Measure the level of various chess playing activities through ELO mechanism

0 introduction

      There are many competitions in daily life , Like one-on-one chess 、 Go and other chess competitions , There are also competitions between teams , Such as football 、 Basketball and other ball games . In these competitions , We always know that there are some strong players 、 A strong team , however , How strong are they ？ Or to say , We all think that player a is better than player B , But how much better is a than B , There is a 60% winning rate , Or 80% of the time , Or is it almost certain to win ？ Can we quantify this problem through mathematical methods ？

therefore ,elo The hierarchical subsystem was born .

     Elo The hierarchical system is defined by the Hungarian American physicist Arpad · Ello created an evaluation method to measure the level of various chess playing activities , Its purpose is to solve the above problems .

1 problem

How to measure the level of the players in the competition ？ How to use python Realization elo fraction ？

2 Method

Elo The idea is very simple , Than the size . If we can use a score to evaluate the strength of the players , nail 2000 branch , B 1800 branch ,2000 Than 1800 Be big , That means that the strength of a is stronger than that of B .

however , B also has the possibility of defeating a . Because a may not play well in a certain game , Only played out 1800 The level of , And B plays supernormal , Reached 2000 The level of the points , In this way, B defeated a .

To solve this problem , We may as well think that the players' performance follows the normal distribution —— For example, the average value of a is 2000 Is a normal distribution , That is to say, most of the time, his level of play is 2000 near , There is also a very low probability of arrival 1800 Below or 2200 above . such , According to the formula of normal distribution , You can get the expected winning rate among the players . This formula was originally an integral formula that was difficult to calculate , But it can be calculated by another very simple approximate formula .

Now we can use a score to represent the strength level of a player , Now players a and B have their own grade points , If they play , The winner represents his stronger strength , Therefore, we should improve the elo integral , In the same way, we should also reduce the elo integral .

For example, at present, a is 1500 branch , B is 1600 branch . We know , A and B fight , Obviously, B is more likely to dominate , So if B wins

Now Party A and Party B are competing , According to the formula ,

If a wins , A will update his elo The grade is divided into 1520.5 branch , And the integral of B will fall to 1579.5 branch , It is equivalent to deducting the amount of B 20.5 Give it to a . If B wins , A's... Will be deducted 12 Share to B , A becomes 1488 branch , B becomes 1612 branch .

And if it is a game with great disparity in strength , nail 2000 Points against B 1200 branch , A's expected winning rate is extremely close to 100%, So their elo The score will not change .

Let's assume that , At a particular time , The average strength of a player will not fluctuate greatly , So the more games he plays , His elo The grade score will be closer and closer to the grade score of his real strength .

Now we can think of a team as a player , So when teams play , You can get a team's elo The grade is divided .

3 Experimental results and discussion

Code list 1

Calss  Eloscore: ELO_RESULT_WIN=1 ELO_RESULT_LOSS=-1 ELO_RESULT_TIE=0 ELO_RATING_DEFAULT=1500 ratingA=0 ratingB=0 def __init__(self): self.ratingA= ratingA self.ratingB= ratingB def comuteK(self,rating1,rating2): return 1/(1+pow(10,(rating2-rating1)/400)) if __name__==’__main__’: eloscore=Eloscore() print(eloscore.computeScore(1500,1800)) print(eloscore.computeK(1500)) print(eloscore.computeK(1800))

4 Conclusion

For many similar balls , The fairness of games and other chess games , Use elo Mechanism score measurement method , By seeking elo Fraction experiment , Prove that you can use elo The mechanism measures the level of individual players or teams , To achieve the fairness of the game or game . This method only considers the competition results unilaterally , Not taking into account other special circumstances , So if you want to achieve a fairer game , It also needs to be considered from multiple aspects , Upgrade algorithm , More accurate assessment .