ELO ranking system is a very famous ranking system. The biggest point of this system is that when the strong hand beats the weak hand, it doesn't earn much points; Instead, you can earn more than usual. Each player has a physical strength value. The higher the physical strength value, the higher the ranking.
The main calculation formula of the ELO ranking system is as follows:
New physical strength value = old physical strength value +K (winning or losing value-expected winning rate)
First, each contestant is initially given the same initial physical strength value, and different systems range from 1300 to 1600.
Two. The winning or losing value: win 1, negative 0, and tie 0.5.
Three. K is the maximum possible increase or decrease after a game.
Four. Expected winning rate: calculate the winning probability of both sides according to their physical strength before the game (old).
1(a)K value
The ranking of USCF mainly adopts a three-level system. According to the strength value of the contestants, the K value is determined in three aspects:
If the intensity value is 0-2099, the k value is 32;
If the strength value is 2 100-2399, the k value is 24;
Physical strength value > =2400, and k value is 16.
Why do amateur k values need to be higher?
There is a saying that avoiding accidental miscalculation. For example, a person's physical strength value is around 2500, but the initial physical strength value is 1 600, so upgrading to the expiration point requires many matches. Adjusting the value of k can speed up the realization of the due grade field.
Another way of saying this is that the strength of novices may change rapidly, while the stability of professional level is relatively good. ...
In order to make the master who just joined the system get the proper rating as soon as possible, the World Chess Federation (FIDE) simply requires the new entrants to use a higher K value, and then return to the general level after 30 games. FIDE sets the value of k as follows:
In the first 30 games, the k value is 25;
If the intensity value is less than 2400, the value of k is15;
If the physical strength reaches 2400 and you have played for more than 30 rounds, the k value is 10. The value of k will not change in the future.
To sum up, the value of k plays an important role in the system, and the analysis is as follows:
First, the need for a low K value is to prevent advanced people from earning climbing points by "defeating low-level opponents". For example, when the strength values of the two sides differ by several hundred points, the advanced won't win a point, and under the system without decimal point, the advanced won't even earn a little cheaper.
Two. A high k value is needed for beginners to catch up with those with high scores.
Three. From low intensity value to high intensity value, the value of k will gradually decrease.
Other systems adjusted according to the ELO ranking system, including some online chess matches, will set different K values, and some will simply treat all matches with the same K value.
18thCandidate An article on Elo rating (thing) points out that the higher the importance of an event, the higher the K value. The initial ELO system does not include the importance of events, but the FIFA ranking system does, so let's leave it in the second part to introduce the FIFA ranking system.
1(b) Expected winning percentage
Expected winning percentage refers to evaluating the probability of winning in the upcoming competition according to the opponent's record (strength value) before the competition. The expected winning percentage is calculated as follows:
Expected winning percentage =1/(1+10 (dr/400))
Dr = opponent's physical strength value-own physical strength value.
The setting of 400 and 10 can be roughly explained as: when there is a difference of 400 intensity values, the winning probability of the next level is only one tenth.
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 contestant before the competition.
Before the game, each player can calculate the result physical value of both sides after winning or losing or drawing as long as he knows the current physical value of his opponent.
ELO system was originally used in chess, then gradually adjusted and widely used in different fields, such as football and Go, and now it has become the central equation in the ranking system.