Editing Elo rating system (section)

== Different ratings systems ==
The phrase "Elo rating" is often used to mean a player's chess rating as calculated by FIDE. However, this usage may be confusing or misleading because Elo's general ideas have been adopted by many organizations, including the USCF (before FIDE), many other national chess federations, the short-lived [[Professional Chess Association]] (PCA), and online chess servers including the [[Internet Chess Club]] (ICC), [[Free Internet Chess Server]] (FICS), [[Lichess]], [[Chess.com]], and [[Yahoo!]] Games. Each organization has a unique implementation, and none of them follows Elo's original suggestions precisely.

Instead one may refer to the organization granting the rating. For example: "As of April 2018, [[Tatev Abrahamyan]] had a FIDE rating of 2366 and a USCF rating of 2473." The Elo ratings of these various organizations are not directly comparable, since Elo ratings measure the results within a closed pool of players rather than absolute skill.

===FIDE ratings===
{{See also|FIDE world rankings}} {{See also|List of FIDE chess world number ones}}
For top players, the most important rating is their [[FIDE]] rating. FIDE has issued the following lists:
* From 1971 to 1980, one list a year was issued.
* From 1981 to 2000, two lists a year were issued, in January and July.
* From July 2000 to July 2009, four lists a year were issued, at the start of January, April, July and October.
* From July 2009 to July 2012, six lists a year were issued, at the start of January, March, May, July, September and November.
* Since July 2012, the list has been updated monthly.

The following analysis of the July 2015 FIDE rating list gives a rough impression of what a given FIDE rating means in terms of world ranking:
* 5,323 players had an active rating in the range 2200 to 2299, which is usually associated with the [[Candidate Master]] title.
* 2,869 players had an active rating in the range 2300 to 2399, which is usually associated with the [[FIDE Master]] title.
* 1,420 players had an active rating between 2400 and 2499, most of whom had either the [[International Master]] or the [[International Grandmaster]] title.
* 542 players had an active rating between 2500 and 2599, most of whom had the [[International Grandmaster]] title.
* 187 players had an active rating between 2600 and 2699, all of whom had the [[International Grandmaster]] title.
* 40 players had an active rating between 2700 and 2799. <!-- do not change this unless updating the whole list, it is correct for July 2015 -->
* 4 players had an active rating of over 2800. ([[Magnus Carlsen]] was rated 2853, and 3 players were rated between 2814 and 2816). <!-- do not change this unless updating the whole list, it is correct for July 2015 -->
 
The highest ever FIDE rating was 2882, which [[Magnus Carlsen]] had on the May 2014 list. A list of the highest-rated players ever is at [[Comparison of top chess players throughout history]].

====Performance rating====
{{See also|Performance rating (chess)}} 
{| class="wikitable" style="width:100px; float:right; text-align:center; margin-top:0; margin-left:10px;"
|-
! style="width:50%;"|<math>p</math>
! style="width:50%;"|<math>d_p</math>
|- 
| 1.00 || +800
|- 
| 0.99 || +677
|-
| 0.9 || +366
|-
| 0.8 || +240
|-
| 0.7 || +149
|-
| 0.6 || +72
|-
| 0.5 || 0
|-
| 0.4 || −72
|-
| 0.3 || −149
|-
| 0.2 || −240
|-
| 0.1 || −366
|-
| 0.01 || −677
|-
| 0.00 || −800
|}
Performance rating or special rating is a hypothetical rating that would result from the games of a single event only. Some chess organizations{{r|uschess2020|p=p. 8}} use the "algorithm of 400" to calculate performance rating. According to this algorithm, performance rating for an event is calculated in the following way:
# For each win, add your opponent's rating plus 400, 
# For each loss, add your opponent's rating minus 400, 
# And divide this sum by the number of played games.

Example: 2 wins (opponents {{mvar|w}} & {{mvar|x}}), 2 losses (opponents {{mvar|y}} & {{mvar|z}})<br />
<!--Please see Talk page for the formatting changes I made here. Thanks!-->
:<math>
\begin{align}
& \frac{w+400+x+400+y-400+z-400}{4} \\[6pt]
& \frac{w+x+y+z+400(2)-400(2)}{4}
\end{align}
</math>
This can be expressed by the following formula:
:<math> \text{performance rating} = \frac{\text{total of opponents' ratings } + 400 \times (\text{wins} - \text{losses})}{\text{games}}</math>
Example: If you beat a player with an Elo rating of 1000,
:<math>
\text{performance rating} = \frac{1000 + 400 \times (1)}{1} = 1400</math>
If you beat two players with Elo ratings of 1000,
:<math> \text{performance rating} = \frac{2000 + 400 \times (2)}{2} = 1400</math>
If you draw,
:<math> \text{performance rating} = \frac{1000 + 400 \times (0)}{1} = 1000</math>

This is a simplification, but it offers an easy way to get an estimate of PR (performance rating).

[[FIDE]], however, calculates performance rating by means of the formula<math display="block">\text{performance rating} = \text{average of opponents' ratings} + d_p,</math>where "rating difference" <math>d_p</math> is based on a player's tournament percentage score <math>p</math>, which is then used as the key in a lookup table where <math>p</math> is simply the number of points scored divided by the number of games played. Note that, in case of a perfect or no score <math>d_p</math> is 800.
{{Clear}}

===Live ratings===
[[FIDE]] updates its ratings list at the beginning of each month. In contrast, the unofficial "Live ratings" calculate the change in players' ratings after every game. These Live ratings are based on the previously published FIDE ratings, so a player's Live rating is intended to correspond to what the FIDE rating would be if FIDE were to issue a new list that day.

