Elo ratings

By Frank “Boy” Pestaño
Chessmoso

ELO is not an abbreviation like Fide or RP, but is actually the name of a person, Arpad Elo (1903-1992), a Hungarian-born American physics professor, who developed a rating system for calculating the relative skill levels of players in two-player games such as chess.

In short, it is your chess IQ. A player rated 2500 and above is likely to have a grandmaster title and a player rated above 2400, an international master title.

Fide Masters normally have a rating of 2300, National masters 2200, experts around 2000 and strong club players between 1800-2000. An average club player has a rating of 1400-1700, while beginners start at 900.

As of the latest Fide ranking, all of the top 100 players in the world have ratings over 2600 with 15 players over 2700 and one, Garry Kasparov, at 2813.

Prior to the Elo rating system, the United States Chess Federation (USCF) used a numerical ratings system, developed by Kenneth Harness, in terms other than wins and losses. It was quite fair but in some circumstances gave rise to ratings, which some observers consider inaccurate.

Elo’s central assumption was that the 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 any given player changes slowly over time. Elo thought of the mean of a player’s random variable as that player’s true skill.

Elo’s system was adopted by the USCF in 1960 and by Fide in 1970.

Furthermore, subsequent statistical tests have shown that chess performance is almost certainly not uniformly distributed and weaker players have greater chances of winning. Therefore, the system as used by both USCF and Fide is based on logistic distribution, an improvement over that originally proposed by Professor Elo, although in deference to him, it is still called the Elo system.

The formula to calculate a player’s new rating is based on his/her previous rating and takes into consideration the skill of the opponent. The formula is R’ = R + C (S - E), where R’ is the new rating, R is the old rating, C is a constant, S is the score (1 for win , 0.5 for draw and 0 for loss) and E is the expected score of the player.

The constant is the maximum allowed adjustment per game and is placed at 16 points for masters and 32 for weaker players.

E is a little more complicated as it is the core of the Elo system. One can’t conclude that after a series of moves that his/her performance is 2350. Performance can only be inferred from wins, draws and losses and the playing strength of the opponent should be considered.

If player A has true strength RA and player B has true strength RB, the exact formula (using the logistic curve) for the expected score of player A is

Similarly, the expected score for player B is

Please note that EA + EB = 1

An example will help clarify. Suppose player A has a rating of 1613. He plays a five-round Swiss format and loses to a player rated 1609, draws with a player rated 1477, wins over a player rated 1388, wins again over a player rated 1586, and loses to a player rated 1720.

His actual score is (0+0.5+1+1+0)= 2.5. His expected score, using the formula above, is (0.506+0.686+0.785+0.539+0.351) =2.867.

Therefore his new rating is 1613+32 (2.5-2.867) = 1601

CEPCA VS. LADIES SELECTION. It’s all systems go for this once in a lifetime match on Sunday 1:30 p.m. at the Handuraw Café in Mabolo between selected lady varsity chess players and members of the Cebu Executives and Professionals Chess Association Inc.

The members of the ladies selection are: Therese Gonzales, Angelie Giangan, Ma. Theresa Letegio, Marefe Serentas, Cherille Brocoy, Jenny Rose Chiong Palomo, Sarah Jane Letegio, Shiela Marie Alvarado, Mary Llenos, Lorie Mie Seno, Marygrace Jane Gacang.

Completing the ladies’ line-up are Jennyfer Lynn Abejan, Sherlina Gumapon, Jellyn Villarin, Maria Dyan Sofia Balite, Sunshine Lacorte, Maricor Loyola, Lyndace Mae Mentupa, Jessa Marie Balbona and Jocelyn Arnejo.