--- date: "2020-03-01" title: How do Elo ratings work? summary: "And what are Monte Carlo simulations?" ---

Physics professor Arpad Elo invented Elo ratings to rank chess players, but Elo is now used for all manner of competitions. His simple but effective system sets the average player or team at 1500 and then adds or subtracts from this rating after each matchup depending on each team’s initial rating and the so-called K-factor which determines how many points are up for grabs in each game. In leagues like the NFL, where there are few but highly-meaningful games, the K-factor is high. In the 144-game KBO season, the K-factor is much lower. We set the K at 4 points and then make adjustments for home field advantage and margin of victory. After each season, we regress each team’s rating by 25%. In other words, we expect that the best teams from 2019 probably won’t be quite as good this year, the worst teams probably won’t be so bad, and the average teams will probably be about the same. That’s the starting point for the season, at least. You can see Elo ratings calculated after every game since 2013—the start of the ten team era—here.

Elo ratings can also be used to make predictions about future matchups. We calculate the likelihood that each team will win every upcoming matchup and then simulate the season 100,000 times using the Monte Carlo method of drawing random numbers. The result is the series of final standings probabilities found here.