# How does the Elo rating work in chess

## Calculation of the Elo ratings

### Calculation of the Elo numbers

The effect of a game result on the Elo rating is very easy to calculate if both players already have Elo numbers. In this case, each player can determine the change in his or her Elo rating himself. In addition to the table below or the corresponding formula, you need the following three data:

1) Elo (own, old) last published Elo number 2) Elo (opponent, old) last published Elo number 3) Result 1 or 0.5 or 0

The influence on the Elo number is calculated as follows:

1) Factor = [3400 - Elo (own, old)] ² / 100000) 2) Difference = Elo (own, old) - Elo (opponent, old) 3) Expectation = according to table or formula 4) Change = (result - Expectation) x factor

**Note:**

A factor reduction usually takes effect after a certain number of games have been played. Since the number of games on PSM Chess is comparatively high, the factor reduction was deactivated on December 13, 2004.

At PSM Schach, every player always has an Elo number, so there are no rules for unrated players.

*1st example:*

1) Elo (own, old) = 1830 2) Elo (opponent, old) = 1980 3) Result = 0.5

**Calculation:**

1) Factor = (3400 - 1830) ² / 100000 = 24.6 2) Difference = 1830 - 1980 = -150 3) Expectation = according to ↓ table = 0.30 4) Change = (0.5 - 0.30) x 24.6 = +5

The draw brings 5 points.

*2nd example:*

1) Elo (own, old) = 1950 2) Elo (opponent, old) = 1820 3) Result = 0

**Calculation:**

1) Factor = (3400 - 1950) ² / 100000 = 21.0 2) Difference = 1950 - 1820 = +130 3) Expectation = according to ↓ table = 0.68 4) Change = (0 - 0.68) x 21 , 0 = -14

Losing this game costs 14 points.

Each game is rated for itself and has no further influence on the Elo number apart from the change calculated here.

**Final note:** In view of the not necessarily simple calculation, the required one is required **Tables according to Prof. Arpad Elo** waived at this point. Interested readers are advised to obtain further information on the relevant pages. The ELO system on PSM chess was implemented by the player Helge Dietert. Many thanks at this point. The basis for the calculation was the information on the website of the Hietzing chess club. The calculation is printed on PSM Schach with kind permission.

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