1–1 draw had been revoked previously. The match was closely fought, Agdestein won the first game, Carlsen won the second, so the match went into a phase of two and two rapid games until there was a winner. Carlsen won the first rapid game, Agdestein the second. Then followed a series of three draws until Agdestein won the championship title with a victory in the sixth rapid game.

At the end of 2005 Carlsen participated at the World Chess Cup 2005 in Khanty-Mansiysk, Russia. In the knock-out tournament, he upset the 44th-ranked Georgian Zurab Azmaiparashvili in round one, winning 2–0 at rapid chess after a 1–1 tie in the normal length games, and proceeded to beat Tajik Farrukh Amonatov and Bulgarian Ivan Cheparinov (also after rapid chess) to reach the round of 16. There he lost 1½–2½ to Evgeny Bareev, which prevented him from finishing in the top eight. He then won against Joël Lautier 1½–½ and Vladimir Malakhov 3½–2½ securing him at least a tenth place and therefore a spot in the Candidate Matches. Carlsen became the youngest player to be an official World Championship Candidate.

In October 2005 he took first place at the Arnold Eikrem Memorial in Gausdal with eight out of nine points and a performance rating of 2792 at the age of 14.^[12]

2006[link]

In the January 2006 fide list, at the age of 15 years and 31 days, he officially attained 2625 elo rating, which made Carlsen the youngest person to break the 2600 elo barrier. In 2008, Wesley So broke that record. Carlsen qualified for a place in the Corus B group from his 2005 first place in Corus group C. His shared first with Motylev with 9/13 (+6 -1 =6) qualified him to play in the Corus A group in 2007.

In the 2006 Norwegian Chess Championship, Carlsen was close to winning outright, but a last-round loss to Berge Østenstad again tied him for first place with Agdestein. The last-round loss deprived Magnus of beating Agdestein's record of becoming the youngest Norwegian champion ever. Nonetheless, in the play-off 19–21 November Carlsen won 3–1. After two draws in the initial full time games, Magnus won both rapid games in round two, securing his first Norwegian championship.

Magnus won the 2006 Glitnir Blitz Tournament^[13] in Iceland. He won 2–0 over Viswanathan Anand (2003 FIDE World Rapid Chess Champion, 2004 Amber Rapid Chess Champion, 2007 FIDE Classical World Champion) in the semi finals. Carlsen also won 2–0 in the finals.^[14]

Magnus scored 6/8 in the 37th Chess Olympiad in 2006 against opponents averaging 2627 Elo, gaining 18 Elo (a rating performance of 2820 points). One of his notable wins was against top English grandmaster Michael Adams.^[15]

In the Midnight Sun Chess Tournament, Carlsen had some misses and came in second, beaten by Sergei Shipov (FIDE-Elo: 2576).

In the 2006 Biel grandmaster tournament, he achieved second place, after having beaten the eventual winner Alexander Morozevich twice (once with each color).

In the NH Chess Tournament held in Amsterdam in August 2006, Carlsen participated in an 'Experience' v 'Rising Stars' Scheveningen team match. The 'Rising Stars' won the match 22–28, with Carlsen achieving the best individual score for the youngsters, 6½/10 and a 2700 Elo performance, thus winning the right to participate in the 2007 Melody Amber tournament.^[16]

In the World Blitz Championship at Rishon LeZion, Israel in September 2006, he was number 8 of 16 participants with 7½/15 points.

In the rapid chess tournament Rencontres nationales et internationales d'échecs in Cap d'Agde, France he got to the semifinal, losing to Sergey Karjakin.

Carlsen achieved a shared eighth place of 10 participants in the Mikhail Tal Memorial in Moscow with two losses and seven draws. In the associated blitz tournament Tal Blitz Cup he received 17½/34 points and ninth place in a group of 18 participants.

2007[link]

In the 2007 Corus chess tournament Carlsen, playing in group A for the first time, had to settle for the last place after nine draws and four losses, scoring 4½ points in 13 rounds.

