Chess Ranking scores, how is it calculated and what do they reflect?

Question

Chess Ranking scores, how is it calculated and what do they reflect?

Answer 1

Arpad Elo was a master-level chess player and an active participant in the United States Chess Federation (USCF) from its founding in 1939. The USCF used a numerical ratings system, devised by Kenneth Harkness, to allow members to track their individual progress in terms other than tournament wins and losses. The Harkness system was reasonably fair, but in some circumstances gave rise to ratings which many observers considered inaccurate. On behalf of the USCF, Elo devised a new system with a more statistical basis.

Elo's system substituted statistical estimation for a system of competitive rewards. 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.

A statistical endeavor, by contrast, uses a model that relates the game results to underlying variables representing the ability of each player.

Elo's rating system model

Elo's central assumption was that the chess performance of each player in each game is a normally distributed random variable. Although a player might perform significantly better or worse from one game to the next, Elo assumed that the mean value of the performances of any given player changes only slowly over time. Elo thought of a player's true skill as the mean of that player's performance random variable.

A further assumption is necessary, because chess performance in the above sense is still not measurable. One cannot look at a sequence of moves and say, "That performance is 2039." Performance can only be inferred from wins, draws and losses. Therefore, if a player wins a game, he is assumed to have performed at a higher level than his opponent for that game. Conversely if he loses, he is assumed to have performed at a lower level. If the game is a draw, the two players are assumed to have performed at nearly the same level.

Elo did not specify exactly how close two performances ought to be to result in a draw as opposed to a win or loss. And while he thought it likely that each player might have a different standard deviation to his performance, he made a simplifying assumption to the contrary.

To simplify computation even further, Elo proposed a straightforward method of estimating the variables in his model (i.e., the true skill of each player). One could calculate relatively easily, from tables, how many games a player is expected to win based on a comparison of his rating to the ratings of his opponents. If a player won more games than he was expected to win, his rating would be adjusted upward, while if he won fewer games than expected his rating would be adjusted downward. Moreover, that adjustment was to be in exact linear proportion to the number of wins by which the player had exceeded or fallen short of his expected number of wins.

From a modern perspective, Elo's simplifying assumptions are not necessary because computing power is inexpensive and widely available. Moreover, even within the simplified model, more efficient estimation techniques are well known. Several people, most notably Mark Glickman, have proposed using more sophisticated statistical machinery to estimate the same variables. On the other hand, the computational simplicity of the Elo system has proven to be one of its greatest assets. With the aid of a pocket calculator, an informed chess competitor can calculate to within one point what his next officially published rating will be, which helps promote a perception that the ratings are fair.

Implementing Elo's scheme

The USCF implemented Elo's suggestions in 1960, and the system quickly gained recognition as being both fairer and more accurate than the Harkness system. Elo's system was adopted by FIDE in 1970. Elo described his work in some detail in the book The Rating of Chessplayers, Past and Present, published in 1978.

Subsequent statistical tests have shown that chess performance is almost certainly not normally distributed. Weaker players have significantly greater winning chances than Elo's model predicts. Therefore, both the USCF and FIDE have switched to formulas based on the logistic distribution. However, in deference to Elo's contribution, both organizations are still commonly said to use "the Elo system".

Comparative ratings

The phrase "Elo rating" is often used to mean a player's chess rating as calculated by FIDE. However, this usage is confusing and often misleading, because Elo's general ideas have been adopted by many different organizations, including the USCF (before FIDE), the Internet Chess Club (ICC), Yahoo! Games, and the now defunct Professional Chess Association (PCA). Each organization has a unique implementation, and none of them precisely follows Elo's original suggestions. It would be more accurate to refer to all of the above ratings as Elo ratings, and none of them as the Elo rating.

Instead one may refer to the organization granting the rating, e.g. "As of August 2002, Gregory Kaidanov had a FIDE rating of 2638 and a USCF rating of 2742." It should be noted that the Elo ratings of these various organizations are not always directly comparable. For example, someone with a FIDE rating of 2500 will generally have a USCF rating near 2600 and an ICC rating in the range of 2500 to 3100.

