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A word about ratings

By: Adam Plumb 6.6 years ago

I've gotten some requests recently for information about how the rating system works. Here is a quick overview:

A user's rating is meant to represent and distill a user's skill level into a single number. In fact, your current rating tells the game what your "expected" score is in each round you play. And if you don't match up to your expected score, your rating will go down. If you surpass your expected score, your rating will go up. It's as simple as that.

Let us say there are three people playing in a room. After a game, but before recalculating their ratings, they have the following ratings and scores:


Based on each of these players' scores and ratings, each player gets an "expected" score. This is the score that they need to get in order to have their ratings stay the same. Expected scores are calculated by dividing the sum of scores (40+90+70=200) by the sum of ratings (1100+1600+1300=4000). The resulting quotient, .05, is multiplied by each person's current rating (i.e. 1100 x .05) to get their expected score. Here's a table...

NameExpected ScoreScore

You can see here that both Alex and Jenny did better than expected, but poor Adam did worse. Therefore, we know that both Alex's and Jenny's ratings will go up, but Adam's will go down. But, how much?

Here is where things get a bit tricky. There is no one perfect way of determining how much their ratings change, because the amount of change is mostly arbitrary. It is simply a matter of making up some rules for what the maximum amount of change per game will be, and how much over or under the expected score the player has to be in order to get that maximum. In our case, I've decided that the maximum change in points one can get per game is 16 (the current number), and in order to get +/- 16 points per game you either have to get a score that is 75% greater than expected or 75% worse than expected. For example, Jenny's expected score is 65 points. But if she get's 75% greater than that (or 1.75 x 65), which is 114, then her rating will improve by 16 points. However, if she get's 75% worse than expected (or .25 x 65), which is 16, then her rating will decrease by 16 points. Anywhere from 25% of the expected score to 175% the expected score will bring a range of -16 to +16 points. If you fall outside of that range, your rating will be limited to the maximum change (+/- 16). Also, there is a mimimum allowable rating of 100 and a maximum of 9999, so players will never exceed those amounts.

Let's look at how the players' ratings changed:

NameExpected ScoreScoreOld RatingNew Rating

I hope this shines some light on the ratings system. If you have any questions, shoot me an email and I'll do my best to answer.

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