# Maths trick for competitive intelligence: counting World War II tanks

Neatorama recently covered an intelligence story that was news to me (although covered by The Guardian before).

British military intelligence during World War II wanted to calculate how many tanks the Germans manufactured every month. Here is how they did it:

*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.

The application of such analysis to competitive intelligence is obvious - it becomes an option for calculating the production rate of any numbered device. Indeed, The Guardian again referred to this in a later **article about iPhones**. This type of solution would appeal to many competitive intelligence analysts, although it is probably overkill for most real-life business situations - few companies would be interested in applying it. Still, if you have any spare mathematicians lying around, you may wish to enrol them onto your competitive intelligence team.