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I know how to calculate elo rating (in chess) and etc but why when it was made the inventor of elo rating decided to use constant $400$ and $10$ in expected score formula? The formula: $$ExpectedScoreA=\frac{1}{1+10^{(RactingB-RatingA)/400}}$$

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  • $\begingroup$ I suppose the values the function more flat, for the spectrum of elos. $\endgroup$ – ty. Jul 10 '18 at 15:47
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I would assume the $10$ is just because we like computing powers of $10$. Then Wikipedia claims:

Elo suggested scaling ratings so that a difference of 200 rating points in chess would mean that the stronger player has an expected score ... of approximately 0.75.

And indeed, $\frac{1}{1+10^{-1/2}}\approx 0.7597$.

(If we'd started with a base of $e$ instead of $10$, the scale factor would probably have ended up as $200$ or $225$.)

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