# Tournament System Math Explanation

When two teams play, each set (i.e., game) of the match is treated separately. The winning team’s ranking will increase and the losing team’s ranking will decrease, according to the following formulae:

Assume Team A beats Team B:

TeamA_New_Rating= TeamA_Old_Rating + (1- Probability_of_winning) * 32points
TeamB_New_Rating= TeamB_Old_Rating + Probability_of_winning * -32points

The probability of winning formula is calculated based upon the rankings:
Probability_TeamA_wins = 1/(1+(10^-((TeamA-TeamB)/400)))

For example, if Team A’s rating is 1600 and Team B’s rating is 1500 (and A beats B):

TeamA_New_Rating = 1600 + (1 - 1/(1+(10^-((1600-1500)/400)))) *32
= 1600 + (1 - 1/(1+(10^-(1/4)))) *32
= 1600 + (1 - 1/(1+(10^-(1/4)))) *32
= 1600 + (1 - 1/(1+.56)) *32
= 1600 + (1 - 1/(1+.56)) *32
= 1600 + (1 - .64) *32
= 1600 + 12
= 1612

The table below shows how ratings relate to probability of winning:

Your Rating - Opponent Rating Probability that you should win
400 91%
300 85%
200 76%
150 70%
100 64%
50 57%
0 50%