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Airplane top-view with multiple red dots indicating bullet holes

This is a famous diagram. It is used extensively to demonstrate the concept of "Survivorship Bias".

Here is a typical example claim associated with this diagram:

In World War 2 the allies famously statistically plotted on returning aeroplanes the key areas of damage with a view to reinforcing those parts of the plane Statistician Abraham Wald pointed out the fallacy here; they were focusing on the ‘planes which had survived, so by definition those damaged areas were the places the ‘planes could survive damage. It was the unmarked areas of planes that needed reinforcing.

There are no shortage of other examples. In fact, it is well-recognised enough to stand alone as an emblem of the problem.

It strikes me that it doesn't look like a typical diagram from the 1940s. Is this a diagram from Wald's research? Is it a modern re-creation based on Wald's data? Is it just made up?

Related Question: Did the Center for Naval Analysis recommend that the damaged areas be reinforced on all bombers, creating a famous case of survivorship bias?

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  • Do you have an actual example of someone claiming that the diagram is from the 1940s?
    – TimRias
    Jun 18 at 22:23
  • @TimRias: I thought it strongly implied, but note the claim discusses the data being "plotted" and "unmarked areas", whereas the answer points out there was no diagram during the war.
    – Oddthinking ♦
    Jun 19 at 0:31

1 Answer 1

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You can just look at the Wikipedia page for the very same image, and find the following information:

Description English: Illustration of hypothetical damage pattern on a WW2 bomber. Based on a not-illustrated report by Abraham Wald (1943), picture concept by Cameron Moll (2005, claimed on Twitter and credited by Mother Jones), new version by McGeddon based on a Lockheed PV-1 Ventura drawing (2016), vector file by Martin Grandjean (2021). This file was derived from: Lockheed PV-1 Ventura BuAer 3 side view.jpg: Lockheed PV-1 Ventura BuAer 3 side view.jpg This file was derived from: Survivorship-bias.png: Survivorship-bias.png
Date 21 March 2021
Source Own work
Author Martin Grandjean (vector), McGeddon (picture), Cameron Moll (concept)

The linked PNG image has the following information:

Description English: Illustration of hypothetical damage pattern on a WW2 bomber, dot pattern roughly based on that given at http://www.motherjones.com/kevin-drum/2010/09/counterintuitive-world which gives credit to Cameron Moll. This file was derived from: Lockheed PV-1 Ventura BuAer 3 side view.jpg: Lockheed PV-1 Ventura BuAer 3 side view.jpg
Date 12 November 2016
Source Own work
Author McGeddon

Basically, in 2005, Cameron Moll created the very first image, based on the original paper (1980 reprint) (archived here), which did not feature any images, and was not based on real-world data, but instead used hypothetical observations of damage. That image was used in 2010 by Kevin Drum in the article "The Counterintuitive World". That illustration was then later used as basis for a new illustration based on the Lockheed PV-1 Ventura by Wikipedia user McGeddon (in 2016), before being converted to a vector image by Martin Grandjean in 2021.

Martin Grandjean writes about the image on Twitter:

We owe this observation to Abraham Wald (1943), but it is Cameron Moll (2005) who is at the origin of its visual expression with the red dots. The image of McGeddon (2016) on Wikipedia was then widely circulated. Note that a simpler version can be found in Howard Wainer (1997)

Cameron Moll has weighed in themselves on the origin of the image in "Abraham Wald and the airplane diagram with red bullet holes – here’s the origin story":

At the time I was actively speaking at web conferences in the US & Europe on the topic of problem solving among other things, and Wald's story was a terrific demonstration of solving (and defining) the right problem. I wasn't aware of anyone who had visualized this, so sometime around 2005 I hastily plotted fictitious red dots on a poorly-chosen commercial aircraft outline and began including this in slide decks and blog posts. [...] The image you've seen repeatedly on the socials is from Wikipedia (creator unknown) and is a recreation of my diagram.

This seems to quite comprehensively summarize the genesis of the image.

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  • The link to the original paper appears to be dead. The wiki article on Wald has this Wayback Machine link to an archived scan of a reprint of the work in question, which worked for me.
    – Danila Smirnov
    Jun 20 at 11:06
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    @DanilaSmirnov The link to the paper works perfectly fine for me, but I can additionally include an archived version.
    – Polygnome
    Jun 20 at 11:52
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    In summary: the image is based on real WWII research. Specifically, see pages 62-65 of the original linked report (begins on page 72 of the PDF). However, the original, while likely based on brief observations of actual aircraft, was more of a mathematical model to provide a foundation for a later more-detailed statistical study, rather than the statistical study itself, and was more about theoretical mathematics. The image, specifically, came much later (2005).
    – Joel Coehoorn
    Jun 20 at 14:42

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