Almost Beaten By Maths

BlackEdelweiss

I thought this was an interesting little article, a good one to tell the kids when they ask where are they going to use maths in real life.

"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."

marcsignal

excellent little gem BlackEdelweiss

where did you find that ??

.

amcalester

I'd be interested in seeing how they came to settle on the forumla.

Good article though.

Morlar

I'd imagine the German method for calculating Russian tank production had numbers going off the page into the margins. You would think that they would have numbered them differently, like the early party membership numbers, ie start off at a random high number and count upwards from there.

marcsignal

The Germans were always up to sneaky tricks with their bomb fuses too, they'd make a fuse that was easy to defuse, and mark it with a number like '17'

The British bomb disposal guys would defuse it and then lecture their crews on the technique of how to defuse a 'Type 17' for example.

Then the Germans would modify the fuse with a trip switch, but still mark it '17'

BOOM !!!!!


.

FiSe

It's nice and interesting reading, but there are some flaws.

I think that different series of Werk Numbers were allocated to different factories for the same type, so let's say Krupp had series 33002-33132 and 34180-34200, Alkett had 31156-31215 and 35216-35300/* and the lowest numbers were not necessarily manufactured before the higher numbers in the series.
Which basically could mean that higher No's would be out and fighting and the lower No's could be still on production line.

/*I don't know the numbers, only example. It was like that within the aircraft industry and I pressume it would be the same with the mudrollers

Another thing is, when I checked one of the many Panzer production charts out there, it shows that average monthly production of 1941-1943 is somewhere between 550-600 new tanks.

marcsignal

^
^
^
^
Hmmm....nice detective work Fise

BlackEdelweiss

Here is the link, nothing more on it I'm afraid.
I presume that he is dealing with Panzer IV only as Panthers were not in full production in 1942, that might be where the lower number comes from. Maybe not!!

http://www.guardian.co.uk/world/2006/jul/20/secondworldwar.tvandradio

Tony EH

FiSe wrote: »

It's nice and interesting reading, but there are some flaws.

I think that different series of Werk Numbers were allocated to different factories for the same type, so let's say Krupp had series 33002-33132 and 34180-34200, Alkett had 31156-31215 and 35216-35300/* and the lowest numbers were not necessarily manufactured before the higher numbers in the series.
Which basically could mean that higher No's would be out and fighting and the lower No's could be still on production line.

/*I don't know the numbers, only example. It was like that within the aircraft industry and I pressume it would be the same with the mudrollers

Another thing is, when I checked one of the many Panzer production charts out there, it shows that average monthly production of 1941-1943 is somewhere between 550-600 new tanks.

Plus, it wasn't uncommon for a German tank to be a hybrid like many German aircraft. So, a Pzkpfw IV Ausf. D made in 1939 (with a short 24 caliber 75mm gun), could be found on the battlefield sporting a new turret with a long barrelled 43/48 caliber 75mm gun in 1943.