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

- Firstly, the total over the several sessions will usually be calculated using only the end total scores of the individual sessions. The specific board scores need not be kept. Formulas must be at hand to deal with this.
- Secondly, all problems concerning ‘different tops’ come back to haunt us in even greater complexity.

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.

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 :

- The simplest is to calculate every board of the second session using the Neuberg formula towards the same top as the first. Quite a lot of work.
- Or you could simply recalculate the whole lot at once, at the end of the second session. For our first pair in the example above, this produces : 144 + 24 (one for each board) = 168; 168/6x8= 224; 224 - 24 = 200 = 59.52%. You can then use the formula or simply add the mp to give 410 mp over 52 boards with top 14. The second pair would have : (167+28)/6x8-28 = 232 mp, added to their first session result of 179, to give 411 mp.
- It can be proven mathematically that it does not matter in which direction you ‘Neubergize’. Therefore you could also recalculate all the boards from the first session towards the top you would like to use in the second.
- Or finally, you could recalculate the totals from the first session all together. This makes the most sense to me, as these calculations can be done during the second session, thus sparing a lot of work at the end of that session.

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.

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

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