ECF Grading

The grade is an average of points gained from games played in the current period. If the number of games played in the current period is less than 30, the most recent games played in the previous period are included. If more than 30 games are played in the current period, all of the results are included in the calculation.

For a win the points are the opponent's Grade plus 50, for a draw the points are the opponent's Grade and for a loss the points are the opponent's Grade minus 50. The opponent's Grade is taken from the appropriate current Grading list subject to the proviso that if a difference in Grade is greater than 40 it is assumed to be exactly 40. This is to prevent a player increasing his Grade by losing to a much stronger player, or decreasing his Grade by beating a much weaker player. If the opponent is ungraded, his Grade is estimated, using available information. The ECF have quite a useful Grading FAQ [1].

For juniors under the age of 18, an enhancement is added to their Grade to take into account their expected improvement over the year. This enhancement is six (for juniors of age 15 to 17), eight (for juniors of age 11 to 14) and ten (for juniors under the age of 11) points and is included in the published Grade.

Other Grading Systems

Elo

The Elo rating system as developed by Professor Arpad Élő [2] is a statistical system [3], that can in practice be simplified to the use of a table and a basic formula. This allows chess players to easily calculate ratings changes themselves. The table contains a Normal Probability, which is used to estimate the player's strength distribution. The formula to calculate a player's new rating based on his/her previous one is:

Rn = Ro + K * (S - Se) , where: Rn = new rating, Ro = old rating, S = score, Se = expected score and K = constant.

The score S is 1 for a win and 0 for a loss. The expected score Se is looked up in the table using the difference between the two players' ratings. When the winner increases their rating by amount D, the loser decreases their rating by the same amount. The maximum change in the score is determined by K and this constant varies with the player's rating as set by the different chess organisations.

Glicko

The Glicko system [4] is a refinement of the Elo system by Professor Mark E. Glickman [5] of Boston University. The system overcomes issues to do with the reliability of a player's rating and incorporates elements such as how frequently a player plays and the length of player inactivity into the equation. Largely due to the mathematical complexity, its use is confined to internet chess servers, where the maths can be calculated automatically. Glicko-2 [6] is a further refinement.

It is interesting to note that in the Glicko system, rating changes are not balanced as they usually are in the Elo system. If one player's rating increases by x, the opponent's rating does not necessarily decrease by the same amount. The Free Internet Chess Server [7] (FICS) use the Glicko system. The Internet Chess Club (ICC) seems to be using an Elo variant [8].

Elo Conversions

FIDE Elo and ECF Grading

The FIDE represents the World Chess Federation [9] and consequently, its rating system carries some weight. The FIDE has been using Elo since 1970.

ECF to FIDE Elo	FIDE Elo to ECF
ECF < 216, Elo = (ECF x 5) + 1250	Elo ? 2325, ECF = (Elo - 1250) / 5
ECF ? 216, Elo = (ECF x 8) + 600	Elo > 2325, ECF = (Elo - 600) / 8

USCF Elo

USCF ratings are the official ratings of the United States Chess Federation. The USCF have been using the Elo rating system since 1960 (Arpad played for the USCF). USCF ratings are 100 points over that of the FIDE ratings:

FIDE to USCF	USCF to FIDE
USCF_Elo = FIDE_Elo + 100	FIDE_Elo = USCF_Elo - 100

Foreign National Elo

Conversions to and from foreign national ratings use the traditional formula, which is defined as follows:

ECF to National Elo	National Elo to ECF
N_Elo = (ECF x 8) + 600	ECF = (N_Elo - 600) / 8