The ELO system
The ELO system was developed for the International Chess Federation by mathematician Arpad Elo in 1978. It was based on the following ideas:
- The scores of the two players are compared before the duel. Let's call A the one with the best score, and B the other.
- If A wins, it is considered normal: he was better ranked. A will win only a few points (very few if B was far from him, more points if B was closer). Likewise, B will lose very few points.
- If B wins, then it means that the original ranks were incorrect. B will win many points, and A will lose many. The number of points won/lost will increase as A and B were far apart.
This way, after many games with various players, A and B will end up "at their place". After that, if they always beat players who are below them, and are always beaten by better ranked players, then nothing happens, their ranks are stabilized.