Most people know how a Butler is calculated:First all the scores are added and an average is calculated. Usually the top and bottom score are not counted when calculating this average. Then all scores are compared to this average, and the difference is converted into IMP's using the well-known scale.

However, several problems have to be resolved when one tries to put this system into a computer program :

- How is the average actually calculated. Is it rounded ?
- What if the average ends on a five ? Is this rounded up or down ?
- Is it normal that +110 and +120 yield the same result, but +120 and +130 not ?
- What do you do if there are only few results (say 3, 4 or 5), do you still drop the extreme scores. Where do you start ? Should you not drop more extreme scores if there are say 20, 30 results ?

A fine example of what the Butler system can lead to was provided in a tournament in Scheveningen early in 1994. The main players are none other than Hamman-Wolff and Leufkens-Westra :

In the last round of that tournament, a board had been scored 2NT+1 : +180. The opponents on the board, Mrss Hamman-Wolff, sought and got a rectification. They expected to gain one IMP and consequently one place, but instead lost one place and 2000 Dutch guilders.

What had happened ? Together with a change of score, this rectification induced a change of datum-score, the average with which all scores are compared. This average fell from +240 to +230.

Hamman-Wolff originally got 240-180 = 60 = 2 IMP

After the rectification, this became 230-150 = 80 = 2 IMP

On the other hand, the Dutch pair of Leufkens-Westra (playing North-South) originally scored 400-240 = 160 = 4 IMP. This became 400-230 = 170 = 5 IMP, gaining them one IMP and a lone sixth place (originally they had been classed equal sixths).

Let's now see what the Bastille system makes of this all :

First of all, the average is calculated, but not rounded. In our example, this would give something like +237. Then the difference is calculated, but how do you convert +57 into IMP's ?

This is done using a linear equivalent of the IMP-scale. On the normal scale, 10 scores 0, and 20 scores 1. On the linear version, 15 is converted into 0.5 IMP. The complete IMP-table becomes :

from 0 to 45 : IMP = score / 30

from 45 to 165 : IMP = (score + 15)/ 40

from 165 to 365 : IMP = (score + 60)/ 50

from 365 to 425 : IMP = (score + 145)/ 60

from 425 to 495 : IMP = (score + 240)/ 70

from 495 to 595 : IMP = (score + 555)/100

from 595 to 895 : IMP = (score + 1130)/150

from 895 to 1495 : IMP = (score + 1805)/200

from 1495 to 2495 : IMP = (score + 2630)/250

over 2495 : IMP = (score + 7755)/500

without an absolute top of 24 IMP's.

So +57 will yield +1.8 IMP's.

What would the Bastille scoring have made of this ? Let us suppose the original
average, before rounding, was +237. (any other average between 235 and 240
will give the same outcome)

The original score for Hamman-Wolff was : 237-180 = 57 = 1.8 IMP

The original score for Leufkens-Westra was : 400-237= 163 = 4.45 IMP

After recalculation, the average would go down 5 points (there were 8 tables,
so the average is a total divided by 6) and would, in our presumption, now
be +232. As you can see, this coincides beautifully with the Butler change
from 240 to 230.

Now Hamman-Wollf would score : 232-150 = 82 = 2.425 IMP (gain +.625)

And Leufkens-Westra : 400-232 = 168 = 4.56 IMP (gain +.11)

As we can see, the rounded IMPs for Hamman-Wolff remain at +2, those for
Leufkens-Westra jump over the 4.5 mark and would give an extra IMP in the
Butler version.

The very nature of the Duplicate Bridge Game makes that every good thing you do, also helps your 'friends', meaning those that play at other tables in the opposite direction. Yet a system that permits these 'helpings' to be greater than your own benefit can surely do with some improvements.

That is the version I have been using since 14 July 1989 (the 200th anniversary of the storming of the 'Bastille'), to great success. On 14 July 1995 however, I introduced a second, smaller change to the system, in particular with regards to the calculation of the average.

As I have mentioned, it is not clear what one should do when there are few scores, or when there are many. How many extreme scores should one drop ? In my new version, I have put this at a uniform 10% of scores either side. So for 10 results this is exactly the same, otherwise the average will be slighty different.

On 14 July 2000 (the third time Bastille day falls on a friday) we have played a simultaneous tournament between the Royal Squeeze BC in Antwerpen and the Young Chelsea BC in London.

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Written 1996-02-16 - Last Modified 2000-07-12