Calculating Bridge Tournaments

Problem 8. Split-Scores

Description of the problem

A Split-Score is the result of an intervention by the tournament director, usually even after review by the appeals committee. It is therefor not a common occurrence, and has not received much attention in the past.

The usual way in which results of boards containing a split-score was calculated was to consider the board twice : once for the North-South results, once for East-West.

There is however one problem with this approach : the results of the NS and EW-pairs at any one table need no longer be the complement of each other. There are certain disadvantages to this.
If no better way were to be found, these disadvantages could well be classed with many others, which make that winning a Bridge Tournament still needs some luck.
There is however a better approach : if you consider a split-score two separate scores, each with only half the 'weight' of a normal score, one can employ the normal rules for the system used.
This will be described in more detail for every separate system. In every example we have the same board, calculated first normally, and then when one score of +450 is changed to -50 for NS, +450 for EW. We give a frequency table for each.

Solutions

1) Mitchell 1-3

The same principle is applied after changing the +450 into -50/+450 : both scores have a frequency of one half.

Obviously the NS pair (-50) scores 3.5, and the EW pair (+450) scores the complement of 13.5 = 4.5. Another way of explaining this method would be to go back to the official way in which the Mitchell system is included in the International Laws. In this description, every score has to be compared to every other score. If it is the higher, two scoring-units are attributed; if it is equal, one; if it is lower, none. This can be completed : if comparing to a split-score, one scoring-unit is attributed for being higher than each of the separate scores, one half point when equalling either of the scores. There is one major disadvantage to this method, when using the Mitchell (Neuberg) system. Suppose the NS pair would get an even worse score of -150. The frequency table then becomes :

The NS pair scores a negative result ! I do not consider this an illogical result. It is the complete Mitchell system that is illogical in giving 0 points to a pair who has scored a normal result. In the Ascherman system, this strange result becomes quite normal indeed.

2) Ascherman

Exactly the same reasoning, with of course one extra point for each pair :

after changing to the split-score :

or with the NS pair getting -150 :

The negative result has now changed into a very bad 2.5% !

3) Cross-IMPs

The same principle should be applied : when comparing to the split-score, one should compare with each score separately, then convert into IMPs and halve both these IMP-scores before adding them to the grand total. For the split-scores themselves, you should also compare with the other splitscore (and with the own score, but that's always 0 IMPs), halve the conversion in IMPs and add. This is another reason why I consider it better to divide by the number of scores, not by the number of comparisons.

Calculation for the pairs scoring +420 :

-Comparing with +480 :		 -60 =  -2 IMP x 1   =  -2
-Comparing with +450 :		 -30 =  -1 IMP x 3.5 =  -3.5
-Comparing with +420 :		   0 =   0 IMP x 2   =   0
-Comparing with  -50 : 		+470 = +10 IMP x 2   = +20
-Comparing with -100 : 		+520 = +11 IMP x 1   = +11
-Comparing with -150 : 		+570 = +11 IMP x 0.5 =  +5.5
Total of the comparisons : +31 IMP, divided by 10 = +3.1 IMP

4) Butler, Bastille

Only one average is calculated : (example only in Bastille, Butler = rounding)

The average is calculated as : (450x3.5 + 420x2 - 50x2.5) / 8
and with the NS pair getting -150 :

In this last example, the average was calculated as follows. The total of all the scores is 2620 (480+3,5*450+2*420-2*50-100-75), from which we subtract the 480, and -75 (half the lowest score) and -50 (half the second lowest score) :
2620-480+125 = 2265 / 8 = 283.125

Remember that in the Bastille system the average is NOT rounded, but normally only the integer part will be displayed.

Last Modified : 1996-09-22