Magnus Carlsen vs. Levon Aronian at Linares 2007

In the prestigious Linares chess tournament Carlsen met the following top-rated players: Veselin Topalov, Viswanathan Anand, Peter Svidler, Alexander Morozevich, Levon Aronian, Peter Leko, and Vassily Ivanchuk (replacing Teimour Radjabov). With the significantly lowest Elo rating, he achieved a second place (on tiebreaks) with 7½ points after four wins, seven draws and three losses, and an Elo performance of 2778.

In March 2007, Carlsen played for the first time in the Melody Amber blind and rapid chess tournament in Monte Carlo. In the 11 rounds he achieved eight draws and three losses in the blindfold, and three wins, seven draws and one loss in the rapid part. This resulted in a shared ninth place in the blindfold, shared second place in the rapid (beaten only by Anand), and an eighth place in the overall tournament.

In May–June 2007, he participated in the Candidates Tournament for the FIDE World Chess Championship 2007. He was paired with the top seed Levon Aronian. The six-game match was drawn (two wins, two draws, and two losses), with Carlsen coming from behind twice. The four-game rapid playoff was drawn as well (one win, two draws, and one loss), with Carlsen winning the last game to stay in the match. Finally, Aronian won both tiebreaker (blitz) games, to eliminate Carlsen from the Championship.

In the July 2007 FIDE list, at the age of 16 years and 7 months, he officially attained 2710 Elo rating, which made Carlsen the youngest person to break the 2700 Elo barrier. As of January 2011, this record has not been broken.

In July–August 2007, he won the International Chess Festival Biel Grandmaster Tournament 2007, with a +2 record (an Elo performance of 2753). His score was equalled by Alexander Onischuk and by the tie-breaker rule of the tournament, they played a tie-breaker match to determine the winner. After drawing two rapid and two blitz games, Carlsen won the armageddon game. He became the youngest person ever to win a category 18 tournament.

Immediately after the Biel tournament, Carlsen entered the open Arctic Chess Challenge in Tromsø, but his +5=4 and fourth place result was somewhat disappointing. In the first round, Carlsen surprisingly conceded a draw to his classmate Brede Hagen (rated 2034)^[17] after having a lost position at one point.^[18] A game which attracted some attention was his sixth round win over his own father, Henrik Carlsen.^[19]

In December 2007, he reached the semi-final round of the World Chess Cup 2007, after defeating Michael Adams in the round of 16, and Ivan Cheparinov in the quarter-finals. In the semi-final, he was eliminated by the eventual winner Gata Kamsky, ½:1½.

2008[link]

Carlsen in Bilbao, 2008

Playing for the second time in the top group A of the Corus chess tournament, Carlsen showed a big improvement over his 2007 performance. His final score was eight points in 13 rounds, an Elo performance of 2830. Carlsen scored five wins (including as Black against former World Champion Vladimir Kramnik), two losses and six draws. He shared first place with Levon Aronian, becoming the youngest person ever to win a category 20 tournament.

At the 2008 Linares chess tournament, Carlsen had another 2800+ Elo performance, scoring eight out of fourteen (five wins, three losses and six draws). He finished in sole second place, ½ point behind the winner, world champion Viswanathan Anand.

In March 2008, Carlsen played for the second time in the Melody Amber blind and rapid chess tournament, which was held in Nice for the first time. In the 11 rounds he achieved four wins, four draws and two losses in the blindfold, and three wins, six draws and two losses in the rapid part. This resulted in a shared fifth place in the blindfold, shared third place in the rapid and a shared second place in the overall tournament.

Carlsen was one of 21 players in the six-tournament FIDE Grand Prix 2008–2009, a qualifier for the World Chess Championship 2012. In the first tournament, in Baku, Azerbaijan, in April–May 2008, he finished in a three-way tie for first place, with another 2800 Elo performance. Carlsen later withdrew from the Grand Prix cycle despite his initial success, citing "dramatic change[s] to ... regulations."^[20]

Carlsen won a rapid match against Peter Leko held at Miskolc, Hungary, scoring 5:3 (two wins, six draws).^[21]

In June, Carlsen won an annual Aerosvit event.^[22] In his strongest tournament performance at that point in his career, he finished undefeated with eight out of eleven (five wins, six draws) in a category 19 field. His Elo performance was 2878.

