Player Game Play Ratings

Why Have Player Ratings?

The best Euro strategy games, like traditional strategy games, enable skill improvement through repeat play and study. Within any group of players there is likely to be a range of abilities and levels of interest. Games tend to be more rewarding when played among people of similar abilities, though of course there are exceptions. Maintaining player ratings on a per game basis provides information on each player's relative strength in individual games and permits players, if they wish, to consider ratings when hosting or joining games.

The Multiplayer Elo System

The Elo rating system is widely used by chess federations and other sports bodies. As originally designed by Arpad Elo it was for two-player games. However, the underlying mathematics can be extended to handle multiplayer games. Danny Cunningham, in Developing a Generalized Elo Rating System for Multiplayer Games, did just that. In addition, he published Multielo, a Python package that implements his solution and includes an extensive demo of its use.

Multielo has four parameters whose values effect ratings calculations. The K, D, and Score function parameter values are Multielo's defaults:

• Initial rating (per player and game) -- 1200. There is no generally agreed upon initial rating, but the range across many systems is between 1200 and 1500 (see Lichess).

• K -- 32. This effects the extent of change when ratings are updated after a game. Larger K values produce greater shifts.

• D -- 400. Lower D values increase the expectation that stronger players will win, which in turn reduces ratings shifts.

• Score function base -- 1 (linear). With a linear score function, improving from 5th place to 4th is just as valuable as improving from 2nd to 1st. In contrast, an exponential score function (a parameter value such as 1.5 or 2), gives more of the rewards to players who finish at the top — improving from 2nd to 1st is worth a lot, while 4th is only rewarded a small amount more than 5th.

In the Elo system, each player has some rating before a game is played, and after we observe the outcome of the game, we use a simple formula to calculate each player’s new rating. That makes it easy to track each player’s rating over time. The ratings change as you would expect. Winning always improves a player’s rating and losing always hurts it. Beating a strong player is worth more than beating a weaker player.