*To handle hands with a different
number of scores, in a pairs contest with match point scoring, the Neuberg method is recommended
to combine the scores. This method is sometimes considered difficult or even incomprehensible. However a few examples
show that this solution is quite obvious. We present a simple derivation.
*

session 1 3 tables | session 2 6 tables | |||||||

score | number | MP | percent | score | number | MP | percent | |

430 | 1 | 4 | 100 | 430 | 2 | 9 | 90 | |

400 | 1 | 2 | 50 | 400 | 2 | 5 | 50 | |

‑50 | 1 | 0 | 0 | ‑50 | 2 | 1 | 10 |

We should be able to do better then that. Of course we want every hand to be equally important, but we can do something about the percentages. A natural and obvious way is to award the same percentages in session 1 as in a comparable session with 12 pairs, such as session 2. Also if the distribution of scores is more complicated the recipe is simple. Let 50% remain 50%, and, in session 1, multiply the difference from 50% by a factor 0.8.

The above is an example of the method of Neuberg for combining results for hands that
do not all have the same number of scores. It is often said the Neuberg is difficult
and complicated, but in fact it is nothing more that a consequent application of the
idea outlined above.

- n = the number of scores actually present
- N = the number of scores that should be present
- P
_{n}= the percentage before Neuberg, from a normal calculation with n scores - P
_{N}= the percentage after converting to N scores.

| (1) |

All that is left to do is to determine the number A, for any given N and n.

In the special case that N is 2n, as in the introduction,
we want a full top for a hand with n scores (P_{n}=100) to be equivalent with
a top shared by 2 pairs for a hand with N scores. More generally, if N/n is an integer number,
say m, then P_{n}=100 should correspond to a top shared by m pairs for a hand with N scores.

Thus a top shared by m pairs yields a percentage of

| (2) |

| (3) |

| (4) |

| (5) |

| (6) |

Usually this relation is expressed in terms of matchpoints. When we write P

| (7) |

| (8) |

| (9) |

The relation between P

At the value of 50% P

If N/n is integer the top at n scores corresponds to a shared top at N scores, shared by N/n pairs.

Generalising this idea, we use the same dependency on N and n, when N/n is not integer.

In the literature the Neuberg formula is often given without any clarification, as something that is difficult to understand. We see here there is a simple and logical explanation for this formula.

Formulae translated from T