The ELO ranking system is a very well-known ranking system. The most important point of this system is that when a strong player defeats a weak player, they can't earn many points; otherwise, they can earn more points than usual. Each contestant has a strength value, the higher the strength value, the higher the ranking.
The main calculation formula of the ELO ranking system is as follows:
new strength value = old strength value + K (winning value-expected winning percentage)
i. Each participant is initially assigned the same initial strength value, which is in different types of systems They are all different, ranging from 1300 to 1600.
ii. Winning value: win is 1, loss is 0, tie is 0.5
iii. K-value is the maximum possible value that can be increased or decreased after the end of a round.
iv. Expected winning percentage: Calculate the probability of both sides winning based on the strength value (old) of both sides before the game.
1(a) K-value
in the ranking of the United States Chess Federation (USCF) mainly adopts a three-level system. According to the strength value of the contestant, it is divided into three areas to determine the K-value: the
strength value of 0-2099, K -value is 32; those with a
strength value of 2100-2399 have a K-value of 24; those with a
strength value >=2400 have a K-value of 16.
Why does the amateur K-value need to be higher?
There is a saying to avoid accidental miscalculations. For example, a person's strength value is about 2500, but if the initial strength value is 1600, it will take a lot of matches to upgrade to the due points. Adjusting the K-value can speed up reaching the desired level.
Another argument is that the strength of beginners may change rapidly, while the stability of the professional level is relatively good...
In order to let the masters who have just joined the system get their due ratings as soon as possible, the World Chess Federation (FIDE) simply Let the new entrants use a higher K-value and return to the normal level after 30 rounds. FIDE sets the K value as follows: for the
first 30 rounds, the K-value is 25; if the
strength value is less than 2400, the K-value is 15; if the
strength value reaches 2400 and more than 30 rounds have been played, the K-value is 10. K-value will not change in the future.
In summary, the size of K-value plays a decisive role in the system. The analysis is as follows:
i. The need for low K-value is to prevent high-level players from "beating low-level opponents" to earn points. For example, when the strength of the two sides differs by a few hundred points, the high-level player won by less than a little bit. Under a system that does not take a decimal point, the high-level player can't earn even a little bit of cheapness.
ii. The need for high K-value is to enable newcomers to catch up with high scorers by a large margin.
iii. The K-value should gradually decrease from a low power value to a high power value.
Other systems adjusted according to the ELO ranking system, including some online chess competitions, will set different K-values, and some simply use the same K-value to handle all games.
An article on Elo rating(thing) on 18th Candidate stated that the higher the importance of the event, the higher the K-value. The original ELO system did not include the importance of the event, but the FIFA ranking system does, so I will leave it in the second part of the introduction to the FIFA ranking system.
1(b) Expected winning percentage The
expected winning percentage refers to the probabilities that the two teams will win in the upcoming game based on the player's past performance (strength value) before the game. The calculation method of the expected winning rate is as follows:
Expected winning rate = 1/(1+10^(dr/400))
dr = opponent’s strength value – the setting of your own strength value of
400 and 10, the meaning can be roughly interpreted as the difference of 400 points of strength value, the lower-level player’s The chance of winning is only one in ten.
In various adjusted ELO systems, the settings of 400 and 10 may be different, but the overall intention is to calculate the expected winning rate of each participant before the game.
Before the round, each contestant only needs to know the current strength value of the opponent, and then they can calculate the result strength value of both sides after winning, losing or tying.
The ELO system was originally used in chess, but has been gradually adjusted and widely used by competitions in different fields, such as football and Go. Now it has become the central equation in the ranking system.
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