I’d suggest fitting an isotonic regression instead. I think it’s a reasonable expectation that online and FIDE ratings are monotonically related but it seems unlikely to me that they are linearly related even though it may be an ok approximation for players in a particular rating range.
I suspect that the online population — especially at lower ratings — is significantly different to the over the board population. I also expect — especially in the FIDE case — that ratings stratify the players into hobbyists, serious amateurs, professionals, etc and so different FIDE rating ranges are likely to scale to online ratings differently.
All of the above should be implicitly accounted for in an isotonic regression so long as monotonicity holds globally. You can easily do it with sklearn and I suspect it may give you better results.