Playing in a category 18 Biel tournament, Carlsen finished third with six points out of ten (three wins, one loss, six draws), with Elo performance of 2741, his first sub-2800 performance of 2008.

In the Mainz World Rapid Chess Championship, Carlsen finished in second place after losing the final to defending champion Anand 3:1 (two losses, two draws).^[23] To reach the final Magnus played against Judit Polgár scoring 1½ point out of two (one win, one draw), against Anand scoring one point out of two (two draws) and against Morozevich scoring one point out of two (two draws).

In the category 21 Bilbao Masters, Carlsen finished second with a 2768 performance rating (three wins, three losses, four draws).

2009[link]

Playing in Group A of the Corus chess tournament, Carlsen tied for fifth with a 2739 performance (two wins, one loss, ten draws).^[24]

In the Linares chess tournament, Carlsen finished third with a 2777 performance (three wins, two losses, nine draws). In this tournament, he defeated World Champion Viswanathan Anand^[25] and the eventual winner Alexander Grischuk^[26] for the first time under classical time controls.

Carlsen tied for second place with Veselin Topalov at the M-Tel Masters (category 21) tournament in Sofia, Bulgaria. He lost to eventual winner Alexei Shirov in their final game, dropping him from first.^[27]

Carlsen won the category 21 Nanjing Pearl Spring tournament, 2½ points ahead of second-place finisher Topalov, the world's highest-rated player at the time.^[28] He scored 8/10 (six wins, four draws, no losses), winning every game as White (against Topalov, Wang Yue, Leko, Radjabov, and Jakovenko), and also winning as Black against Jakovenko. By rating performance, this was one of the greatest results in history, with a performance rating of 3002.^[29] This lifted his FIDE rating to 2801, making him the 5th and youngest player to ever surpass 2800.

In the Tal Memorial 2009, played from 5 November to 14 November, Carlsen started with seven straight draws, but finished with wins over Ruslan Ponomariov and Peter Leko. This result put Carlsen in shared second place behind Kramnik and equal with Ivanchuk.^[30][31]

After the Tal Memorial, Carlsen won the 2009 World Blitz Championship, played from 16 November to 18 November in Moscow, Russia. His score of 28 wins, 6 draws and 8 losses left him three points ahead of Anand, who finished in second place.^[32]

Carlsen entered the 2009 London Chess Classic as the top seed in a field including Kramnik, Hikaru Nakamura, Michael Adams, Nigel Short, Ni Hua, Luke McShane and David Howell. He defeated Kramnik in round one and went on to win the tournament with 13/21 (three points were awarded for a win, and one for a draw; using classical scoring he finished with 5/7) and a performance rating of 2844, one point ahead of Kramnik. This victory has propelled him to the top of the FIDE rating list, surpassing Veselin Topalov.

Carlsen's average rating from the July 2009 and January 2010 FIDE lists will enable him to qualify for the Candidates Tournament of the World Chess Championship 2012 cycle.

In early 2009 Carlsen engaged former world champion Garry Kasparov as a personal trainer.^[33] In September 2009 their partnership was confirmed in Norwegian newspapers.^[34][35]

In a December 2009 interview with TIME Magazine, in response to a question whether he used computers when studying chess, Carlsen revealed that he does not use a chess set when studying on his own.^[36]

He won the Chess Oscar for 2009.^[37] The Chess Oscar is awarded to the year's best player according to a worldwide poll of leading chess critics, writers, and journalists conducted by the Russian chess magazine 64.

