The Paradox
During WWII, the Allies estimated German tank production from captured serial numbers.
With k captured tanks and maximum serial m:
N̂ = m + m/k - 1
This frequentist estimator beats naive guessing. The Bayesian posterior is even more informative.
Historical: Statisticians estimated ~256 tanks/month. The true number was 271. Military intelligence guessed 1,400!