The Planes That Didn't Come Back

The evidence, row by row

Each row is a claim the essay makes, then the evidence recorded for it and the source it was checked against. For verified rows that is usually the exact words, where they sit and the day they were read. The label says how far it was checked.

1. W1 Verified Read 13 Oct 2026

   Wald's work on aircraft vulnerability is a series of eight memoranda, originally published in 1943 by the Statistical Research Group at Columbia University for the National Defense Research Committee. Scope: these are the words of the abstract that the Center for Naval Analyses wrote for its 1980 reprint, not Wald's own.

   a series of eight memoranda originally published by the Statistical Research Group at Columbia University for the National Defense Research Committee in 1943

   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors (eight memoranda, 1943), reprinted by the Center for Naval Analyses as CRC 432, July 1980; abstract on the reprint's Report Documentation Page · Report Documentation Page, block 20 (Abstract), which follows printed p. 89 and is outside the body's page numbering (PDF p. 99). Block 18 on the same page lists the eight memo numbers. · cna.org

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   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors (eight memoranda, 1943), reprinted by the Center for Naval Analyses as CRC 432, July 1980; abstract on the reprint's Report Documentation Page, Report Documentation Page, block 20 (Abstract), which follows printed p. 89 and is outside the body's page numbering (PDF p. 99). Block 18 on the same page lists the eight memo numbers, https://www.cna.org/reports/1980/0204320000.pdf. Checked in: Claim Ledger, "The Planes That Didn't Come Back", The Durability Curve, row W1, https://durabilitycurve.com/claims/the-planes-that-didnt-come-back/#c-W1 (source read 2026-10-13).

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2. W2 Verified Read 13 Oct 2026

   Wald's method starts from two kinds of count: the total number of planes that took part in combat and, for each number of hits, the number of planes that took exactly that many hits and returned. Scope: the memoranda define their data in these terms and do not say who examined the aircraft or how the hits were recorded.

   The total number N of planes participating in combat … planes that received exactly i hits but have not been downed, i.e., have returned from combat

   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors, Part I, An Equation Satisfied by the Probabilities That a Plane Will Be Downed by i Hits (SRG memo 85), reprinted by the Center for Naval Analyses as CRC 432, July 1980 · Part I, Introduction, printed p. 1 (PDF p. 10) · cna.org

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   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors, Part I, An Equation Satisfied by the Probabilities That a Plane Will Be Downed by i Hits (SRG memo 85), reprinted by the Center for Naval Analyses as CRC 432, July 1980, Part I, Introduction, printed p. 1 (PDF p. 10), https://www.cna.org/reports/1980/0204320000.pdf. Checked in: Claim Ledger, "The Planes That Didn't Come Back", The Durability Curve, row W2, https://durabilitycurve.com/claims/the-planes-that-didnt-come-back/#c-W2 (source read 2026-10-13).

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3. W3 Verified Read 13 Oct 2026

   Wald names the gap in his own words: the share of planes that actually survived a given hit in a particular combat is unknown, because the distribution of hits on the planes that did not return is not known.

   is unknown, since we do not know the distribution of hits on the planes that did not return

   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors, Part VII, Miscellaneous Remarks (SRG memo 109), reprinted by the Center for Naval Analyses as CRC 432, July 1980 · Part VII, remark 2 (Non-probabilistic interpretation of the results), printed p. 76 (PDF p. 85) · cna.org

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   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors, Part VII, Miscellaneous Remarks (SRG memo 109), reprinted by the Center for Naval Analyses as CRC 432, July 1980, Part VII, remark 2 (Non-probabilistic interpretation of the results), printed p. 76 (PDF p. 85), https://www.cna.org/reports/1980/0204320000.pdf. Checked in: Claim Ledger, "The Planes That Didn't Come Back", The Durability Curve, row W3, https://durabilitycurve.com/claims/the-planes-that-didnt-come-back/#c-W3 (source read 2026-10-13).

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4. W4 Verified Read 13 Oct 2026

   To estimate how vulnerable each part of the plane is, Wald's method needs a second input besides the damage on returning planes: how hits are distributed over the parts of the plane. He states that the two cannot both be estimated from the returning planes' damage alone, and he takes the hit distribution as known beforehand or as measured by firing dummy bullets.

   it is impossible to estimate both … from the damage to returning planes only … can be assumed to be known a priori … or can be established experimentally by firing with dummy bullets

   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors, Part V, Subdivision of the Plane into Several Equi-Vulnerability Areas (SRG memo 96), reprinted by the Center for Naval Analyses as CRC 432, July 1980 · Part V, printed p. 57 (PDF p. 66). The two quantities are defined on printed p. 56 (PDF p. 65); the worked example sets the hit distribution equal to each part's share of the plane's area (printed p. 62, PDF p. 71). · cna.org

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   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors, Part V, Subdivision of the Plane into Several Equi-Vulnerability Areas (SRG memo 96), reprinted by the Center for Naval Analyses as CRC 432, July 1980, Part V, printed p. 57 (PDF p. 66). The two quantities are defined on printed p. 56 (PDF p. 65); the worked example sets the hit distribution equal to each part's share of the plane's area (printed p. 62, PDF p. 71), https://www.cna.org/reports/1980/0204320000.pdf. Checked in: Claim Ledger, "The Planes That Didn't Come Back", The Durability Curve, row W4, https://durabilitycurve.com/claims/the-planes-that-didnt-come-back/#c-W4 (source read 2026-10-13).

