How a statistical formula won the war

[syscom3]

To help solve the intelligence riddle of the production rates of the German war machine, one has to adopt the view of "Germans being Germans" and that they are quite logical and predictable.

Guardian Unlimited | The Guardian | Gavyn Davies does the maths

Gavyn Davies does the maths

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

[Soren]

"By 1941-42, the allies knew that US and even British tanks had been technically superior to German Panzer tanks in combat" The guy who wrote this obviously doesn't know much about the history of WWII armoured warfare.

[syscom3]

Originally Posted by Soren

"By 1941-42, the allies knew that US and even British tanks had been technically superior to German Panzer tanks in combat" The guy who wrote this obviously doesn't know much about the history of WWII armoured warfare.

I saw that too.

[delcyros]

Very cool info, Syscom!

[the lancaster kicks ass]

i was more bugged by the fact he said

US and even British tanks

firstly america was only just in the war by 1942 and hadn't engaged jerry in tank warfare and at the time the British Matilda series for example could take on german tanks and were superior to american designs (unless the sherman was out then... but we improved it anyway)......

[syscom3]

Originally Posted by the lancaster kicks ***

i was more bugged by the fact he said



firstly america was only just in the war by 1942 and hadn't engaged jerry in tank warfare and at the time the British Matilda series for example could take on german tanks and were superior to american designs (unless the sherman was out then... but we improved it anyway)......

Dont be bugged by the fact he was wrong on that point.

Be thankfull some allied statistics experts figured out the German tank production rates.

[delcyros]

It would be interesting to know whom did the staff believed, the statistical intellegence or the standart intellegence during wartime. It would also be interesting to know which conclusions did they draw from the material...

[syscom3]

This question is for you WW2 German tank experts out there.....

Did the S/N of an individual tank contain the date of manufacture (or acceptance)?

[schwarzpanzer]

Formula that won the war = E=MC2

I wouldn't be surprised if some Panzers had no markings at all Syscom.

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.

It could be said that, 'till the advent of the PzIV F2 (Special) that the Stuart, Grant and Sherman were the best tanks of '41-'42, but it up for debate...

It would be interesting to know whom did the staff believed, the statistical intellegence or the standart intellegence during wartime.

The Allies were often kept ignorant as much as possible, unsurprising really; if they knew about the superiority of German equipment - that could be bad.

It's like with tactics too - look at what Rommel did to morale when his capabilities were known to the soldiers.

[Soren]

Originally Posted by syscom3

I saw that too.

And thats not all he got wrong, he apparently also thinks that the PzKpfw.V came before the PzKpfw.VI :
"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."

[syscom3]

Originally Posted by schwarzpanzer

......
I wouldn't be surprised if some Panzers had no markings at all Syscom.

That would not be normal for the German "mindset".

.......The Allies were often kept ignorant as much as possible, unsurprising really; if they knew about the superiority of German equipment - that could be bad...

This was high level industrial production analysis. The statisticians probably werent even privy to tactical information.

....It's like with tactics too - look at what Rommel did to morale when his capabilities were known to the soldiers.

a better question should be .."how accurate was the German analysis of US and british production"

[DerAdlerIstGelandet]

Very interesting article but I do have to have a laugh at something.

By 1941-42, the allies knew that US and even British tanks had been technically superior to German Panzer tanks in combat,

Tell that to Rommel in France and the Poles and the British in France!

[HealzDevo]

I think it was more weight of numbers rather than a superiority of British and American tanks that led to victory. There were very few British and American tanks that could go toe to toe with a German Panther tank. Only one US tank could defeat a Tiger in a tank to tank slug-fest. So no, UK and US WW2 tanks were not superior to German WW2 tanks. They were inferior and only won by numbers.

[timshatz]

Actually, the guy got part of it right. "The Germans being Germans" happened at least one other time of great significance. Enigma wheels had a given number of digits on them (I believe there were 26 but am not sure). But the actual digit at each spot could be anything. The Poles (I am pretty sure it was them, going on memory) when they were making their "Bombe" (which was a copy of Enigma made from scratch) did the same thing the stat types did and figured the digits were sequential (Germans being an orderly people). One through 26, all the way around the dial. Turns out, they were right. It was a stroke of genius and it worked.

As for the statistical analysis, it seems to work. Questions I would have about it would be:

1. Which serial number did they use? Is there a master number or is there one for the Transmission, Gun, Engine, Frame, ect? Which of the parts is most difficult to make or is the entire tank the real tricky part.

2. As somebody else alluded to in this discussion, what did the serial numbers mean? Probably not tough to find with all the captured soliders but it would be something you would need to know.

The Germans had figured out that the Allies were keeping track of their serials in at least one case. U-boats did not have sequential hull numbers after a certain point but skipped some digits to keep the Allies thinking there were more subs out there than there really were.

The Germans did do a statistical analysis of the US production (not sure if they did it for the other allies but I think they did). Were on the money to slightly high for 1942 but missed 1943/1944 badly. Way underestimated on both years.

Lastly, the Brits were doing plenty of statistical analysis throughout the war. One only needs to look at the bombing survey in which it was found that one in five bombers got anywhere close to their targets to see that. Brought about a huge change in Bomber Command (starting with the replacement of Portal with Harris).

Good post Sys, good topic.

[Cojimar 1945]

The German tiger and panther tanks seem rather disappointing. It seems really wasteful to build such large vehicles but put small calibre guns on them. The armor protection also seemed low given the size of the vehicles.