Although Live ratings are unofficial, interest arose in Live ratings in August/September 2008 when five different players took the "Live" No. 1 ranking.<ref>Anand lost No. 1 to Morozevich ([http://www.chessbase.com/newsdetail.asp?newsid=4860 Chessbase, August 24 2008] {{Webarchive|url=https://web.archive.org/web/20080910150925/http://www.chessbase.com/newsdetail.asp?newsid=4860 |date=2008-09-10 }}), then regained it, then Carlsen took No. 1 ([http://www.chessbase.com/newsdetail.asp?newsid=4892 Chessbase, September 5 2008] {{Webarchive|url=https://web.archive.org/web/20121109045914/http://chessbase.com/newsdetail.asp?newsid=4892 |date=2012-11-09 }}), then Ivanchuk ([http://www.chessbase.com/newsdetail.asp?newsid=4901 Chessbase, September 11 2008] {{Webarchive|url=https://web.archive.org/web/20080913210432/http://www.chessbase.com/newsdetail.asp?newsid=4901 |date=2008-09-13 }}), and finally Topalov ([http://www.chessbase.com/newsdetail.asp?newsid=4908 Chessbase, September 13 2008] {{Webarchive|url=https://web.archive.org/web/20080915230303/http://www.chessbase.com/newsdetail.asp?newsid=4908 |date=2008-09-15 }})</ref>

The unofficial live ratings of players over 2700 were published and maintained by Hans Arild Runde at [https://web.archive.org/web/20080603001814/http://chess.liverating.org/ the Live Rating website] until August 2011. Another website, [http://www.2700chess.com 2700chess.com], has been maintained since May 2011 by [[Artiom Tsepotan]], which covers the top 100 players as well as the top 50 female players.

Rating changes can be calculated manually by using the FIDE ratings change calculator.<ref>{{cite web |url=https://ratings.fide.com/calculator_rtd.phtml |title=FIDE Chess Rating calculators: Chess Rating change calculator |last=Administrator |website=ratings.fide.com |access-date=2017-09-28 |archive-date=2017-09-28|archive-url=https://web.archive.org/web/20170928150121/https://ratings.fide.com/calculator_rtd.phtml |url-status=live}}</ref> All top players have a K-factor of 10, which means that the maximum ratings change from a single game is a little less than 10 points.

=== United States Chess Federation ratings ===
The [[United States Chess Federation]] (USCF) uses its own classification of players:<ref>[http://archive.uschess.org/ratings/ratedist.php US Chess Federation] {{webarchive|url=https://web.archive.org/web/20120618103954/http://archive.uschess.org/ratings/ratedist.php |date=2012-06-18 }}</ref>
*2400 and above: Senior Master
*2200–2399: National Master
**2200–2399 plus 300 games above 2200: Original <!--The title has been changed, though I am too lazy to find a source--> Life Master<ref>[http://main.uschess.org/content/view/7327#Master USCF Glossary Quote:"a player who competes in over 300 games with a rating over 2200"] {{Webarchive|url=https://web.archive.org/web/20130308182917/http://main.uschess.org/content/view/7327#Master |date=2013-03-08 }} from The United States Chess Federation</ref>
*2000–2199: Expert or Candidate Master
*1800–1999: Class A
*1600–1799: Class B
*1400–1599: Class C
*1200–1399: Class D
*1000–1199: Class E
*800–999: Class F
*600–799: Class G
*400–599: Class H
*200–399: Class I
*100–199: Class J

====The K-factor used by the USCF====
The ''K-factor'', in the USCF rating system, can be estimated by dividing 800 by the effective number of games a player's rating is based on ({{math|''N''<sub>''e''</sub>}}) plus the number of games the player completed in a tournament ({{mvar|m}}).<ref>[http://www.glicko.net/ratings/approx.pdf "Approximating Formulas for the US Chess Rating System"] {{Webarchive|url=https://web.archive.org/web/20191104083935/http://www.glicko.net/ratings/approx.pdf |date=2019-11-04 }}, [[United States Chess Federation]], Mark Glickman, April 2017</ref>
: <math>K = \frac{800}{N_e + m} \, </math>

====Rating floors====
The USCF maintains an absolute rating floor of 100 for all ratings. Thus, no member can have a rating below 100, no matter their performance at USCF-sanctioned events. However, players can have higher individual absolute rating floors, calculated using the following formula:
:<math>AF = \operatorname{min}\{100+4N_W+2N_D+N_R , 150\}</math>

where <math>N_W</math> is the number of rated games won, <math>N_D</math> is the number of rated games drawn, and <math>N_R</math> is the number of events in which the player completed three or more rated games.

Higher rating floors exist for experienced players who have achieved significant ratings. Such higher rating floors exist, starting at ratings of 1200 in 100-point increments up to 2100 (1200, 1300, 1400, ..., 2100). A rating floor is calculated by taking the player's peak established rating, subtracting 200 points, and then rounding down to the nearest rating floor. For example, a player who has reached a peak rating of 1464 would have a rating floor of {{math|1=1464 − 200 = 1264}}, which would be rounded down to 1200. Under this scheme, only Class C players and above are capable of having a higher rating floor than their absolute player rating. All other players would have a floor of at most 150.

There are two ways to achieve higher rating floors other than under the standard scheme presented above. If a player has achieved the rating of Original Life Master, their rating floor is set at 2200. The achievement of this title is unique in that no other recognized USCF title will result in a new floor. For players with ratings below 2000, winning a cash prize of $2,000 or more raises that player's rating floor to the closest 100-point level that would have disqualified the player for participation in the tournament. For example, if a player won $4,000 in a 1750-and-under tournament, they would now have a rating floor of 1800.