# ICU Rating Calculations

Vincent Bissett

This article part of the series: ICU Bulletins 2004-05 - 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

There are two cases: the first for players with an estabilished rating, and the second for players entering the rating pool for the first time.

### Continuous Rating Formula

A rated player's new rating after a rated event is given by the formula

```Rn = Ro + K(W  We)
```

where

```Rn  is the new rating after the event
Ro  is the old rating before the event
K   is the rating factor, which determines the maximum change per game
W   is the actual game score (each win counting 1, each draw 0.5)
We  is the expected game score based on Ro
```

The ICU uses four different K values:

```K = 40 where rating < 2100 and age < 21
K = 32 where rating < 2100 and age ≥ 21 and playing experience < 8 years
K = 24 where rating < 2100 and age ≥ 21 and playing experience ≥ 8 years
K = 16 where rating ≥ 2100
```

A player's expected score, wg, depends on the difference, Rd, between his rating and his opponent's. If the two players have the same rating then they each have an expected score of 0.5. As the rating difference increases, the expected score goes up for the higher-rated player and down for the lower-rated according to:

```wg = 1 / (1 + 10^(Rd/400))
```

The player's expected score for an event, We, is the sum of expectations of the individual games:

```We = w1 + w2 + ...
```

### Performance Rating Formulae

New (unrated) players who enter the rating pool are processed by the Performance Rating Formula for a provisional period.

```Rp = Rc + Dp
```

where

```Rp is the performance rating
Rc is the average competition rating
Dp is to be read as the difference based on the percentage score P
```

When sufficient data accrues on their performances against rated players (20 games), subsequent calculations are taken over by the Continuous Rating Formula.

Created 2005-06-06 ◦ Last updated 2014-07-23 ◦ Editor MO