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5. W5 Verified Read 13 Oct 2026

   In the worked example that closes Part V, a single hit on the engines is survived with probability .61 and downs the plane with probability .39; for the fuselage the figures are .95 and .05. Wald concludes that, for this example, the engine area is the most vulnerable. Scope: Wald calls the example hypothetical, so the figures illustrate the method and are not measurements from combat.

   Engines .61 .39 … Fuselage .95 .05 … for the observed data of this hypothetical example, the engine area is the most vulnerable in the sense that a hit there is most likely to down the plane

   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors, Part V, Subdivision of the Plane into Several Equi-Vulnerability Areas (SRG memo 96), reprinted by the Center for Naval Analyses as CRC 432, July 1980 · Part V, Numerical Example, summary table and closing paragraph, printed p. 65 (PDF p. 74). The table's two figure columns are the probability of surviving a single hit and the probability of being downed by a single hit. · cna.org

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   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors, Part V, Subdivision of the Plane into Several Equi-Vulnerability Areas (SRG memo 96), reprinted by the Center for Naval Analyses as CRC 432, July 1980, Part V, Numerical Example, summary table and closing paragraph, printed p. 65 (PDF p. 74). The table's two figure columns are the probability of surviving a single hit and the probability of being downed by a single hit, https://www.cna.org/reports/1980/0204320000.pdf. Checked in: Claim Ledger, "The Planes That Didn't Come Back", The Durability Curve, row W5, https://durabilitycurve.com/claims/the-planes-that-didnt-come-back/#c-W5 (source read 2026-10-13).

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6. W6 Verified Read 13 Oct 2026

   In the Part V worked example the engines are not free of hits on the planes that came back. Of the 202 hits counted on returning planes, 39 are on part 1, the engines (.193 of the total), and 78 are on part 2, the fuselage (.386). Scope: the figures are hypothetical; they show the engines hit less often than the fuselage, which is not the same as untouched.

   The hits on the returning planes were distributed as follows … 1 39 .193 … 2 78 .386 … Total number of hits 202

   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors, Part V, Subdivision of the Plane into Several Equi-Vulnerability Areas (SRG memo 96), reprinted by the Center for Naval Analyses as CRC 432, July 1980 · Part V, Numerical Example, table of hits by part, printed p. 64 (PDF p. 73). Columns: part number, number of hits observed on part, ratio to total observed hits. Part 1 is the 2 engines and part 2 the fuselage, with shares of the plane's area of .269 and .346 (printed p. 63, PDF p. 72). · cna.org

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   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors, Part V, Subdivision of the Plane into Several Equi-Vulnerability Areas (SRG memo 96), reprinted by the Center for Naval Analyses as CRC 432, July 1980, Part V, Numerical Example, table of hits by part, printed p. 64 (PDF p. 73). Columns: part number, number of hits observed on part, ratio to total observed hits. Part 1 is the 2 engines and part 2 the fuselage, with shares of the plane's area of .269 and .346 (printed p. 63, PDF p. 72), https://www.cna.org/reports/1980/0204320000.pdf. Checked in: Claim Ledger, "The Planes That Didn't Come Back", The Durability Curve, row W6, https://durabilitycurve.com/claims/the-planes-that-didnt-come-back/#c-W6 (source read 2026-10-13).

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7. W7 Verified Read 13 Oct 2026

   The memoranda's one statement about armour is that the conclusions drawn from the Part VIII vulnerability table, in which the plane is most vulnerable to a hit on the engine area when the type of bullet is not specified, can be used as guides for locating protective armour. Scope: the table comes from data Wald calls hypothetical; a search of the reprint's text finds armour mentioned in this sentence only, and the sentence makes no recommendation about any actual aircraft.

   the hypothetical data would lead to the conclusion that the plane is most vulnerable to a hit on the engine area if the type of bullet is not specified … can be used as guides for locating protective armor

   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors, Part VIII, Vulnerability of a Plane to Different Types of Guns (SRG memo 126), reprinted by the Center for Naval Analyses as CRC 432, July 1980 · Part VIII, Comments on Results, printed pp. 88 and 89 (PDF pp. 97 and 98). The first part of the quote is on PDF p. 97; the armour clause is on PDF p. 98. · cna.org

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   Abraham Wald, A Method of Estimating Plane Vulnerability Based on Damage of Survivors, Part VIII, Vulnerability of a Plane to Different Types of Guns (SRG memo 126), reprinted by the Center for Naval Analyses as CRC 432, July 1980, Part VIII, Comments on Results, printed pp. 88 and 89 (PDF pp. 97 and 98). The first part of the quote is on PDF p. 97; the armour clause is on PDF p. 98, https://www.cna.org/reports/1980/0204320000.pdf. Checked in: Claim Ledger, "The Planes That Didn't Come Back", The Durability Curve, row W7, https://durabilitycurve.com/claims/the-planes-that-didnt-come-back/#c-W7 (source read 2026-10-13).

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