Editing Elo rating system (section)

==== Most accurate K-factor ====
The second major concern is the correct "{{mvar|K}}-factor" used. The chess statistician [[Jeff Sonas]] believes that the original <math>\; K = 10 \;</math> value (for players rated above 2400) is inaccurate in Elo's work. If the {{mvar|K}}-factor coefficient is set too large, there will be too much sensitivity to just a few, recent events, in terms of a large number of points exchanged in each game. And if the K-value is too low, the sensitivity will be minimal, and the system will not respond quickly enough to changes in a player's actual level of performance.

Elo's original {{mvar|K}}-factor estimation was made without the benefit of huge databases and statistical evidence. Sonas indicates that a {{mvar|K}}-factor of 24 (for players rated above 2400) may be both more accurate as a predictive tool of future performance and be more sensitive to performance.<ref>A key Sonas article is {{cite news |first=Jeff |last=Sonas |title=The Sonas rating formula — better than Elo? |website=chessbase.com |url=http://www.chessbase.com/newsdetail.asp?newsid=562 |access-date=2005-05-01 |archive-date=2005-03-05 |archive-url=https://web.archive.org/web/20050305143008/http://www.chessbase.com/newsdetail.asp?newsid=562 |url-status=live }}</ref>

Certain Internet chess sites seem to avoid a three-level K-factor staggering based on rating range. For example, the ICC seems to adopt a global {{math|1=''K'' = 32}} except when playing against provisionally rated players.

The USCF (which makes use of a [[logistic distribution]] as opposed to a [[normal distribution]]) formerly staggered the K-factor according to three main rating ranges:
:{|
|- 
! {{mvar|K}}-factor !! Used for players with ratings ...
|- style="vertical-align:top;"
| <math>\; K = 32 \;</math> || below 2100 
|- style="vertical-align:top;"
| <math>\; K = 24 \;</math> || between 2100 and 2400 
|- style="vertical-align:top;"
| <math>\; K = 16 \;</math> || above 2400 
|}

Currently, the USCF uses a formula that calculates the {{mvar|K}}-factor based on factors including the number of games played and the player's rating. The K-factor is also reduced for high rated players if the event has shorter time controls.<ref name="uschess2020">{{cite report |title=The US Chess Rating system |date=April 24, 2017 |via=glicko.net |url=http://www.glicko.net/ratings/rating.system.pdf |access-date=16 February 2020 |archive-date=7 February 2020 |archive-url=https://web.archive.org/web/20200207072639/http://www.glicko.net/ratings/rating.system.pdf |url-status=live}}</ref>

FIDE uses the following ranges:<ref name="FideRules">{{cite report |title=FIDE Rating Regulations effective from 1&nbsp;July 2014 |date=2014-07-01 |website=FIDE Online (fide.com) |publisher=[[FIDE]] |url=http://www.fide.com/fide/handbook.html?id=172&view=article |access-date=2014-07-01 |archive-date=2014-07-01 |archive-url=https://web.archive.org/web/20140701031750/http://www.fide.com/fide/handbook.html?id=172&view=article |url-status=live}}</ref>

:{|
|- style="vertical-align:top;"
! {{mvar|K}}-factor !! Used for players with ratings ...
|- style="vertical-align:top;"
| <math>\; K = 40 \;</math> || for a player new to the rating list until the completion of events with a total of 30&nbsp;games, and for all players until their 18th birthday, as long as their rating remains under 2300.
|- style="vertical-align:top;"
| <math>\; K = 20 \;</math> || for players who have always been rated under 2400.
|- style="vertical-align:top;"
| <math>\; K = 10 \;</math> || for players with any published rating of at least 2400 and at least 30&nbsp;games played in previous events. Thereafter it remains permanently at 10.
|}

FIDE used the following ranges before July&nbsp;2014:<ref name="FideRulesOld">{{cite report |title=FIDE Rating Regulations valid from 1&nbsp;July 2013 till 1&nbsp;July 2014 |date=2013-07-01 |website=FIDE Online (fide.com) |url=http://www.fide.com/fide/handbook.html?id=161&view=article |access-date=2014-07-01 |archive-date=2014-07-15 |archive-url=https://web.archive.org/web/20140715002648/http://www.fide.com/fide/handbook.html?id=161&view=article |url-status=live }}</ref>

:{|
|-
! {{mvar|K}}-factor !! Used for players with ratings ...
|- style="vertical-align:top;"
| <math>\; K = 30 \;</math><br/>(was 25) || for a player new to the rating list until the completion of events with a total of 30 games.<ref name="Changes to FIDE Rating Regulations">{{cite press release |title=Changes to Rating Regulations |website=FIDE Online (fide.com) |publisher=[[FIDE]] |date=2011-07-21 |url=http://www.fide.com/component/content/article/1-fide-news/5421-changes-to-rating-regulations.html |access-date=2012-02-19 |archive-date=2012-05-13 |archive-url=https://web.archive.org/web/20120513170023/http://www.fide.com/component/content/article/1-fide-news/5421-changes-to-rating-regulations.html |url-status=dead }}</ref>
|- style="vertical-align:top;"
| <math>\; K = 15 \;</math> || for players who have always been rated under 2400.
|- style="vertical-align:top;"
| <math>\; K = 10 \;</math> || for players with any published rating of at least 2400 and at least 30 games played in previous events. Thereafter it remains permanently at 10.
|}

<!-- I find the remainder of this section incomprehensible. Help!! -->
<!-- I think -- but am not certain -- that it is saying a high K-factor helps high rated players exploit other flaws in the rating system in situations where they can choose their opponents. -->
The gradation of the {{mvar|K}}-factor reduces rating change at the top end of the rating range, reducing the possibility for rapid rise or fall of rating for those with a rating high enough to reach a low {{mvar|K}}-factor.

In theory, this might apply equally to online chess players and over-the-board players, since it is more difficult for all players to raise their rating after their rating has become high and their {{mvar|K}}-factor consequently reduced. However, when playing online, 2800+ players can more easily raise their rating by simply selecting opponents with high ratings – on the ICC playing site, a [[grandmaster (chess)|grandmaster]] may play a string of different opponents who are all rated over 2700.<ref>{{cite web |title=''K''-factor |series=ICC Help |website=Chessclub.com |date=2002-10-18 |url=http://www.chessclub.com/help/k-factor |access-date=2012-02-19 |url-status=dead|archive-url=https://web.archive.org/web/20120313023307/http://www.chessclub.com/help/k-factor |archive-date=2012-03-13 }}</ref> In over-the-board events, it would only be in very high level all-play-all events that a player would be able to engage that number of 2700+ opponents. In a normal, open, Swiss-paired chess tournament, frequently there would be many opponents rated less than 2500, reducing the ratings gains possible from a single contest for a high-rated player.