# How do you calculate error bars on elo rating?

In season 14 of TCEC, Stockfish defeated Leela 50.5-49.5 in a 100-game match (the closest possible winning margin). Using an elo calculator such as this one, we can see that the elo difference between the two engines was +3.

However it must be that this isn't a statistically significant result - after all the match was only 100 games, and it's the smallest possible winning margin. Therefore the error bars on this calculation should be at least 3. The calculator doesn't give the error bars though, and I can't find any equations on how to calculate the error. How do you calculate the error on this estimate?

Related: How do you calculate elo?

Edit: Looks like 3dkingdoms have improved their calculator, which is now capable of calculating an error margin. I'd still be interested in seeing how that error margin is calculated, though.

• I'm voting to close this question as off-topic because it is a maths question, not a chess question. May 23, 2019 at 9:09
• LOL. People ask questions about shogi and things like that all the time May 23, 2019 at 20:38
• I'd put this on Math.SE, but then first I'd have to explain what elo is, how it translates to expected performance, etc. May 23, 2019 at 21:29
• @Allure I think CrossValidated (Stats.SE) can handle this if Chess.SE won't allow it. You could probably reword it to "What is the uncertainty on the rating estimate in the Elo model? in order to make it suitable here. Feb 13, 2023 at 13:08
• Voting to reopen. If the math involved here isn't sufficiently chess related, then neither is almost any other "chess question". Feb 13, 2023 at 16:20