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Elo ratings

  • A common ranking system for chess, soccer, e-sports
  • Ratings depend on the final score of each game and where it was played
  • Teams always gain Elo points after winning games and lose points after losing them
    • More points for upset wins and winning by wider margins
  • The system is zero-sum, however many points one team wins the opposing team loses them
  • K-factor
    • Determines how quickly the rating reacts to new game results
    • Optimal k-factor for NBA was found to be 20 by 538
    • This value is higher than baseball and it makes sense because basketball is subject to less randomness and better teams win more often than not
  • Home court advantage
    • Set to 100 Elo ranting points in NBA
  • Margin of victory (MOV+3)0.87.5+0.006×elodiff\frac{(MOV+3)^{0.8}}{7.5+0.006\times elo_{diff}}
  • Elo ranking is carried over year-to-year to maintain some sense of memory
    • Uses 3/4 of the rating to start a new season and 1/4 of the league average