# How do you calculate error bars on elo rating? [closed]

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?

• I'm voting to close this question as off-topic because it is a maths question, not a chess question. – Brian Towers May 23 '19 at 9:09
• LOL. People ask questions about shogi and things like that all the time – David May 23 '19 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. – Allure May 23 '19 at 21:29