The German Tank Problem

The year was 1944, and the Allies were preparing for the D-Day landings. They planned to use Sherman tanks (made by the US) in the assault, since they performed well against the tanks that the Germans had used thus far in the war – the Panzer III and Panzer IV models. Recently the Germans had begun to use a new model – the Panzer V – with higher-velocity guns and heavier frontal armour, which would have been a worse match-up for the Sherman tanks. These new tanks had only been seen in small numbers so far, but rumours had been circulating that the Germans had been producing these in high numbers. The Allies needed to work out some way of estimating how many of these tanks there were in existence in order to plan their strategy effectively.

The war for statistics

Probability is confusing. It didn’t really make much sense to me (why are random variables neither random nor variables?) until I took my first course in measure theory, which really helped to put things into perspective.

Statistics is even more confusing, adding real-world aspects onto the back of theoretical probability. I hoped that there would be some sort of deeper picture here that would straighten things out for me, in much the same way that measure theory did for probability.

It turns out that there are two. And they don’t like each other very much.