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This artcle cam across a WWII mailing list I'm on a few weeks back.
To me it seems like it is one of those made up 'truths' that tries to simplify a very complex process. Has anyone else seen this and can anyone definitly prove or disprove statements in it?

For example - Were Panthers sequentually serial numbered in a way that could be used in such a formula?

How a statistical formula won the war

Thursday July 20, 2006
The Guardian

Here is a story about mathematical deduction that I love, mainly
because it is said to be true, and because it had an impact (albeit
small) on the outcome of the second world war. It is the story of how
a simple statistical formula successfully estimated the number of
tanks the enemy was producing, at a time when this could not be
directly observed by the allied spy network.
By 1941-42, the allies knew that US and even British tanks had been
technically superior to German Panzer tanks in combat, but they were
worried about the capabilities of the new marks IV and V. More
troubling, they had really very little idea of how many tanks the
enemy was capable of producing in a year. Without this information,
they were unsure whether any invasion of the continent on the western
front could succeed.

One solution was to ask intelligence to guess the number by secretly
observing the output of German factories, or by trying to count tanks
on the battlefield. Both the British and the Americans tried this,
but they found that the estimates returned by intelligence were
contradictory and unreliable. Therefore they asked statistical
intelligence to see whether the accuracy of the estimates could be
improved.
The statisticians had one key piece of information, which was the
serial numbers on captured mark V tanks. The statisticians believed
that the Germans, being Germans, had logically numbered their tanks
in the order in which they were produced. And this deduction turned
out to be right. It was enough to enable them to make an estimate of
the total number of tanks that had been produced up to any given
moment.

The basic idea was that the highest serial number among the captured
tanks could be used to calculate the overall total. The German tanks
were numbered as follows: 1, 2, 3 ... N, where N was the desired
total number of tanks produced. Imagine that they had captured five
tanks, with serial numbers 20, 31, 43, 78 and 92. They now had a
sample of five, with a maximum serial number of 92. Call the sample
size S and the maximum serial number M. After some experimentation
with other series, the statisticians reckoned that a good estimator
of the number of tanks would probably be provided by the simple
equation (M-1)(S+1)/S. In the example given, this translates to (92-1) (5+1)/5, which is equal to 109.2. Therefore the estimate of tanks
produced at that time would be 109

By using this formula, statisticians reportedly estimated that the
Germans produced 246 tanks per month between June 1940 and September
1942. At that time, standard intelligence estimates had believed the
number was far, far higher, at around 1,400. After the war, the
allies captured German production records, showing that the true
number of tanks produced in those three years was 245 per month,
almost exactly what the statisticians had calculated, and less than
one fifth of what standard intelligence had thought likely.

Emboldened, the allies attacked the western front in 1944 and
overcame the Panzers on their way to Berlin. And so it was that
statisticians won the war - in their own estimation, at any rate.

Dirk

David Kahn stated something similiar in hs book on German Military Intelligence during WWII.

Something to the effect of 5 by 8 inch ID plates being recovered from Russian tanks on the East front.

These plated gave the Serial number , Factory and date of production of the tank in question.

Cheers

Dirk

IIRC this is explained in the chapter titled 'The Military Economists'.

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