2010[link]

Ahead of 2010, Carlsen said that he would be playing in fewer tournaments the coming year. The cooperation with Kasparov continued until March that year.^[38]

Carlsen won the Corus chess tournament played 16–31 January with 8½ points (five wins, seven draws, one loss). His ninth-round loss to Kramnik ended a streak of 36 rated games undefeated.^[39] Carlsen appeared to struggle in the last round against Fabiano Caruana, but saved a draw leaving him half a point ahead of Kramnik and Shirov.^[40]

The March 2010 FIDE rating list showed Carlsen with a new peak rating of 2813, a figure that only Kasparov has bettered.^[41] In the same month it was announced that Carlsen had split from Kasparov and would no longer be using him as a trainer,^[41] although this was put into different context by Carlsen himself in an interview with the German magazine Der Spiegel stating that they would remain in contact and that he would continue to attend training sessions with Kasparov.^[42]

Carlsen shared first place alongside Ivanchuk in the Amber 2010 blindfold and rapid tournament. Carlsen scored 6½ points in the blindfold and 8 points in the rapid, giving 14½ points from a possible 22 points.

In May 2010 it was revealed that Carlsen had helped Viswanathan Anand prepare for the World Chess Championship 2010 against challenger Veselin Topalov, which Anand won 6½-5½ to retain the title. Carlsen had also helped Anand prepare for the World Chess Championship 2007 and World Chess Championship 2008.^[43]

In his first tournament since his announced departure from Kasparov, Carlsen played in the Bazna Kings Tournament in Romania on 14–25 June. The tournament was a double round robin event involving Wang Yue, Boris Gelfand, former FIDE world champion Ruslan Ponomariov, Teimour Radjabov, and Liviu-Dieter Nisipeanu. After drawing his first three games, Carlsen won his next four and set a personal livechess rating peak of 2825.1.^[44] He finished with 7½/10 and a 2918 performance rating, winning the tournament by two points over Radjabov and Gelfand.^[45][46] The victory ensured that Carlsen remained at the top of the Elo rating list. His official rating hit 2826, a figure exceeded only by Kasparov and just 25 points shy of tying Kasparov's all-time record.

Carlsen then played in a rapid tournament 28–30 August at the Arctic Securities Chess Stars tournament in Kristiansund, Norway. The field featured world champion Viswanathan Anand, female world #1 Judit Polgár, and Jon Ludvig Hammer. In the preliminary round robin, Carlsen scored 3½/6 to qualify for the final, second behind Anand.^[47] In the final, Carlsen defeated Anand 1½-½ to win the championship.^[48]

Following this event, Carlsen suffered setbacks in his next two tournaments. In the 39th Chess Olympiad from 19 September to 4 October, he scored 4½/8, losing three games, to Baadur Jobava, Michael Adams and Sanan Sjugirov; these were his first losses with the black pieces in more than a year.^[49] His team, Norway, finished 51st out of 149 teams.^[50]

Carlsen's next tournament was the Grand Slam Masters Final on 9–15 October 2010, which he had qualified for automatically by winning three of the previous year's four Grand Slam chess events (2009 Nanjing Pearl Spring, 2010 Corus, 2010 Bazna Kings). Along with Carlsen, the finals consisted of World Champion Viswanathan Anand and the highest two scorers from the preliminary stage held in Shanghai in September, which featured Vladimir Kramnik, Levon Aronian, Alexei Shirov, and Wang Hao; Shirov and Kramnik qualified.^[51][52] The official September 2010 ratings of Carlsen, Anand, Kramnik and Shirov made the Grand Slam final the strongest tournament in chess history, with an average ELO of 2789. In the first round, Carlsen lost on the black side of the Queen's Indian Defense to Kramnik; this was Carlsen's second consecutive loss to Kramnik, and placed his hold on the world #1 ranking in serious jeopardy. In his second round, Carlsen lost with the white pieces to Anand in the Ruy Lopez; this was his first loss as white since January 2010, and dropped him to world #2 in the live rankings behind Anand. Carlsen recovered somewhat in the latter part of the tournament, finishing with 2½/6, including a win over Shirov; the tournament was won by Kramnik with 4/6.^[53] Carlsen finished this tournament with a rating of 2802, two points behind Anand at 2804 who officially ended Carlsen's reign at world #1. These setbacks called into question from some whether Carlsen's activities outside chess, such as modelling for G-Star Raw, was distracting him from performing well at the chess board.^[54] Carlsen said he did not believe there was a direct connection, and that he was looking forward to the Pearl Spring tournament, where he had scored 8/10 in 2009.^[55]

