Laws & Ethics Committee Section- Articles

The Neuberg Formula - the Principle

I'm afraid that this is where life begins to get complicated in which case I would urge the reader to just trust us and leap to section 6 or beyond!

This said, let us return to our original example - the board with 10 results where 11 results were expected. The correct (i.e. mathematically sound) approach to the problem is as follows:-

(a) We were expecting 11 results, but in fact we have only 10. The ratio of 11/10 is 1.1.
(b) So, assume that each of the 10 results have occurred 1.1 times (rather than only once) and match-point accordingly
(c)

Example:

N/S
Score

Actual
Frequency

Factored
Frequency

Match
Points

+ 520

1

1.1

19.9

+ 500

1

1.1

17.7

+ 490

1

1.1

15.5

+ 480

1

1.1

13.3

+ 460

1

1.1

11.1

+ 450

1

1.1

8.9

+ 430

1

1.1

6.7

+ 420

1

1.1

4.5

+ 400

1

1.1

2.3

- 50

1

1.1

0.1

 

Total 10

Total 11

 

(d) The match points quoted are out of a theoretical top of 20. The top score of 19.9 is arrived at by subtracting the frequency (1.1 in this case) from 21 (i.e. 1 more than the theoretical top). This is exactly the same process that you use already, possibly without realising it, when match pointing normally. If the best score had occurred only once, you would give it 20 out of 20 (i.e. subtract 1 from 21) - had it occurred twice (a shared top) you would give it 19, and so on. The match points for subsequent scores go down in units of 2.2 rather than 2.0. 2.2 is the sum of the previous frequency (1.1 in this case) and the frequency of the result you are trying to calculate (also 1.1 in this case).
(e)

A second example may help to illustrate the principle, this time using whole numbers only. Say a board should have been played 16 times (top = 30), but has actually only been played 8 times. So, the ratio of 16/8 is exactly 2 this time. So, imagine that each of the eight actual results had occurred exactly twice, and match point accordingly.

Let us say that our 8 results are as follows:-

N/S score

Freq

Normal match points
(top of 14)

Factored frequency

Factored match points (top of 30)

Calculation

+ 490

1

14

2

29

31 -2

+ 460

2

11

4

23

29 - 2 - 4

+ 430

3

6

6

13

23 - 4 - 6

+ 400

1

2

2

5

13 - 6 - 2

- 50

1

0

2

1

5 - 2 - 2

Total

8

 

16

 

 

You can verify this by match pointing a board yourself in the usual way with two scores of + 490, four of + 460, six of +430, two of +400 and two of - 50. You will end up with match point scores of 29, 23, 13, 5 and 1 for the five different results
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Neuberg Formula

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