1.15 Simply stated, the Elo Rating System is a numerical system in which differences in rating may be converted into scoring or winning probabilities.
1.22 So that one may say how much or how many times one player exceeds another, an interval or ratio scale is desirable.
1.67 Eventually differences in ratings will be generated which conform to the percentage expectancy curve on which the system is based.
3.51 His true challenge is maintenance of the integrity of the ratings in his pool, so that from one year to the next, or from one decade to the next, a given rating will represent essentially the same level of chess proficiency.
2.61 The valid test of a rating system, as of any theory, lies in its success in quantitative prediction, in forecasts of the scores of tournaments or matches.
Elo, Arpad E. (1978). The Rating of Chessplayers past & present. ISBN 0-7134-1860-5
FIDE (2021). Rating Regulations