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Scoring:  Neuberg's formula

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Tomas Brenning
tomas@brenning.se
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Neuberg's formula is used for scoring a board where rulings, misduplication or some other event have caused a reduced number of results for that board.

The rulings are scored according to separate rules that are not affected by Neuberg's formula. When there are played boards with normal results, e.g. +450 or -50, the scoring for those results is based on how many results are compared.

At least seven results, at most three deviant results in one scoring group
There is a special case that is applied for contests with at least seven results and at most 3 deviant results. This can occur at misduplication where the board has been played once, twice or three times.

  • At one deviant result both pairs get 60%.
  • At two deviant results the top is 65% and the bottom is 55%. At equal results both pairs get 60%
  • At three deviant results the top is 70%, average is 60% and the bottom is 50%. At two or three equal results the points are awarded by sharing, e.g. 65-65-50% or 60-60-60%.

Other cases (Neuberg's formula)
North-South and East-West share the same number of points as in old-style scoring, i.e. the top of the board.

Old-style scoring means reducing the top by one point per result that can not be compared with.

The effect of Neuberg's formula is that the top is not lowered by as much as before. Another effect is that the awarded points become decimal numbers. One decimal is shown but scoring is down to the last decimal.

Neuberg's formula looks like this:

S
 
= (N / n) * (s + 1) - 1
N = Normal number of results
n = Number of results in the scoring group
s = The awarded score in the scoring group according to normal scoring (third score table to the right)
S = The awarded score according to Neuberg's formula

The formula is best explained through the example to your right.

Example


The original 11 results look like this:

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


Suppose the TD rules one +170 to be changed into A+A+. Then the score table would look like this according to old-style scoring:

# Result   N-S E-W
1 450       19 1
5 420       13 7
2 170       6 14
2 -50   2 18


If you had completely ignored that a result was missing the score table would have looked like this (the value s in the formula corresponds to the score of this score table):

# Result   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 this will be the result (the value S in the formula corresponds to the score of this score table):

# Result   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 +450 is achieved this way:

S = (11 / 10) * (18 + 1) - 1 = 19.9