# Neuberg’s formula

Neuberg’s formula is used for scoring a board that has been played fewer times than other boards due to incomplete movement, misduplication or rulings.

Rulings are scored separately according to rules that are not affected by Neuberg’s formula. The remaining normal results, for instance +450 or -50, are scored using Neuberg’s formula based on how many comparisons are left after the ruling is removed.

.

## Special case for an overall minimum of seven scores and at most three scores in a scoring group

There is a special case that is applied for events with an overall minimum of seven scores and at most three results in a scoring group. This happens for misduplicated boards that are played at most three times.

• With one result, 60% is awarded to both pairs.
• For two results, top is 65% and bottom is 55%. If both results are the same, 60% is awarded.
• For three results, top is 70%, average is 60%, and bottom is 50%. When results are the same, the scores are shared brotherly, i.e. 65-65-50, 70-55-55 or 60-60-60.

.

## Other cases where Neuberg’s formula is applied

Just like before, North-South and East-West share the same score as before, i.e. the top.

The old method of scoring, with one or more results in another scoring group, meant that the top was lowered by 1 mp for each non-comparable result (see note below about turning off Neuberg’s formula).

The effect of Neuberg’s formula is that the top is not lowered as much as before. Another effect is that the awarded scores are decimals. One decimal is shown, but exact scoring is applied behind the façade (see also Number of decimals).

.

## Neuberg’s formula works like this

The actual formula looks like this: where

• N = Normal number of scores
• n = Number of scores in the scoring group
• s = Awarded score in the scoring group
• S = Awarded score by applying Neuberg’s formula

Let us use an example with eleven results according to this, where 2-1-0 matchpoints scoring is assumed:

 # Score N-S E-W 1 +450 20 0 5 +420 14 6 3 +170 6 14 2 -50 1 19

Now we assume that the TD changes a result from +170 to A+. Then it looks like this, with a top being 2 less than before, i.e. the lower case s values from the formula above:

 # Score N-S E-W 1 +450 18 0 5 +420 12 6 2 +170 5 13 2 -50 1 17

When Neuberg’s formula is finally applied, it looks like this, i.e. the upper case S values from the formula above:

 # Score N-S E-W 1 +450 19.9 0.1 5 +420 13.3 6.7 2 +170 5.6 14.4 2 -50 1.2 18.8

The score for instance for +450 is calculated this way: .

## Turn off Neuberg’s formula

Select Contest menu > Settings > Scoring and the Matchpoints (more) tab.

You can turn off Neuberg’s formula by unchecking Score adjustments > Neuberg’s formula. This gives you the old scoring method without decimals.