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URL:  https://boards.fool.com/pm-abraham-walds-memo-is-an-old-story-ive-heard-30397991.aspx

Subject:  Re: 5 Statistics Problems To Change Your View Date:  11/25/2012  8:05 AM
Author:  tim443 Number:  409503 of 567629

PM

ABRAHAM WALD'S MEMO is an old story I've heard before and a great description of the myths of survival in war. While survivors attribute it to an assortment of factors such as skill, training, bravery, heavenly intervention and even the lucky dice it really was a case of survivor bias and really mostly just chance.

A more interesting example of statistics used to good purpose would have been the RAF reduction of pilot losses in bomber command by 50%. They accomplished this by reducing the number of pilots in the bombers from two to one. Bomber losses were for the most part caused by night fighters and flak. Once the basics (fly as high as possible and stay in the bomber stream (an interesting statistical story in itself***)) there was almost nothing the crew could do to improve the odds. There was about a 10% chance of aircrew surviving by bailing out of an RAF bomber that had been shot down.

*** - The bomber stream was based on the difficulty the German night fighter controllers had when many were concentrated in a small area with the basic RADAR of the day. They were therefore assigned to geographical boxes. The concentrated bomber stream would provide a wealth of targets for those few night fighters in the boxes the "stream" went through but those few fighters would only be able to engage a limited number of bombers and would also soon run out of ammo.


Tim

http://en.wikipedia.org/wiki/Bomber_stream

British analysis of the loss of bombers to night fighters of the Kammhuber Line was one of the first applications of statistical analysis which would become known as operational research. The introduction of GEE allowed the RAF bombers to fly by a common route and at the same speed to and from the target, each aircraft being allotted a height band and a time slot in a bomber stream to minimize the risk of collision. Data provided to the British scientists allowed them to calculate that the bomber stream would overwhelm the six potential interceptions per hour that the German night fighters could manage in any one Himmelbett zone. It was, then, a matter of calculating the statistical loss from collisions against the statistical loss from night fighters to calculate how close the bombers should fly to minimise RAF losses.
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