In the movie “Social Network”, Mark asked Eduardo for the formula to “rank girls” in facemesh.com.
The formula above is commonly known as the Elo rating system. It is used to calculate the relative skill levels of players or teams in competitive games, such as chess or sports.
In the formula:
- Ea represents the expected probability of Player/Team A winning the match.
- Eb represents the expected probability of Player/Team B winning the match.
- R_a represents the rating of Player/Team A.
- R_b represents the rating of Player/Team B.
The Elo rating system assumes that the probability of winning is solely determined by the difference in ratings between the two players/teams. The higher the rating difference, the greater the expected probability of winning for the higher-rated player/team.
The formula calculates the expected probabilities using the difference in ratings. The difference (R_b – R_a) is divided by 400 and then used as an exponent for the base of 10. The result is added to 1, and the reciprocal is taken to obtain the expected probabilities.
For example, if Player A has a rating of 1500 and Player B has a rating of 1600, we can calculate their expected probabilities using the formula:
Ea = 1/(1+10(1600 – 1500)/400) Eb = 1/(1+10(1500 – 1600)/400)
After calculating these values, Ea would represent the expected probability of Player A winning, and Eb would represent the expected probability of Player B winning.
It’s important to note that the Elo rating system has various variations and adjustments depending on the specific application and sport/game in which it is used. The formula you provided is the basic form of the Elo system.