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Why use Neuberg?

Bridge players are probably not aware of the way in which their matchpoint scores are calculated for boards that are not played as many times as others in many events. This may occur where a board has been fouled, an average is awarded by the director or a player becomes ill and has to leave the movement for a round or two. At the club level it is more often due to the movement dictating the situation where some boards are played a different number of times.

The important and overriding requirement of any bridge tournament is that all boards in the event should be of equal value. Therefore where some results are missing from a board, a method must be adopted to estimate the scores achieved by the players that is fair and equitable. It must be fair to the pairs that played the board and those that did not.

In 1991 the WBF, ACBL and others chose to adopt a method using the Neuberg formula. The administrators arbitrarily chose this formula from a number of possibilities they had at the time.

Myself and other scoring program writers at the time were not aware of, disagreed with or chose to ignore this political decision. It seems to be clear that the mathematics of this decision was not properly understood at the time and they chose to ignore any other mathematicians that disagreed with their decision.

The mathematics of this issue are not simple and generally not of interest to most if not all bridge players. When I recently presented a discussion paper to Peter Buchen (mathematician and Honorary Associate Professor, Sydney University) on the alternative to the Neuberg method known as the Factor Method, he chose to take a much closer look at the problem. His findings are most interesting if not surprising.

So there we have it. The Neuberg method has been in use for about 27 years in bridge tournaments around the world and yet there is no clear reason for using this method. In fact there is no clear mathematical reason for using any of the methods available.

In many situations the alternative called the Factor Method is simpler, just as statistically correct as any other method and very easy to understand by all bridge players. This cannot be said about the Neuberg Method. It is time for the administrators of bridge to review this decision.

Please view this link to see my discussion paper on this subject.http://www.asecomputing.com/Downloads/OnEstimatingMatchpoints.pdf

There you will find that all the alternative methods to this problem are based on the same mathematics. In addition I have supplied another method that I believe is better than the Neuberg method in many ways. None of the many choices are based on any mathematical certainty and yet the simplicity and accuracy of the easily understood Factor Method appears to be rejected for no good reason.

Also view this link to see Peter Buchen’s definitive paper on the mathematics of this subject. http://www.asecomputing.com/Downloads/Neuberg.pdf

Ian McKinnon

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