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?

This is a rather asinine notion. Conflating the statistical probability of some generic person performing some feat with “proving” that an actual historical individual who actually *did* perform that feat merely did so by chance seems to me like a rather serious error of judgment. Based on this quote, perhaps the error is with the summary more than the authors, though: “Richthofen’s score is thus within the reach of chance”

Within the reach. Not “he was lucky.” A false an inaccurate summary.

It is quite well established that Richthofen was a great tactical innovator and a magnificently accurate shot with nerves of steel which allowed him to hold his fire until he was close enough to shoot effectively using the notoriously random machineguns of the era. Also, it is a matter of record that very many of his kills were made against inexperienced pilots and/or damaged aircraft. Some have claimed that this cheapens his record, but that is the sort of thing claimed by video gamers and hobbyists obsessed with “honor” and no understanding of the reality of war. Elite warriors picking off the weak at every opportunity is a very effective strategy, one that saps enemy morale and reserves while exposing one’s own fighters to very little risk.

One could just as easily summon some foolish statistical argument that, for instance, the sporting achievements of Michael Jordan are “within the reach of chance” and therefore he was “just lucky.” But anyone who ever saw him play would know that this is just stupid academic nonsense, confusing the theoretical with the actual.

So do the allies claim 810 victories and 6759 defeats? I would think not. Clearly something is suspicious with these numbers, the obvious motivation is that the Germans did not want to advertise their defeats. I can’t see how one could simply take these two numbers as valid without any confirmation or further analysis.

> And the chance of one of the German’s

> 2894 fighter pilots achieving this feat is:

> 1 – (1 – 10^(-4))^2894 = 0.29.

Not true! This assumes that all 2894 pilots had a chance to fight 80 times. Yet the average number of fights per pilot is only (6759+810)/2894 = 2.6. So they need to take into account the fact that most pilots only flew a few times. There can’t be many pilots who flew more than 20 times.

A point of historical correction: The Germans WERE part of the Triple Alliance. They were opposed to the Triple Entente.

I’d say that Tyler provides a better analysis.

Interesting line of study, but its glib packaging disregards the fact that some pilots could readily best any of their squadron mates in mock combat. Jimmy Thach (American carrier pilot from VF-3) would challenge every new pilot and obtain a superior position within a minute of a neutral approach — while reading a newspaper or eating an apple. Skill is definitely a part of aerial combat where such raw ability and tactics count, or where guns must be employed.

Luck does, however, have a major part when many-on-many aerial fights develop, as no pilot can track all targets and threats simultaneously. Though he can shape the peril profile, he cannot truly master it. Again, however, teamwork and doctrine — elements of skill that transcend the individual’s personal effort but may draw upon his or someone else’s leadership or the skill of the unit again come into play.

It’s all chance?

How very PC of them.

They show Richtoven doesn’t strongly diverge from a subset group with a very strong survivorship bias that he’s the largest contributing member of.

By definition he won’t.

The correct plot is for all pilots in which case we find that even first time German pilots shot down the Allied pilots 75% of the time despite the fact that the Germans were outnumbered and had inferior grade fuel.

After the war, it turned out the top German, French, UK and US aces all had the same key rules but only the Germans had a formal program to teach them.