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approx range of rating based on centipawn loss

It doesn't work that way. Many variables affect it; it's useless for most purposes.
There is a way but not just random analysis. there is easy ways to modify cpl like playing out hopeless endgame. if player has lost the game then all moves are good and playing to check mate will reduce acpl a lot. other way it play game with loads of immediate trades and then agreeing on draw. First problem can addresses making estimate only for contested part of game. Original article http://www.ailab.si/matej/doc/Using_Heuristic-Search_Based_Engines_for_Estimating_Human_Skill_at_Chess.pdf

and small trial implementation by now defunct chess site
web.archive.org/web/20161124110504/http://chess-db.com/public/research/qualityofplay.html

I worth to note that this high correlation visible in chart is stronger for for strong players. So you can estimate with about 10ish games players strength. If you are willing to write some softwate that is.

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