Calculating Bridge Tournaments

Problem 1 : Byes

Description of the problem

Sometimes a tournament is conducted thus, that one or more pairs play some boards more or less than their competitors. This is not an ideal tournament, but as was stated in the introduction, this manual deals solely with results. The person responsible for the movement may be cursed, but results have to be provided nevertheless, and as equitable to all players as possible.

There are two distinct aspects to this problem.

• When the possible results are all positive, as in the MP-systems, playing more boards provides a possibility of scoring a greater number of points. But even when the average result is zero (as in the IMP-systems), scoring a certain number of points above this average, is easier when playing more boards.
• When playing fewer boards, the statistical chances of error are bigger. It is a well-known phenomenon that in a one-day tournament, more players reach a given total, say 60%, than in a tournament over several sessions. The chances of the 'luck' element evening out are bigger, the more boards are played. The same is true within one session.

I shall only deal with the first problem. The second problem is indeed too 'statistical', and too small within the scale of, for instance 24 boards as opposed to 28. The second problem should however be remembered, and it is a bad thing to class pairs in one ranking, when a different number of sessions have been played (1,2,3 sessions).

Solutions

1) Mitchell

In the Mitchell system, it is very common practice to 'Average'. This is usually done by giving the final results in percentages. Each pairs' score is divided by the maximum number of points they could have got. This maximum is equal to the 'Top' on each board, multiplied by the number of hands played. Thus every total score is divided by the number of boards played by the pair.

Another way is to multiply the total results of pairs having played a 'minority' number of boards, by a correction factor. Consider for example a tournament of 23 pairs, where every pair plays 28 boards, except 7 pairs that are 'bye' and play only 24. The total of these pairs could well be multiplied by 28/24 (or 7/6).

2) Mitchell-Neuberg, Ascherman

The same principles apply in the Neuberg and Ascherman systems.

3) Cross-IMPs, Butler, Bastille

The same principle should also be applied to the different IMP-based systems.

This is not always being done, primarily because Tournament Directors have not been aware of the problem. Since the average score is zero, it is quite normal for pairs having played fewer boards, still to be ahead of others. But these pairs have actually gained about two IMPs per board. If they had been able to play the other boards, they could have gained two IMPs on those too.

In these systems, a similar rectification should take place at the end of the tournament. I propose as a standard, comparable to the 'percentage' in Pairs scoring, that all total IMPs be factored toward 32 boards.

Another possibility might be to convert IMPs into Victory Points (VP), using the official WBF-table. This would solve the second above mentioned problem as well : Example : when scoring +20 over 8 boards, this would give 21 VP, but if you score +40 over 16 boards, this shows a greater consistency and yields 24 VP. However there is the disadvantage that the table does not change for every number of boards played, and the VPs are the same for a number of adjacent IMPs.

Last Modified : 1996-07-03