Following the Grand Slam Masters Final, Carlsen's next tournament was the 2010 Pearl Spring chess tournament on 19–30 October in Nanjing, China, against Anand, world #2 Veselin Topalov, Vugar Gashimov, Wang Yue, and Étienne Bacrot.^[56] This was the only tournament in 2010 to feature Anand, Carlsen and Topalov, at the time the top three players in the world, and was the first tournament in history to feature three players rated at least 2800. With early wins over Bacrot, Yue, and Topalov with white, Carlsen took the early lead, extending his winning streak with white in Nanjing to eight. This streak was halted by a draw to Anand in round seven, but in the penultimate round Carlsen secured first place by defeating Topalov with the black pieces. This was his second victory in the tournament over the former world #1, and improved his score to 6½/9.^[57] The victory clinched Carlsen a place in the 2011 Grand Slam Chess Masters final, his final score of 7/10 (with a performance rating of 2903) was a full point ahead of runner-up Anand, and moved him back to world #1 on the live rankings.

Carlsen next played in the 2010 World Blitz Championship, in Moscow on 16–18 November, attempting to defend his 2009 title. With a score of 23.5/38, he finished in third place behind Teimour Radjabov and winner Levon Aronian.^[58]

Carlsen won the 2010 London Chess Classic on 8–15 December in a field comprising world champion Viswanathan Anand, former world champion Vladimir Kramnik, American number one Hikaru Nakamura, and British players Michael Adams, Nigel Short, David Howell, and Luke McShane.^[59] Carlsen had a rocky start, losing his Black games to McShane and Anand in rounds 1 and 3, but winning with White against Adams and Nakamura in rounds 2 and 4. He joined the lead with a Black win over Howell in round 5, and managed to stay in the lead following a harrowing draw with Black against Kramnik in round 6, before defeating Short in the last round with White. Since the tournament was played with three points for a win, Carlsen's +4=1-2 score put him ahead of Anand and McShane who scored +2=5 (a more traditional two-points-for-a-win system would have yielded a three-way tie, with Carlsen still on top having the better tiebreaker due to four games with black – Anand and McShane had to play only three times with black).

Carlsen won the Chess Oscar for 2010 by narrowly beating Viswanathan Anand.^[60]

2011[link]

Carlsen competed in the GM-A group of the Tata Steel Chess (Corus) tournament on 14–30 January in Wijk aan Zee in an attempt to defend his title;^[61] the field included world champion Viswanathan Anand, reigning world blitz champion Levon Aronian, former world champion Vladimir Kramnik, Alexander Grischuk, Hikaru Nakamura, and former FIDE world champion Ruslan Ponomariov among others. Despite losing games with White against Anish Giri and reigning Russian champion Ian Nepomniachtchi, Carlsen finished with 8.0/13, including victories over Kramnik and tournament winner Hikaru Nakamura. Although Carlsen's performance raised his rating from 2814 to 2815, Anand's 8.5/13 score elevated his rating to 2817, making him the official world #1 for the March 2011 FIDE rating list.

The first tournament victory of 2011 came in the Bazna Kings tournament, a double round-robin played in Medias on 11–21 June. Carlsen finished with 6.5 points (+3=7), equal with Sergey Karjakin but with a better tiebreak score. Carlsen won his White games against Nakamura, Nisipeanu, and Ivanchuk and drew the rest of the games.^[62] This result raised Carlsen's rating by six points to 2821, and returned Carlsen to first place on the live rating list.

As of November 2011^[update], Carlsen is again #1 on the official FIDE rating list with a 2826 rating.

