Elo rating: How it works to assess chess results and player performance


If you play or follow chess, chances are you have come across the term Elo rating. Simply put, it is a dynamic rating system used in chess to calculate the ability of players and compare them.

What is the Elo rating system

The Elo rating system is a mechanism devised by physicist and Hungarian-American chess player Arpad Elo to determine ratings for chess players.

Initially, the system was not based on an absolute score, but on the possible outcomes of the matches and the difference in the quality of the two players.

Later, the system was also used by other sports, including basketball. Incidentally, even the modern-day dating app Tinder used the rating system for a while.

Currently, FIDE, the governing body of chess, uses a variant of the Elo rating to give a score to players.

What system does the FIDE use?

The entire premise of the point system is based on the difference in quality between two players. The point mechanism, due to the nature of its mathematical calculations, favors lower-rated opponents since they are less likely to win over higher-rated opponents who will be favorites to win.

For example: If two players A and B, with Elo ratings of 2700 and 2300, respectively, face each other, the points offered for B’s win will be higher than what A will get for a win.

For those who love mathematics, the advantage for a lower-rated player is given on two grounds:

The first parameter

The first is the win probability. Since the win probability is lower for lower-rated players, the difference between an actual win (the outcome for which is 1) and the win probability is higher.

Example: In a contest between players A and B mentioned above, A’s probability to win is 0.92 while B’s probability to win is 0.08. This is arrived at using a complex formula based on rating difference, which in A and B’s case is 400. Hence, the rating change for B’s win will be 1 – 0.08 = 0.92

The second parameter

The second point of advantage for lower-rated players is the adjustment factor. The adjustment factor, also referred to as K-factor, is used to give an advantage to younger/newer players. The adjustment factor is multiplied by the rating change (calculated above) and added to the original rating. K-factor is usually 40 for a newly rated player who has played less than 30 rated games. The value of K-factor is taken as 20 for a player with a rating below 2400, while it is 10 for a player with a higher rating.

Continuing with the above example, the change in B’s rating after a win, assuming K as 20, will be 20 X 0.92 = 18.4. The change will, however, be rounded off to 18.

What’s more

Another key factor is that the rating system used by FIDE follows the zero-sum game theory. This means that the points gained by the winning player would mean an equal loss of points for the losing player. Hence, player A will lose 18 points in a loss to player B.

Importance of the rating system in chess

Elo rating is used to determine the strength of chess players, and hence titles such as Grandmaster, International Master, and FIDE Master are awarded after players reach a certain level.

The rating system is devised in a way which prevents a single player from taking a substantial lead in terms of points. This is because the highest-rated player will have a higher win probability, and hence an actual win will yield fewer points.

In turn, a loss, or even a draw, to a lower-rated opponent will lead to a bigger deduction of points, and eventually, reduce any significant advantage.

Players with the highest Elo rating

Magnus Carlsen holds the record for the highest Elo rating achieved at 2882. The Norwegian reached this level in 2014. Carlsen, currently, has a rating of 2864 and still on top.

Chess legend Garry Kasparov is the only other player to have crossed the 2850 mark. India’s chess icon Viswanathan Anand is among 14 players to have breached 2800. In the latest rankings released by FIDE in July 2022, only Carlsen and China’s Ding Liren have a rating above 2800.

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