# Chess Ratings

The rating system used on Caissa's Web is based on the standard Elo rating system. It uses statistical and probability theory to derive a numeric value which can be used to accurately predict the performance of any player relative to another. The rating is updated continually according to recent results against other rated players. As long as a player performs exactly as expected, his rating remains more or less unchanged. If a player scores better (or worse) than his rating would predict, then his rating is adjusted accordingly so that future projections will be more accurate.

## Provisional and Official Ratings

New members are assigned **provisional ratings** for live games when they first log on. Provisionally rated members must play and finish 10 live games before their **official rating** is established. A provisional rating is represented by two numbers — a standard 4 digit rating and a single number from 1 to 10 representing the number of live games played (e.g. 1470/5). A member must complete 10 games for each time control category and type of game, i.e. Fast and Slow time controls, and Chess and Chess960 game types. 5 completed games are required to establish an official rating for Chess and Chess960 Correspondence games.

The basic theory of this system is that the unknown skill level of a new member entering the established rating pool should not greatly affect existing (official) ratings until that new member has demonstrated his/her skill level.

## How official ratings are calculated

Games involving provisionally rated players are calculated differently than games with two officially rated players. There are three scenarios for ratings computation--two provisionally rated players playing each other, a provisionally rated player playing an officially rated player, and two officially rated players playing each other.

The difference in ratings of two officially rated players can be used to determine the probability of either player winning a single game. The "winning probability" can be calculated from the following formula:

`WP = 1 / [ 10^(dR/400) + 1 ], where dR is the difference in the ratings.`

Here are some sample probability calculations:

Diff in ratings WP (higher-rated player) WP (lower-rated player) --------------- ------------------------ ----------------------- 0 .500 .500 50 .571 .429 100 .640 .360 150 .703 .297 200 .760 .240 250 .808 .192 300 .849 .151 350 .882 .118 400 .909 .091

From this it can be seen that a 1400-rated player should win three out of four games against a 1200-rated player, and a 1600-rated player should win ten out of every eleven.

A player's rating is adjusted after each game. The amount of change is determined by subtracting the winning probability (the formula above) from the actual score (1 for a win, 0 for a loss, .5 for a draw) and multiplying the result by a constant (32 for players rated 0-2099, 24 for 2100-2399, and 16 for 2400 and above). For example if a 1200-rated player wins against a 1400-rated player his rating will change by (1 - .240) * 32 = +24 points. If he had lost the same game, his rating would be changed by (0 - .240) * 32 = -8 points.

The following titles are assigned to each division within the rating system:

Senior Master............2400 and above Master (Class M).........2200-2399 Expert (Class X).........2000-2199 Class A..................1800-1999 Class B..................1600-1799 Class C..................1400-1599 Class D..................1200-1399 Class E..................under 1200

## How provisional ratings are calculated

The rating change is different when a provisionally rated player is involved. The provisional formula is quite standard and in widespread use (although often modified in various ways):

`Prov Rating = {Average Rating of Opponents} + 400(Wins-Losses)/{Number of Games}`

This basic formula is commonly used with Elo-based systems to handle the first few games since the actual Elo equations cannot be used without an "official" rating figure.

Note that during the provisional rating period it is possible to have your rating decrease even though you won the game. The loss of points after winning a game may be surprising but it is the natural result of the equation which is intended solely to assign a reasonable figure as quickly as possible without trying to be exact. Fine-tuning of the rating happens after the provisional period has ended.

Although many organizations use this exact formula, some do "disguise" it in some way to avoid confusion. One common method is to not display any number at all until after, say, 5 games have been played, which makes the issue much less noticeable (USCF used to do it this way). Another way is to display a fixed value (e.g. 1200) until the entire provisional period is over, and then switch to the calculated value (many online sites do this). Note that these methods do not change the actual calculations, they just keep players from seeing the intermediate results.

One thing to keep in mind is that sole purpose of rating adjustments is to increase future predictability. Rating points should not be thought of as "rewards" for winning a game, and losing points is not a punishment. Rating points have no inherent value, and only serve as predictors of relative performance. If we arbitrarily deducted 100 points from everyone's ratings, nothing would actually change. Likewise if we added 100 points. Ratings have to be viewed as a complete system, and individual adjustments must be considered in that context.