|
Ping Pong Points
The Ultimate Ping Pong Player Rating System
How We Calculate Rankings
PingPongPoints.com strives to provide the most accurate player ranking system possible. The following document not only describes the exact mechanisms employed to provide such accurate ratings, but also highlights potential areas for improvement in the future.
Origins
PingPongPoints.com borrows heavily from the Elo chess ranking system. This system was Arpad Elo in the early 1900's. His system, and variations of his system, are still used today to rank professional chess players. The Elo system, as well as the PingPongPoints.com system, rank players. Players start with a a ranking of 1500. As they win and lose matches, the loser will "give" points to the winner. Roughly, A difference of 200 points indicates that the player with more points will win 75% of the time.
Algorithm
The first step to the algorithm is determining the chance a player will win. The easiest way to do this is to calculate the chance the lower rated player will win. The chance the higher rated player will win is then one minus that value.
Chance Lower Rated Player Will Win: 1/(e^(rating_difference/200) + 1)
where e is the natural number(2.71....)
and rating_difference is the higher rating minus the lower rating The second step is to determine the amount of points that will change hands based on the winner. The following formula determines the point swing: margin_of_victory_mulitiplier * K * (did_higher_rated_player_win - chance_higher_rated_player_will_win)
where margin_of_victory_multiplier ensures that major victories are worth 150% as much as minor victories
K is the maximum number of points that you can receive from a victory. This is currently 64 points. did_higher_rated_player_win is 1 if the higher player won, 0 if they lost. chance_higher_rated_player_will_win is calculated above That's basically it. The winner will be stealing those points from the losing player. Examples
Example #1: Suppose William the Heavy is ranked 2000. Also, Ricky the Washed Out is ranked 400. We can calculate the chance that Ricky the Washed Out will win. The formula we use is 1/(e^(1600/200) + 1). That means that Ricky the Washed Out has basically a 0% chance of winning. If Ricky the Washed Out some how wins by 2 points, he will get K * 1 points. we set K to 64 so he will get 64 points. If Ricky the Washed Out had won by more than 5, he would have gotten 150% of the points; he would have gotten 96 points!
Example #2: Suppose that Bill to Bashful is playing Frank the Fat. Let's assume that Bill the Bashful has 220 more points than Frank the Fat. The chance that Frank the Fat will win is 1/(e+1) which is equal to about 25%. If Bill the Bashful will win, he will get K * (1 - 0.75) points. He will get 16 points.
Example Point Swings
The following table shows some points swings based on the rating difference between the two players.
Awards
PingPongPoints.com has created a number of awards to reward players.
2009 © Jim Englert
|