The following analysis of the January 2006 FIDE rating list gives a rough impression of what a given FIDE rating means:

19743 players have a rating above 2200, and are usually associated with the Candidate Master title.

1868 players have a rating between 2400 and 2499, most of whom have either the IM or the GM title.

563 players have a rating between 2500 and 2599, most of whom have the GM title

123 players have a rating between 2600 and 2699, all (but one) of whom have the GM title

18 players have a rating between 2700 and 2799

Viswanathan Anand is the only player (on the April 2008 list) with a rating above 2800. Only three other players have ever exceded a rating of 2800: Garry Kasparov, Vladimir Kramnik, and Veselin Topalov. Although Kasparov's last rating was 2812, he is now inactive and has been removed from the FIDE list.

The highest ever FIDE rating was 2851, which Garry Kasparov had on the July 1999 and January 2000 lists.

In the whole history of FIDE rating system, only 48 players (to October 2007), sometimes called "Super-grandmasters", have achieved a peak rating of 2700 or more. However, due to ratings inflation, nearly all of these are modern players: all but two of these achieved their peak rating after 1993.

Ratings of computers

Several chess computers are said to perform at a greater strength than any human player, although such claims are difficult to verify. Computers do not receive official FIDE ratings. Matches between computers and top grandmasters under tournament conditions do occur, but are comparatively rare.

As of April 2006, the Hydra supercomputer was possibly the strongest "over the board" chess player in the world; its playing strength is estimated by its creators to be over 3000 on the FIDE scale.[1] This is consistent with its six game match against Michael Adams in 2005 in which the then seventh-highest-rated player in the world only managed to score a single draw.[2] However, six games are scant statistical evidence and Jeff Sonas suggested that Hydra was only proven to be above 2850 by that single match taken in isolation.[3]

On firmer footing is Rybka. As of September 2007, Rybka is rated by several lists within 2900-3120, depending on the hardware it is run on and the version of software used.[4][5][6][7] These lists use Elo formulas and attempt to calibrate to the FIDE scale[citation needed]. Without such calibration, different rating pools are independent, and can only be used for relative comparison within the pool.

The primary goal of Elo ratings is to accurately predict game results between contemporary competitors, and FIDE ratings perform this task relatively well. A secondary, more ambitious goal is to use ratings to compare players between different eras. (See also Greatest chess player of all time.) It would be convenient if a FIDE rating of 2500 meant the same thing in 2005 that it meant in 1975. If the ratings suffer from inflation, then a modern rating of 2500 means less than a historical rating of 2500, while if the ratings suffer from deflation, the reverse will be true. Unfortunately, even among people who would like ratings from different eras to "mean the same thing", intuitions differ sharply as to whether a given rating should represent a fixed absolute skill or a fixed relative performance.

Those who believe in absolute skill (including FIDE[8]) would prefer modern ratings to be higher on average than historical ratings, if grandmasters nowadays are in fact playing better chess. By this standard, the rating system is functioning perfectly if a modern 2500-rated player and a 2500-rated player of another era would have equal chances of winning, were it possible for them to play. The advent of strong chess computers allows a somewhat objective evaluation of the absolute playing skill of past chess masters, based on their recorded games.

Those who believe in relative performance would prefer the median rating (or some other benchmark rank) of all eras to be the same. By one relative performance standard, the rating system is functioning perfectly if a player in the twentieth percentile of world rankings has the same rating as a player in the twentieth percentile used to have. Ratings should indicate approximately where a player stands in the chess hierarchy of his own era.

The average FIDE rating of top players has been steadily climbing for the past twenty ye

Answer 2

It is a mathematical formula in vented by Arapad Elo.  It is too complicated for a short answer.

http://en.wikipedia.org/wiki/Elo_rating_...

Oh apparently Soccer uses it too.