Calculating Bridge Tournaments

General Principles - Mitchell system

1) development

The Mitchell system was developed around 1880 for use in the first-ever duplicate tournaments, not even in Bridge, but in Whist, by John Mitchell.

As he was the first to develop the idea of the duplication principle, he needed a way to determine the winner of his tournaments. He quickly realised that the points won on the hands could not be used to establish clear results. This would still give an importance to the cards held, a principle which was to be discontinued. Only the comparison between the scores would determine the results. The solution is therefore simple :

The lowest scoring table gets 0 points.
The next lowest gets 1 point, and so on.

It was natural for John Mitchell to count like this, and the system is still in use today, all be it with certain modifications.

It is so natural a system, that it has failed all this time to be given a name. In this work, I shall put this wrong right and honour the inventor by calling this system (together with the modifications) the Mitchell system.

2) Modification : equal results - half points

When two tables score the same, they share the points that would otherwise be attributed to two different scores.

The reason for this is that the total points for all should remain the same. If there are 5 scores, the results will be 0,1,2,3 and 4. The total is 10. If two scores are equal, say the 1 and 2, they will both score 1½. Thus the total will remain 10. If three scores are equal, for example the highest, the results will be 0,1,3,3,3; the total is still 10 points.

This leads to half points, and several ways have been suggested for dealing with those. Several signs have been suggested (such as x) that are easier to write than ½. There is however another solution, which seems to have been first introduced by André Lemaitre of Belgium, and which consists of doubling every result.

To restate the previous examples, the results would be :
all different scores : 0,2,4,6,8 (total 20)
two equal scores : 0,3,3,6,8 (total 20)
three equal scores : 0,2,6,6,6 (total 20).

That practice is not in world-wide use, and the Laws state '... scoring units (matchpoints or half matchpoints) ...'.

For all practical uses, using points or half points gives exactly the same reasoning, and I shall stick to using the 0..2..4.. counting from now on. (Americans : sorry)

It is that system which I shall call the Basic Mitchell system.

Mitchell
NS
EW
mp
110 - 15
80 - 9
- 90 3
- 100 0
110 - 15
0 0 6
90 - 12
- 90 3
80 - 9
72

The Basic Mitchell system is the system described in the International Laws as 'Match-Point Scoring'. However, all other systems in this chapter can be described as MP-systems, since they all award two 'scoring units' for every worse result.

3) Different ways of calculating the results

Three ways are described of calculating the results in the Basic Mitchell system (all of course yielding the same result) :

a - direct scoring :

Every score is compared to every other. If that score is lower, the score being considered is awarded two points; if the scores are equal, one point; if the other score is higher, no points. This is the way a computer will calculate the results. It is also the most simple way to define Matchpoints, and therefore the way Matchpoints are mentioned in the International Laws.

b - ranking :

all scores are put in ascending order. Counting from the bottom, the scores 0 .. 2 .. 4 are awarded. This is the easiest, manual way of scoring a scoresheet for a limited number of tables. With a little practice this becomes easy.

c - frequency table :

all scores are put in a separate table, and the frequency of each is counted :

Frequency Table
score
freq
mp
+680 5 86
+660 6 75
+620 11 58
+600 5 42
-100 14 23
-110 2 7
-300 3 2

The lowest score occurs three times, so the result for each of these will be 2 Match-Points (3-1). The next lowest score occurs twice, and its result is calculated as 2+3+2 = 7.
Next you have 7+2+14 = 23 and so on.

Why does this system work ?
The score for the lowest score is equal to its frequency minus 1, which is the number of other scores that are as bad as itself.
Let's now calculate the result for a pair scoring +660, starting with the 58 MP of a pair scoring +620.
There are 24 scores lower than +620. These are of course also lower than +660, so they do not alter the result for +660.
There are 11 scores equal to +620. Within the 58 MP, these have contributed so far 10 (11-1). In the result for +680, they should each contribute 2 points, so we must add 12 (11+1).
There are 6 scores equal to +660. All but one shall contribute 1 MP. We must therefor add 5 MP (6-1).
The +1 and -1 cancel out, and we see that 58+11+6 = 75.

Last Modified : 1996-06-27

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