## Sample Player's Rating History

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### Ratings

A rating is a number which can be used to estimate or predict how a player will perform against other rated players.

A rating is *not* an absolute measure of playing strength.
It can be used to compare the strength of players only if the players are
playing in the same pool or group. It cannot be used to compare players in
different pools.

For example, if player "A" on this site has a rating of 1600, and player "B"
has a
FIDE rating of 1500, it does **NOT**
mean that player "A" is a stronger player than player "B" because the two
ratings are based on different pools of players.

#### The Elo System

The rating system used here is the Elo system (Invented by Arpad Elo). Read about it on Wikipedia

A player starts with an arbitrary number of points (this site uses 1500), and when a game is played, the points of both players are adjusted based on the result of the game, according to a formula.

In simple terms, if the result of a game agrees with what would be expected based on the players' ratings (eg: the higher rated player wins), then the ratings do not change much. However, if the result is not as expected (eg: the lower rated player wins), then the ratings will be adjusted to bring them closer to the theoretically 'correct' values.

Suppose your rating is r1, and the opponent's is r2. You play a game and we assign a value 'w' as follows:

- If you win, w is 1.0
- If you lose, w is 0.0
- If you draw, w is 0.5

1 | ||

r1 + K x [ w - | | ] |

1 + 10 ^ (( r2 - r1 ) / 400 ) |

Your opponent's new rating is calculated in the same way but with r1 and r2 swapped and the value of 'w' set for the opponent's result. K is always 32, which is the largest change your rating can experience as a result of one game.

It is important to remember that the ratings used in the formula are the ratings as they were **at the start of the game**.
The calculated change in rating is then applied to the **current rating**. The start-of-game ratings are used because:

- The rating changes can be calculated in advance (ie: at the start of the game) for all the possible outcomes.
- Using the end-of-game ratings would allow players to manipulate the order of finishing games (by playing slowly) to unfairly maximise their rating.

#### Provisional vs. Established Ratings

If a player has not played many games, we don't have much evidence of their true playing strength. Therefore, their rating must be considered unreliable and we call it a 'provisional' rating. After a player has played a lot of games we have enough evidence to calculate their playing strength fairly accurately so we regard their rating as 'established'.

When applying the rating formula, a provisional ratings will not give accurate results when adjusting the rating of the opponent (because the provisional rating is not accurate). For this reason, the value of K is multiplied by a scale factor to reduce the amount that the opponent's rating can change.

The scale factor is: (1+n)/(1+min)

where:

- 'n' is the number of games your opponent has played (if it is 12 or fewer)
- 'min' is the number of games you have to play before your rating is no longer provisional (in this case 12 games).

This means that if you play someone who has a completed no games (P0), your rating will change very little regardless of the result. However, the more games your opponent has completed (up to 12), the more your rating can change.