The Grand Slam Chess Final was held as a double-round robin with six players, in São Paulo (25 September – 1 October) and Bilbao (5–11 October). Although Carlsen had a slow start, including a loss against bottom ranked Vallejo Pons, he finished +3=6-1, equal with Ivanchuk (whose +4=3-3 finish was equal due to three points for a win). Carlsen then won the blitz tiebreak against Ivanchuk. The other players were Anand, Aronian, Nakamura, and Vallejo Pons.^[63]

Another tournament victory was achieved in the Tal Memorial in Moscow 16–25 November 2011 as a round robin with ten players. Carlsen won two games, against Gelfand and Nakamura, and drew the rest. He finished equal on points with Aronian, and finished ahead since the first tiebreak was the number of Black games; Carlsen had five Black games while Aronian only had four.^[64]

In the London Chess Classic, played 3–12 December, Carlsen's streak of tournament victories ended when he finished third, behind Kramnik and Nakamura. Carlsen won three games and drew five. Although he did not win the tournament, Carlsen continued to gain rating points, and rose to a new personal record of 2835.^[65]

2012[link]

Carlsen in 2012

At the Tata Steel Chess Tournament held January 14–29, Carlsen finished in a shared second place with 8 points out of 13 (four wins, eight draws, one loss), behind Aronian, and equal with Radjabov and Caruana. Carlsen defeated Gashimov, Aronian, Gelfand, and Topalov, but lost against Karjakin. His score was approximately on par with rating expectations with an overall loss of one point, but he remained in first place on the live rating list.^[66]

Playing style[link]

As a teenager, Carlsen became known for his attacking playing style. His win over Sipke Ernst in the 2004 Wijk aan Zee C-group^[67] which ended with an epaulette mate was an example of the play that was admired by several other chess players. As he matured, Carlsen found that this risky playing style was not as well suited against the world elite. Around 2005 Carlsen was struggling against more experienced grandmasters, and had trouble getting much out of the opening. To progress, Carlsen became a more universal player, capable of handling all sorts of positions well. In the opening, Carlsen has alternated between various opening moves. Instead of specializing in either 1.d4 or 1.e4, Carlsen has alternated between them, thus making it harder for opponents to prepare against him.^[68]

Since the announcement that he was coaching Carlsen, Garry Kasparov has repeatedly stated that Carlsen has a positional style similar to that of past world champions such as Anatoly Karpov, José Capablanca and Vassily Smyslov, rather than the tactical style of Alexander Alekhine, Mikhail Tal and himself.^[69]

Rating[link]

In the October 2006 FIDE Elo ratings, Carlsen advanced to world number 22 with a rating of 2698.^[70] In the January 2007 ratings he dropped to 2690 and rank 24.^[71] In the July 2007 ratings, after a series of strong results, Carlsen advanced to become world number 17 with a rating of 2710.^[72] On the January 2008 FIDE rating list he was rated at 2733,^[73] and on October 2008 he reached 2786 Elo rating.^[74] He was placed sixth in the July 2008 list, but if his Aerosvit result had been included he would have been ranked second. The omission of the Aerosvit result, which finished after the cut-off date for the July 2008 list, caused some controversy.^[75]

On 5 September 2008, after winning round 4 in the Bilbao Grand Slam chess championship, Carlsen, still under 18, briefly became number one on the unofficial live ratings list.^[76][77]

Carlsen's September–October 2009 victory in the Nanjing Pearl tournament raised his official rating to 2801, making him at age 18 the youngest player ever to break 2800.^[78] The youngest before him was Vladimir Kramnik at age 25.^[79] Besides Carlsen, only Kasparov, Topalov, Kramnik, and Anand had achieved a 2800 rating (Levon Aronian later accomplished the feat in October 2010). Carlsen said that he hoped his victory would mark the "beginning of a new era."^[80]

After the Tal Memorial (November 2009) he became number one in the unofficial live chess rating list with his new peak rating of 2805.7, 0.6 point over the number 2, Veselin Topalov.^[81]

The official FIDE rankings were published on 1 January 2010, and the 16 games played at the Tal Memorial and the London Chess Classic were enough to raise his rating by 8.6 rating points to 2810.^[82] This meant that Carlsen started 2010 by being the official (and, at the age of &1000000000000001900000019 years, &1000000000000003200000032 days, the youngest ever) world number one, and also the first player from a western nation to reach the top in the FIDE rating list since Bobby Fischer in 1972.^[83][84] The press coverage of this feat included an interview and article in Time magazine.^[85][86]

Standing on each top 100 FIDE list[link]

Magnus Carlsen Elo rating evolution from 2001 to 2010.