# Knowing that AlphaZero beat Stockfish 8 (28 wins, 0 losses, and 72 draws), what would AlphaZero's rating be?

I found three different questions here on SEC that asked what Stockfish 8's rating was for the match against AlphaZero, but none that asked what AlphaZero's rating should have been after (if it had been in a rated event, and assuming that it previously had an established, not provisional, rating).

Stockfish 8 was rated 3378 at the time per the official rating list. There was some dispute that it was handicapped, but since we cannot really factor that in accurately, it is better to ignore that for now.

+28, =72, -0 corresponds to a score of 64%.
The FIDE Rating Regulations effective from 1 July 2017 give details for calculating rating differences in table 8.1a. According to that table a fractional score of 0.64 corresponds to a rating difference of 102.

Hence if Stockfishes rating is 3378 then AlphaZero's is 3378+102 = 3480

• depends on what sort of significance you expect from a rating. i used a weighted average of draws = identical rating and wins means the player is about 300 higher. but that might need to be increased since alpha won zero games. Feb 22 '20 at 15:29

Here's an online calculator for this. 28 wins, 0 losses, and 72 draws is an elo difference of exactly 100.

Do remember that this score +28 =72 -0 score was against a handicapped version of Stockfish. In the full paper, AlphaZero scored +155 =839 -6, which is an elo difference of 52.

Statistically it should be about 3450 +/- 200 but it depends on the fine print of the rating system.

SEE edit where another site estimates 3750!!

Does game order matter?
Are they all rated as a group at the end?
Are their special rules for rating matches like USCF used to have?

And it depends on how accurate the statistical assumptions the rating system is based on were to begin with.

I love when non statisticians weigh in with nonsense reasons why that number is wrong. Perhaps I should have put a +/- error band on it initially.

From another site I found this estimate I estimate AlphaZero's playing strength at around 3750. Computer ratings are pretty compatible with FIDE, since we know Stockfish can beta Carlsen 3,000 times out of 100, making its 3441 or whatever accurate. ... It was also incorrectly thought that the positional sacrifice had been refuted by correct evaluations, but AlphaZero blew that out of the water. It plays more like Alekhine. Now when I train with Stockfish I don't treat the evaluations as gospel the way I might have before. ... What AlphaZero really shows is the value of othinking for yourself unless you want to be like th ecarbon-copy players who get to 2700 at age 14 and barely 2750 a decade later.

• I do not buy that. Recently, Caruana went +7 at Tata Steel and gained 20 points. I would think that it would have to be much higher. Any mathematical proof? As far as how they are rated, I would think either ICCF rules or even FIDE...no special USCF bonus points, etc. Feb 22 '20 at 14:25
• @PhishMaster the statistics are what they are. based on the ratings to give the results shown the estimate i gave is a good one for the rating of alphazero. i do not know the details of how computer ratings are done only some of the ones that have been used for humans. And they are all still just estimates based on past performance subject to future improvement/decline as well as a healthy dose of randomness since humans are not 100% consistent and can make mistakes at any time. Feb 22 '20 at 15:27
• Assuming +/- comes from something like 2 stddevs, it doesn't really make sense to use that since it's quite unlikely that AlphaZero is rated worse than Stockfish based on these samples. Feb 23 '20 at 14:23
• Could you elaborate on how you came about your calculations? Did you assume some sort of error bound on the samples? Perhaps with some distribution for the error? How did you move from that to your elo error bounds? Feb 23 '20 at 14:25
• thought I mentioned it was statistically. There is a probability of scoring a given % vs the difference in ratings. I used that to estimate the rating, although I did assume that they would play another hundred games and get the same results until the difference stabilized. That would give the true performance rating while just rating those games gives the 'performance' rating which would change if they played more games. Feb 23 '20 at 17:50