Here’s a great anecdote from Mikhail Simkin and Vwani Roychowdhury at the University of California, Los Angeles:

During the “Manhattan project” (the making of the nuclear bomb), physicist Enrico Fermi asked General Leslie Groves, the head of the project, what was the definition of a “great” general. Groves replied that any general who had won five battles in a row might safely be called great. Fermi then asked how many generals were great. Groves said about three out of every hundred. Fermi conjectured that if the chance of winning one battle is 1/2 then the chance of winning five battles in a row is (1/2)^5 = 1/32 . “So you are right, General, about three out of every hundred. Mathematical probability, not genius.”

Simkin and Roychowdhury’s interest is not generals but World War 1 fighter pilots. They say an ace fighter pilot is one who has who achieved five or more victories. “Can this be explained by simple probability?” they ask.

At first glance this doesn’t seem likely. The German World War 1 ace Manfred von Richthofen had 80 victories to his name.

If the chance of an aerial victory is 1/2, then the chance of winning 80 on the trot is:

(1/2)^80 = 10^(-24)

That’s not very likely by chance alone and it is tempting to think of von Richtoven as an outstanding pilot .

But Simkin and Roychowdhury say that a more careful analysis proves this conclusion wrong. Their argument is based on the fact that the Germans claimed vastly more victories than losses: 6759 victories versus only 810 losses. That makes the rate of defeat:

810/(6759+810) = 0.107.

So the probability of 80 victories in a row is actually:

(1-0.107)^80 = 10(-4).

And the chance of one of the German’s 2894 fighter pilots achieving this feat is:

1 – (1 – 10^(-4))^2894 = 0.29.

“Richthofen’s score is thus within the reach of chance,” conclude Simkin and Roychowdhury.

The paper goes on to work out that far from being outstanding, von Richtoven was probably merely in the top 27 per cent of pilots ranked by skill.

Basically, he was lucky.

The 90th anniversary of von Richtoven’s first and only loss was last week: the Red Baron was shot down and killed over the Somme on 21 April 1918.

Ref: arxiv.org/abs/physics/0607109: Theory of aces: high score by skill or luck?