The German Tank Problem: How the Allies defeated the Nazis with statistics

In this video, the German Tank Problem is discussed, which is how the allies defeated the Nazis with statistics during World War II. The allies received intelligence reports that there were significantly more German Panther tanks than expected, making it crucial to confirm the validity of these reports. With only two captured tanks, the statisticians used serial numbers found on almost every piece of Nazi equipment to estimate the extent of German tank production. By analyzing the production of tank tires and making reasonable assumptions about the serial numbers, the statisticians were able to estimate the number of tanks being produced, helping the allies defeat the Nazis. Note: I made a notational error while calculating the estimates. For instance, E[N-77] shouldn’t be an expected value but rather N ‘hat’ - 77.

Timestamps:
0:00 Setting the Stage
0:43 Intro
1:20 The Real German Tank Problem
3:13 Estimating Tire Molds
7:24 Estimating Gearboxes
11:30 Historical Impact

References:
- Ruggles, Richard and Henry Brodie. "An Empirical Approach to Economic Intelligence in World War II." Journal of the American Statistical Association (1947): 72-91.
- Johnson, Roger. Estimating the Size of a Population. Northfield, Minnesota: Carleton College, 2011.
- Carruthers, Bob. Eastern Front: Encirclement and Escape by German Forces. Barnsley, South Yorkshire, England: Pen and Sword, 2012.

Music (in order of appearance):
- Violin Concerto in F minor, RV 297 'Winter' by Antonio Vivaldi used from the Public Domain
- Violin Sonata in A major, RV 31 by Antonio Vivaldi used from the Public Domain
- Violin Concerto in F major, RV 293 'Autumn' by Antonio Vivaldi used from the Public Domain

[JUNGELMAN]

@5:39 the average gap = sum of all gaps/n. But no matter at what nr you start if x1=24 and x2=29, then the gap between them is 29-24 = 5 not 4. you claim the second gap has size (x2-x1-1).

[jnv]

I applaud you as a creative, but if you want a wider audience, you should make a conscious effort to speak slower and enunciate. I'm a pretty decent non-native english speaker and I had to focus way too much on deciphering what you were saying. I gave up before the end of the video.

[WagesOfDestruction]

This is a more straightforward method commonly used to solve this problem. Compare the max number found to the sum of all numbers, take the average, and double it. Then use the max of these two numbers. This method has some intuitive appeal. If the numbers are evenly distributed, the average would represent the midpoint, so doubling it could give a reasonable total estimate.

I tested this out by solving a problem by estimating the highest number of houses on a street when we only knew a few of the house numbers on each street.

I tested the tank method with the straightforward process, and the results were about the same.

[_gangsterelite]

Wow this is a very high quality video! Very informative!