   # Neuberg formula

In duplicate bridge pairs tournaments, the Neuberg formula is a method of fairly adjusting match point scores when not all boards have been played the same number of times. The objective is to give equal weight to each board by calculating the expected number of match points that would have been earned if the board had been played the full number of times.

A board might not have been played the full number of times because:

• the movement was not completed, or
• there was a phantom pair, or
• a board had to be averaged because of an irregularity of some sort.

The method is:

• Add 1 to the number of match points scored. (If the North American match point system is in use, where each comparison is worth one point rather than two, add a half-point instead.)
• Multiply by the number of times the board should have been played (this should be the same number for all the boards in the tournament) and divide by the number of times it was actually played.
• Then subtract 1 (or ½, whichever was added above).

## Example

• Board played 6 times.
• Most other boards played 7 times.
• Pair X scored 4 match points (out of 10).
• Then (4+1) x (7/6) - 1 = 4.8333 (out of 12).
• Pair Y scored 9 match points (out of 10).
• Then (9+1) x (7/6) - 1 = 10.6667 (out of 12).
• The scores are usually then rounded to the nearest 0.1, so 4.8 and 10.7 respectively.

The above method is in fairly common use. Note that the formula does not allow for the relative strengths of the partnerships. If, for instance because the movement was not completed, you miss out on playing against the weakest pair in the tournament, you do not benefit from any adjustment for this and you lose out. It would be relatively straightforward to adjust the formula to correct for this, but this is not done - perhaps because it is considered to be over-complicated.

A similar method can 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.