Accuracy And Ratings On Chess.com

In order to establish that Chess.com Accuracy scores, properly adjusted to produce what I call "Quality" numbers, can accurately predict actual ratings, I did two studies involving Chess.com rapid and blitz ratings, and accuracy or Quality numbers.

The first study measures the relationship between accuracy and Chess.com blitz and rapid ratings at various time controls for players in 100 Elo point buckets. Data is from two years ago, but I don't think anything has changed too much in that time. Each specified Elo includes all games where both players are within 100 Elo of that figure in either direction. There was an 80-game minimum (60 for 10-minute games). Note that the 10+0 ratings are a rapid time control, but the others blitz, so the 10+0 data isn't directly comparable to the others since the rapid scale is much more compact.

The draw percentage was small enough that I didn't bother to exclude them here; this is only critical when examining individual results. Since every win was counted for both sides, there was no point in making the 1.5-point win or loss adjustments; it would not change the average. The final column "Linear 10+0 Est." is equal to: rapid Elo divided by 100, plus 64.   

So for three-minute games, each accuracy point from 1600 to 2800 Elo is worth on average about 128 Chess.com Blitz Elo points. For 10+0 rapid games, each accuracy point from 1600 to 2400 Elo is worth on average about 92.6 Elo. Since Chess.com blitz ratings are spread out much more than rapid ratings, these two numbers are quite consistent.

If we expand the rapid range to 1000 to 2400, each accuracy point is worth about 96.6 Elo. If we extend all the way down to 400, each rapid accuracy point is worth 101.9 elo points. So although it's not a perfect linear fit, it seems close enough to linear for practical purposes, and if we say that one accuracy point equals 100 rapid Elo points, we are very close to fitting the data. The simple formula...

Rapid Accuracy = Rapid Elo/100 + 64

... matches the 1600 and above data roughly by mean, with no errors over 1.2 Accuracy (120 Elo) and a median error of only 0.39 (39 Elo). Note that Magnus Carlsen at 2884 Chess.com Rapid would have an estimated accuracy of 92.84, not far from his actual 92.61 accuracy for the last year or 92.64 all-time. So the crude rounded linear approximation appears to be valid all the way from 1600 to 2900, and only off a little all the way down to 400! 

It should also be noted that accuracy scores are consistently higher for White than for Black, by about 1.12 Elo on average, so half an Elo point added to Black and subtracted from White should be an improvement for individual games, though it won't matter for aggregate results assuming colors are roughly in balance.  

In every case (except at 400 Elo, where the 3+0 sample is small), accuracy climbs from 3+0 to 5+0, with the average improvement being 1.174 accuracy point, which is 150 blitz Elo points. Surprisingly, in every case accuracy climbs when going from 5+0 to 3+2, by an average of 1.19, so 152 Elo points! This is very unexpected, since on average 3+2 games take less time than 5+0 games, since the average game length is well below 60 moves.

I suppose the explanation is that no one can predict reliably how many moves a game will go, so without increment one either has to play fast in case the game goes long or risk having to move instantly or premove to avoid forfeit in a long game. Increment budgets your time properly for you almost automatically. Based on this result, I would encourage players to use such increment time controls to get the best quality games in the least amount of time, the difference seems to be quite large. There is a good reason that almost all non-bullet Chess.com events for titled players use increment. 

So we have established that you should be able to estimate Chess.com rapid ratings by taking the average rapid accuracy, subtracting 64, and adding two zeroes at the end, at least if the accuracy is 80 or more. If it is below 80, the formula will overstate your likely rating somewhat, perhaps by 100 Elo or so on average for accuracy numbers in the low- to mid- 70s. This assumes that you play opponents around your own level; if you play mostly much stronger players, it will underestimate your rating by 100 Elo or so, while if you play mostly weaker players, it will overestimate your rating similarly. If you have an unusually high draw percentage, your rating will be overestimated by the formula. 

Of course if you have a meaningful average Chess.com rapid accuracy, you also presumably have a meaningful Chess.com rapid rating, so this might seem pointless. The real point is to demonstrate that these accuracy numbers can predict Elo ratings pretty well as long as there is a reasonable sample of games (even 30 is pretty good), so this can be used to predict Elo in classical time limit games from accuracy numbers, even if the players have no Elo rating, for example for players before FIDE adopted the Elo system in 1970.  

The above analysis groups players by approximate rating, but how valid is this method for rating individual players? The next table attempts to answer this question.

Players on Rapid Leaderboard 2700 and up with at least 40 rated games vs. GMs in the last year, real names known, and "insights" public (which provides the data). Accuracy for last year only; Quality excludes draws and adjusts wins down by 1.5 and losses up by 1.5. Predicted Rapid rating by (adj. Acc - 58.5) x 90. Formula is different from previous table since draws are excluded here, which lowers accuracy scores, especially for highly rated players. 

Now a sampling further down the list; players number 50, 100, 200, 300 or the first one after those numbers meeting the criteria with 40 rated games vs. FIDE titled opponents (not only GMs). 

To extend the list downward while staying above 2000, here is one popular streamer with enough recent rapid games against equal level opposition to be a valid data point: 

Note that the predicted rapid ratings of the top three rated players were also the three highest Quality scores and therefore the three highest predicted ratings, in the same order. Note also that no predicted rating was off by as much as 140 Elo, and that the median error for the twenty players was just 48.5 Elo. Considering all the random factors that affect both Elo and accuracy scores, as well as the wide range of ratings included, I think that this is a very good fit, and shows that adjusted accuracy scores are not only valid for predicting ratings of groups of players, but are pretty good at predicting individual ratings as long as we have about 50 competitive games per player (i.e. excluding gross mismatches).  

I also did some studies on comparing Chess.com rapid ratings with FIDE standard (classical) ratings for players with ratings in both categories. For FIDE titled players (FIDE Master and above, including WGM) the Chess.com rapid ratings run consistently lower by somewhere around 50 Elo or so, except at the very top. Presumably these ratings are mostly based on a significant number of FIDE rated games and should be reasonably accurate.

For players in general (regardless of title), one study shows the crossover point is around 2100, meaning above that level the Chess.com rapid ratings are lower, but below 2100 they are higher. Many of these lower-rated, untitled players may be rapidly improving kids, whose classical ratings haven't kept up with their online ratings, so I would regard the estimate from my titled players study as being the one that shows the true picture for players with reliable FIDE ratings above 2100. If so, it means that if you take your Chess.com rapid rating and add 50 points, this is a reasonable estimate for what FIDE rating you should get if you are able to get full benefit from the much longer time controls, at least if you are over 2000 Chess.com Rapid.