Neuberg formula


In duplicate bridge pairs tournaments, the Neuberg formula is a method of adjusting match point scores achieved on boards which have been played fewer times than other boards. Originally developed by Gérard Neuberg of France, its objective is to achieve a formula for the final score of every pair to which each hand they have played contributes with equal weight.
Although the objective behind the formula is of questionable soundness, the formula itself follows from well-defined mathematical assumptions, and is almost universally applied in computer-scored bridge tournaments.
A board might have been played fewer times than others because:
  • the movement was not completed, or
  • there was a Glossary of [contract bridge terms#Phantom pair|phantom pair], or
  • one or more plays of that board had to be cancelled because of irregularities, entailing explicit percentage assignments for those plays.

    Details

The method is:
  • Add 1 to the number of match points scored.
  • Multiply by the number of times the board should have been played and divide by the number of times it was actually played.
  • Then subtract 1.

    Example

  • Board played 6 times.
  • Most other boards played 7 times.
  • Pair X scored 4 match points.
  • Then x - 1 = 4.8333.
  • Pair Y scored 9 match points.
  • Then x - 1 = 10.6667.
  • The scores are usually then rounded to the nearest 0.1, so 4.8 and 10.7 respectively.

    Criticisms

  • Mistaken objective: No a priori reason to give equal weight to boards played fewer times.
  • Failure to account for diverse partnership strengths.
  • '''Rounding'''

    Gérard Neuberg

The formula was developed by Gérard Neuberg, a French mathematician.
He died at the end of 2016: there is a brief obituary in the
French Bridge Federation magazine

Other uses

The formula can also be used for example in a club competition when it is desired to give equal weight to scores achieved over a number of sessions, but there were different numbers of tables at each session.