The ECF grading system was invented by Sir Richard (Otto) Clarke in the 1960s, based on existing Ingo/Harkness principles. The basis of ECF grading is that a player graded (say) 10 points higher than their opponent would be expected to score 6 from 10, the expected percentage score being 50 plus the difference in grades. If a player wins by 8 games to 2, their percentage score is 80% and their grade is expected to be approximately 30 points higher than that of their opponent.
The grade is calculated as 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. At least 10 results are required to attain a grade.
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. Under this system, for a single win or loss, the minimum that can be gained/lost is 10 points and the maximum that can be gained/lost is 90 points. If the opponent is ungraded, their Grade is estimated, using available information. The ECF have quite a useful Grading FAQ.
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.
There are two sets of grades, one for play using standard time controls and one for Rapidplay.
The Elo rating system as developed by Professor Arpad Élő is a statistical system, 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.
FIDE require at least 9 results before they will provide a rating.
The Glicko system is a refinement of the Elo system by Professor Mark E. Glickman 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 is a further refinement and a slightly modified version is used by the Australian Chess Federation.
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 (FICS) and chess.com both use the Glicko system. The Internet Chess Club (ICC) seems to be using an Elo variant.
Over time, there is a tendency for inflation/deflation to occur. This is when the average rating of all players increases/decreases respectively. For individual players, the effect of deflation is that their grade appears lower than their true playing ability.
The most straightforward attempt to avoid rating inflation/deflation is to have each game end in an equal transaction of rating points. If the winner gains N rating points, the loser should drop by N rating points. The intent is to keep the average rating constant, by preventing points from entering or leaving the system. Unfortunately, this simple approach typically results in rating deflation.
In the "basic form" of the Elo system, the cause of deflation is the fact that on average, players improve. The cause of inflation is that their strength relative to their rating will tend to decline over time with age. Since most players improve early in their career, the system tends to deflate at that time. Inflation doesn't occur until much later in a player's career, but many players will quit before this natural process occurs, so the net result over time is deflation.
In the current ECF grading system, there seems to be a number of causes of inflation/deflation:
The ECF grades are due for adjustment in July 2008, to compensate for deflation observed over the decade.
The FIDE represents the World Chess Federation and consequently, its rating system carries some weight. The FIDE has been using Elo since 1970. The following is for conversions prior to the 2009/20010 season:
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 |
The formula for ECF grades smaller than 216 was introduced because of deflation at the lower end.
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 |
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 |