[11 platform ladder] [Principle Analysis] 11 platform ladder Principle Analysis

Reason for writing

(Elo ratings)Elo ranking systemIt is an authoritative method for assessing the benchmark level. It was originally created by Professor of Physics Arpad Elo and named ero ranking. Oracle ranking was first used in chess and go games. Currently, it is widely used in chess, go, football, basketball, and other sports. The ELO algorithm was first successful in the online game wow. Now the ELO algorithm is introduced on the 11 th platform to implement the ladder system. The platform is very popular among players.

The ranking algorithm is described in detail below.

Algorithm history

The ELO classification system is a statistical method for evaluating the player level. The American Chess Association first used this scoring method in 1960. Since it is more fair and objective than the previous method, this method is very popular soon. In 1970, the International Chess Association officially began to use the level score system.

The ELO model originally adopted a normal distribution. However, in practice, it is obvious that the performance of the players is not normal distribution, so the current level score system usually uses logistic distribution.

Scoring Method

Assume that the current score of chess player a and player B is sum, then the expected value of logistic distribution a for B is

Similar to B's victory over

Assume that a player's real score (score = 1, score = 0.5, and score = 0) is different from his expected score, then his level score should be adjusted accordingly. The specific mathematical formula is

In the formula, the score is adjusted by the player. Generally, 16 is used in master competitions.

Level score and player level

In chess, the level score roughly corresponds to the title of Chess Association

• Over 2500 points: International premium masters
• 2400-2499: International Master
• 2300-2399: chess master

With the previous Foundation, we can figure out the general principle of the 11-platform ladder.This is the case, for example.

Example

For example, Team A (in the game, it can be Dota's natural disasters or really three shuguo) is divided into 1613 levels, and the level is divided into 1573 of the Team B (of course, it is the near Wei army or Wei Guo... ^_^) After matching, a wins. If K is set to 32 (the value of K is not necessarily set as this, and tables can be queried), the expected victory rate of A is about 0.5573. Therefore, the new grade of A is divided into 1613 + 32 · (1 − 0.5573) = 1627.1664 is rounded to 1627, And the level score of the ladder is + 14.

If a loses, the new grade of A is divided into 1613 + 32 · (0-0.5573) = 1595.1664, Which is rounded to 1595, And the Tiandao level score is-18.

Through this example, we will summarize as follows:

The strong team wins the weak team, and adds less. The strong team loses the weak team, and the reduction is more! This is the charm of the ladder and reflects the current real level of contestants. This is also why the ladder system is so popular!

The principle of the 11-day ladder is like this ~ In actual implementation, the 11 platform may have other parameters. Currently, the 11 platform ladder is not perfect:

Pay attention to Genie's ladder points.

Of course, the 11 platform is definitely a breakthrough!

Due to the limitations of the author's level, the analysis will inevitably lead to leaks. You are welcome to criticize and correct them. If you think this article is helpful to you, please click "Green Channel" below --> "follow debuglzq ", exchange progress ~