w + 400 + x + 400 + y − 400 + z − 400 4 w + x + y + z + 400 ( 2 ) − 400 ( 2 ) 4 {\displaystyle {\begin{aligned}&{\frac {w+400+x+400+y-400+z-400}{4}}\\[6pt]&{\frac {w+x+y+z+400(2)-400(2)}{4}}\end{aligned}}}

Performance rating = 2000 + 400 × ( 2 ) 2 = 1400 {\displaystyle {\text{Performance rating}}={\frac {2000+400\times (2)}{2}}=1400} A statistical endeavor, by contrast, uses a model that relates the game results to underlying variables representing the ability of each player. For top players, the most important rating is their FIDE rating. FIDE has issued the following lists: Method for calculating the relative skill levels of players in zero-sum games such as chess Arpad Elo, the inventor of the Elo rating system

The Elo [a] rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess. It is named after its creator Arpad Elo, a Hungarian-American physics professor.

Elo's system replaced earlier systems of competitive rewards with a system based on statistical estimation. Rating systems for many sports award points in accordance with subjective evaluations of the 'greatness' of certain achievements. For example, winning an important golf tournament might be worth an arbitrarily chosen five times as many points as winning a lesser tournament. players had an active rating between 2600 and 2699, all of whom had the International Grandmaster title. If playerA has a rating of R A {\displaystyle \,R_{\mathsf {A}}\,} and playerB a rating of R B {\displaystyle \,R_{\mathsf {B}}\,} , the exact formula (using the logistic curve with base 10) [25] for the expected score of playerA is

From July 2009 to July 2012, six lists a year were issued, at the start of January, March, May, July, September and November. The Elo system was invented as an improved chess-rating system over the previously used Harkness system, [1] but is also used as a rating system in association football, American football, baseball, basketball, pool, table tennis, various board games and esports, and more recently large language models. E A = 1 1 + 10 ( R B − R A ) / 400 . {\displaystyle E_{\mathsf {A}}={\frac {1}{1+10 players had an active rating of over 2800. ( Magnus Carlsen was rated 2853, and 3 players were rated between 2814 and 2816). Performance rating = 1000 + 400 × ( 1 ) 1 = 1400 {\displaystyle {\text{Performance rating}}={\frac {1000+400\times (1)}{1}}=1400}