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Statistical fluctuations


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In the latest issue of the magazine of the Dutch BF, "Bridge", I noticed the remark in a column that allthough the difference between no 1 and no 2 of the recent Dutch pairs championship was only 0.03% it could not be a coincidence (!). Not true, of course, but it made me wonder if any conclusion could be drawn from such an event at all ....

 

26 pairs play 175 boards. Assuming there are only two results per board, a "top NS" and a "top EW", splitting 6/7 or 7/6, and that all pairs are equally strong so that the results are random, the standard deviation becomes 86 matchpoints. Assuming all 13 tables yield different scores, the standard deviation becomes 99 matchpoints. Since the standard deviation was actually 125 matchpoints, it can't be true that all pairs were equally strong. However, pure coincidence could probably explain about half of the variance.

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There are two effects from the movement, that influence your score.

 

Playing a board, it does matter who your opponent is.

If a world class defence can bring you down, who better not have world class opponents at that board.

 

It does matter if the other strong pairs play a board in the same direction as you do, or if they are playing it at the other side. If there are 3 strong pairs and 2 of them play a board NS they gain a shared top at best. The other pair on the EW sides can score a full top.

 

So no matter how many boards you play, there is allways a litte luck left.

 

So i think you are right. Even at 175 boards a 0.03% split does not prove which pair plays better bridge, But it is significant to the question who won the event :P.

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