Many of the most important statistical theorems have been discovered around the 40s, which is the same time in which World War 2 occurred (1939/1945). This is of course not a coincidence, one of the paradoxes of war is that if on the one hand it takes and impacts millions and millions of lives, on the other hand it leads to new scientific and technological discoveries. We all agree that wars are terrible, and we would be better off if there were none, but it is important to know how during WW2 statistics played a crucial role in shaping military strategies, allocating resources, and making informed decisions. It has been scientifically proven that the use of statistics had an enormous influence on the war’s outcome.
ALAN TURING
Known as one of the most brilliant minds of the 20th century, Turing was just 27 years of age when he got hired by the British government to work at Bletchley Park, the British code breaking center. Together with other cryptographists he managed to break the Enigma code, a sophisticated encryption system used by the Germans for military communications. He cracked the code by inventing a machine known as “Turing machine” which was capable of simulating the logic of any algorithm or computation.
This was an extremely important moment in WW2 since in this way the Allies could gain insights into their enemies’ military plans and strategies. Once he and his team were able to intercept and decipher German communications their job was not finished: they also had to make sure that the Germans did not know that the British could listen to their (supposedly secure) secret messages.
Through accurate statistical computations Turing was able to find the optimal solution between saving as many lives and resources as possible and at the same time not letting the Germans know that they already knew their plans. For example, if the British knew exactly which one of their ships was going to get attacked, they would empty its resources (such as food, fuel) and let everybody evacuate the ship. Of course, in this case they could not just simply move the whole ship otherwise the Germans would have understood that they were decrypted and their whole cover would have blown up.
Turing also had to decide which messages to ignore and which ones to decrypt and act upon. Selectivity allowed the British to prioritize intelligence that was strategically, militarily, and financially significant while minimizing the risk of getting detected by the Germans. This unfortunately also involved sacrificing human lives, supplies, defense equipment and territories.
The British also wanted the Germans to believe that they had other sources of information (such as espionage which played a crucial role in WW2), in this way they reduced the possibility that Germans blamed their losses on their messages getting cracked. On the other hand, they shared most of their information with the Allies through top secret channels.
GERMAN TANKS
During WW2 there was a big increase in the production of airplanes and tanks, especially on the German side. Once the Americans noticed it, they started wondering what the exact number of tanks the Germans had produced was to know the size of the threat they were facing.
They first tried to estimate the number of tanks by guessing and through espionage, but it did not lead to any actual conclusion. So, they decided to steal as many tanks as they could and import them to the US to study them. What they discovered was very helpful, in fact they noticed that each German tank had a serial number on its sides. Later, they found out that it stood for the production number. Hence the first tank they produced was numbered 1, the second one 2, and so on.
Their goal was to estimate how many tanks there were by looking at how they were numbered. With a team of statisticians, they started looking at the gaps between the numbers and they came up with the Minimum Variance Unbiased estimator, which estimates the average difference between two observations. The formula they ended up using was m + ((m-k)/k), where m is the highest serial number and k stands for the total number of tanks they captured. After the war ended, the Americans released the estimates and the Germans their official numbers, and their computations were very close to reality.
We can claim that during WW2 statistics emerged as a silent ally providing a scientific foundation for military decision-making, logistical planning, economic mobilization, and intelligence gathering. As you have just read in the previous paragraphs, not only were statistics incredibly helpful for the Allies victory but it also laid the groundwork for the development of today’s data optimization, operations research, and estimation. Experts estimate that breaking Enigma shortened WW2 by at least two years and saved around 15 million lives. The “Turing machine” formed the basis of today’s computer science, and it had a big impact on the design of computing machines.
Most of this information was considered extremely sensitive and was released only in the 1970s and 1980s by the British and the American governments, which publicly admitted the contribution that statisticians gave in WW2.