Yesterday I put a tweet out about average Elo gain vs winrate. It produced the following pretty gapminder-esque graph.

The immediate responses I got were all focused on how to interpret the data, and in attempting to resolve this I discovered one small issue (playing a huge amount of games might mean your team reaches it’s Elo ceiling), meaning players which shuffle a lot and make gains could have it easier.

Fortunately, the solution I came up with not only fixes this, but also allows for an easy dimensionality reduction: just down to skill. In each match there are two input variables (the underlying skills of each team) and the output (the result). When evaluating a player’s career, the prior visualization aggregated Elo gain (based on difference in skills and the result) against winrate (the output); however by instead just looking at average opponent skill and (average) winrate we’re actually in a nifty position.

This is because most rating systems implicitly solve the problem at hand: in a match where we’re equally skilled to our opponent we expect a 50% winrate. By some maths jumbling, we can also calculate that, given for example a 50% winrate against an opponent (over a large sample) we should be similarly skilled (our_skill - their_skill = 0). Likewise, we can calculate this difference for any winrate, so someone we have a 55% winrate against equates to a 34.87 advantage over our opponents (and how x% translates into a y-point advantage).

The only thing left to do is calculate this advantage for each player given their winrate, and then add this to their average opponent rating. This is equivalent to finding an opponent for each player for which they would have a 50% winrate against, and then looking at the average skill of that opponent.

The top 27 of the players with 500+ games.

The 28–54 of the players with 500+ games.

A full sheet is available here.

This methodology is obviously flawed in that it assumes everyone in a team contributes equally in each game, or if there’s a heavily skewed opponent skill distribution (for example if a team has 100% winrate against a 800 skill team and a 0% winrate against a 2600 skill team this doesn’t directly translate to a 50% winrate against a 1700 skill team). That said, in all the players listed (who have 500+ games) their opponent skill distributions are similar enough (Kolmogorov-Smirnov for bins=10), both in terms of Elo 32 and Glicko 2.