Neuberg formula

• the movement was not completed, or
• there was a phantom pair, or
• one or more plays had to be cancelled because of irregularities, entailing explicit percentage assignments for those plays.

  Details

• 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

• Wrong to give equal weight to boards played fewer times. A result achieved by a pair on a board played fewer times is a less reliable, higher variance, estimate of the pair's performance than a result achieved on a board played more times. It is misguided to aim to give equal weight to e.g. a 100% win achieved on the less-played board; it unfairly penalises a pair who have achieved a 100% win on a more-played board, since the latter's 100% win was less likely to have occurred by chance.
• Failure to account for diverse partnership strengths. If you play a board, and a different play of the same board was cancelled involving a weak pair that you would have beaten, the Neuberg formula does not compensate you for your cancelled victory.

  Gérard Neuberg

Other uses