Editing Elo rating system (section)

=== Implementing Elo's scheme ===
The USCF implemented Elo's suggestions in 1960,<ref name="aboutUSCF">{{cite web |url=http://www.uschess.org/about/about.php |title=About the USCF |publisher=United States Chess Federation |access-date=2008-11-10 |archive-date=2008-09-26 |archive-url=https://web.archive.org/web/20080926015601/http://www.uschess.org/about/about.php |url-status=live }}</ref> and the system quickly gained recognition as being both fairer and more accurate than the [[Chess rating systems#Harkness system|Harkness rating system]]. Elo's system was adopted by the [[Fédération Internationale des Échecs|World Chess Federation]] (FIDE) in 1970.<ref>Elo 1986, Preface to the First Edition</ref> Elo described his work in detail in ''The Rating of Chessplayers, Past and Present'', first published in 1978.<ref name="AEE1986">Elo 1986.</ref>

Subsequent statistical tests have suggested that chess performance is almost certainly not distributed as a [[normal distribution]], as weaker players have greater winning chances than Elo's model predicts.<ref>Elo 1986, ch. 8.73.</ref><ref>Glickman, Mark E., and Jones, Albyn C., {{url|http://www.glicko.net/research/chance.pdf|"Rating the chess rating system"}} (1999), Chance, 12, 2, 21-28.</ref> In paired comparison data, there is often very little practical difference in whether it is assumed that the differences in players' strengths are normally or [[Logistic distribution|logistically]] distributed. Mathematically, however, the logistic function is more convenient to work with than the normal distribution.<ref>Glickman, Mark E. (1995), {{url|http://www.glicko.net/research/acjpaper.pdf|"A Comprehensive Guide to Chess Ratings".}}
A subsequent version of this paper appeared in the ''American Chess Journal'', 3, pp. 59–102.</ref>
FIDE continues to use the rating difference table as proposed by Elo.{{r|fiderr2017|at=table 8.1b}}

The development of the Percentage Expectancy Table (table 2.11) is described in more detail by Elo as follows:<ref>Elo 1986, p159.</ref>
<blockquote>
The normal probabilities may be taken directly from the standard
tables of the areas under the normal curve when the difference in rating is
expressed as a z score. Since the standard deviation σ of individual
performances is defined as 200 points, the standard deviation σ' of the
differences in performances becomes σ√2 or 282.84. The z value of a
difference then is {{math|''D'' / 282.84}}. This will then divide the area under the
curve into two parts, the larger giving P for the higher rated player and
the smaller giving P for the lower rated player.

For example, let {{math|1=''D'' = 160}}. Then {{math|1=''z'' = 160 / 282.84 = .566}}. The table
gives {{math|.7143}} and {{math|.2857}} as the areas of the two portions under the curve.
These probabilities are rounded to two figures in table 2.11.
</blockquote>

The table is actually built with standard deviation {{math|200(10/7)}} as an approximation for {{math|200√2}}.{{citation needed|date=August 2023}}

The normal and logistic distributions are, in a way, arbitrary points in a spectrum of distributions which would work well. In practice, both of these distributions work very well for a number of different games.{{cn|date=August 2024}}