Scott Mackie

The Math Behind ELO

If you’ve ever participated in some form of ranked sport or video game, chances are that you have heard about the ELO Rating System. Originally designed for ranking professional chess players, it has been adopted to many other domains such as college football, Scrabble, and video games. ELO’s popularity has been primarily driven by its impressive accuracy considering its simplicity, making it an ideal solution for someone that wants to add a ranking system to their own projects. even the initial version of the “Facebook Algorithm” was implemented using ELO!


I’ll give a brief overview of the ELO algorithm, its applications, and how it can be extended to better model the skill distributions of various playerbases.

The Algorithm

ELO is generally used to rank a set of players by using a set of historical match results. Suppose we have 4 competitive ping-pong players; Amy, Brad, Cindy...

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