Calculating Bridge Tournaments

Problem 7. Several sessions

Description of the problem

Many tournaments are played over more than one session. This gives rise to two types of problems :

Solutions

1) Mitchell

When all boards have equal tops, and all pairs have played the same number of boards, it is possible to calculate the final results directly using matchpoints.
When one or other thing interferes with this however, most frequently percentages are used.

Special care needs to be given to the problem of weighing these percentages.

Example :
A pair has played 28 boards in the first session, scoring 210 mp (the top being 14). This is equal to 53.57%.
In the second session, the top is 10, and our pair score 144 mp out of 24 boards = 60.00%.
Their final result will be : (53.57%x28 + 60.00%x24)/52 = 56.54%.

This formula has been well known for years and should be considered a part of any Mitchell system.

One slightly strange consequence of this method has been much commented upon, and can best be illustrated by continuing the example above.
A second pair plays 24 boards in the first session, scoring 179 mp or 53.27%. They play 28 boards in the second session, scoring 167 mp or 59.64%.
Although they have finished behind the first pair in both sessions separately, they finish ahead of them in the total ranking, as their final percentage will be :
(53.27%x24 + 59.64%x28)/52 = 56.70%.

This is however completely natural. It can best be explained by considering that the second pair had more than half their boards at 60%, while the first pair played less than half of theirs at that percentage.

2) Mitchell-Neuberg

The Mitchell 2 system uses exactly the same formula as the Mitchell 1 does, and has the same implications.
Whereas in the Mitchell 3 system, one should also check the ‘tops’ on each board.

Indeed in a personal conversation with Gerard Neuberg in April 1992, he confirmed that it is his opinion too, that the formula that is generally known under his name, should be used whenever different boards have obtained different numbers of results, regardless of the reason why this occurred.

This is not easy, and there are four ways of achieving this :

3) Ascherman

As you might imagine, the Ascherman system is spared the terrible calculations above. The percentage formula is the most handy, but simply converting matchpoints is also quite easily done.

4) Cross-IMPs, Butler, Bastille

Adding IMPs and checking the total number of boards played is all that is required.

5) Example

I have once encountered an actual tournament where the difference between the Mitchell 2 and Mitchell 3 systems produced a different winner : the Ladies’ Pairs Championships of Antwerp of 1989.
There were 25 competitors, playing in two sessions. The movement was a Mitchell/Double Howell, in which the first round of the Mitchell was left out to accommodate those pairs meeting in the double Howell.

In the first session, there were 26 boards, 24 with 11 results, and 2 with 12. In the second session, there were also 26 boards, all with 12 results. Pairs 3 and 18 produced the following results (including some boards where the Neuberg formula was used after attribution of some artificial adjusted scores to other pairs). Simply using percentages, the result is :

                           pair 3                  pair 18
                         #   mp      perc.    #   mp      perc.
total TOP 20            22  270.13  61.394%  20  213.64  53.411%
total TOP 22             2   31     70.455%   2   13     29.545%
total first session     24          62.149%  22          51.241%
total TOP 22            24  305     57.765%  26  385     67.308%
total second session    24          57.765%  26          67.308%
total percentage        48          59.957%  48          59.944%

On the other hand, if all results are translated to top 20 :

                           pair 3                  pair 18
                         #   mp      perc.    #   mp      perc.
total 11 results        22  270.13  61.394%  20  213.64  53.411%
total 12 results         2   28.25  70.625%   2   11.75  29.375%
total first session     24  298.38  62.163%  22  225.39  51.225%
total second session    24  277.58  57.830%  26  350.75  67.452%
total on TOP 20         48  575.97  59.997%  48  576.14  60.015%

The other pair has won ! Similarly, using top 22 :

                           pair 3                  pair 18
                         #   mp      perc.    #   mp      perc.
total 11 results        22  296.69  61.300%  20  234.88  53.383%
total 12 results         2   31     70.455%   2   13     29.545%
total first session     24  327.69  62.063%  22  247.88  51.215%
total second session    24  305     57.765%  26  385     67.308%
total on TOP 22         48  632.69  59.914%  48  632.88  59.932%

Which of course produces the same ranking. Finally, using the Ascherman system :

                           pair 3                  pair 18
                         #   mp      perc.    #   mp      perc.
total 11 results(TOP 22)22  292.13  60.357%  20  233.64  53.101%
total 12 results(TOP 24) 2   33     68.750%   2   15     31.250%
total first session     24          61.056%  22          51.115%
total second session(24)24  329     57.118%  26  411     65.865%
total percentage        48          59.087%  48          59.104%

In Ascherman, only percentages are important, although one can also calculate directly in matchpoints.

Last Modified : 1996-09-16

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