In the name of science: ![]()
I copied result (first page = 20 games) from top 10 players at chess.com ranking-list (rapid).
After filtering all games with rating diff > 400 (174 games) I got the best expected result (lowest std dev) with the factor 353 (instead of original formula 400).
Expected result = 1 ( 1 + 10^((Ra-Rb)/353)))
I think I need more data in order to really say exactly what factor to use for the most accurate prediction on this level of play, but it seems like the 400 factor is rather good. Which maybe is what to expect when the ranking uses this formula, I guess it is sort of "self-tuning"?
Also, it is Elo, not ELO. It is not an acronym, it is the name of the guy who invented it.
If he wants it to be his namesake, he should have provided the formula.
Professor Arpad Imre Elo did explain his rating system in great detail in his book "The Rating of Chess Players Past and Present". It is out of print but used copies are readily available online. Warning: lots of complicated math is involved.