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German Tank Analysis · 2006-07-22

Another great piece on why nerds will achieve world domination one day. Consider the following problem:

You are a british general planning the invasion in europe in the latter half of the second world war. One question you really need to find an answer to is: "How many german tanks are there?" in other words you have to estimate how many tanks Germany produced up to a given date. What would you do? You would ask intelligence. A handful of desperate guys on the enemy's ground, always at risk of being captured could try to find the answer ... or you could ask statisticians.

Here is what both sources reported. In the last column the true figures according to German records are given:

German Tank Data
Date Statistical
June 1940 169 1000 122
June 1941 244 1550 271
August 1942 327 1550 342

How could statisticians guess that good? Ok, let's go for it: Obviously german tanks were captured by allied troops. Probably in Italy or Noth Africa. Those tanks had serial numbers. Those numbers were not randomly chosen. The German tanks were numbered as follows: 1, 2, 3 ... N, where N was the desired total number of tanks produced. Note that the tanks captured are a random sample of the german tank population. The rest is Order Statistics and led, according to the Guardian, to the following simple estimator N = (M-1)(S+1)/S, with S being the sample size and M being the highest serialnumber in the sample.

Still, the estimates are astonishingly good. Note that the sample should have been drawn iid, which very likely has not been the case.

(via MatheKlein)

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