Abraham Wald and the Case of the Missing Bullet Holes | Reading Comprehension Practice

Introduction and Reading Strategies

Welcome back to our reading practice series! Today we have a historical narrative. Narrative passages on exams like the TOEFL and SAT test your ability to follow a story, understand cause and effect, and identify the main lesson or conclusion.

Here are some strategies for this text:

• Follow the Timeline: This is a story with a beginning, a middle, and an end. Pay attention to words that indicate time and sequence (e.g., “During,” “Initially,” “Then,” “Ultimately”).
• Identify the Problem and Solution: All good stories have a central conflict. As you read, identify the problem the military faced and the different solutions that were proposed. The key is to understand why the final solution was the correct one.
• Look for the “Aha!” Moment: This story has a moment of brilliant insight. Pinpointing this “aha!” moment will help you understand the core message of the entire text.

Recommended Time: You should aim to read the passage and answer all 10 questions in 16-19 minutes.

Reading Passage

During the darkest days of World War II, the Allied forces faced a grim reality: their bombers were being shot down at an alarming rate during raids over enemy territory. Every plane lost meant the loss of a highly trained crew and a costly piece of military hardware. The commanders knew they had to act. The proposed solution was logical enough: add more armor to the planes for protection. However, armor is heavy, and adding too much would make the bombers sluggish, reduce their range, and make them easier targets. The protection had to be applied strategically, only to the most critical areas.

To figure out where to add this armor, the military collected data from the bombers that managed to return from their missions. They meticulously mapped the bullet holes and damage on these surviving aircraft. The data was consistent: the fuselage, the wings, and the tail gunner’s station were frequently riddled with holes. The engines, however, showed remarkably little damage. The initial conclusion, drawn by many high-ranking officers, seemed obvious: reinforce the areas that showed the most damage. The wings and fuselage were clearly the most common targets, so that’s where the extra armor should go.

It was at this point that a Hungarian-born statistician named Abraham Wald, working with the Applied Mathematics Panel in New York, was brought in to analyze the problem. After reviewing the data, Wald proposed a solution that was startlingly counter-intuitive. He advised the military to put the extra armor not where the bullet holes were, but precisely where they were not: on the engines.

His reasoning was profound in its simplicity and represented a masterful leap of logic. The military leaders, he argued, were only looking at the planes that had survived. Their data set was inherently biased. The bullet holes on the returning planes represented areas where a bomber could take damage and still fly back home. The absence of bullet holes on the engines of these survivors, therefore, was the most critical piece of evidence. It didn’t mean the engines weren’t being hit; it meant that when they were hit, the plane did not return at all. The bullet holes in the engines were on the bombers lying at the bottom of the English Channel or crashed in fields across Europe.

This phenomenon is now known as “survivorship bias.” It is the logical error of concentrating on the people or things that “survived” some process and inadvertently overlooking those that did not because of their lack of visibility. We see the successful college dropouts who founded tech companies and conclude that dropping out of college is a viable path to success, forgetting the vast, silent majority of dropouts who did not become billionaires. We study the habits of centenarians and attribute their longevity to their diet or optimistic outlook, ignoring the millions who had the same habits but died younger from unrelated causes.

Abraham Wald’s insight saved countless lives and helped alter the course of the air war. His work serves as a timeless and powerful reminder that the most crucial evidence is often that which we cannot see. To make truly rational decisions, we must learn to ask not just “What do the survivors have in common?” but also, more importantly, “What is it that distinguishes the survivors from those who failed?” It requires us to account for the silent data, the missing pieces that tell the most important part of the story.

Reading Quiz

Keywords & Phrases

1. Grim reality: A harsh, unpleasant, and serious situation. The passage opens by describing the “grim reality” of bombers being shot down.
2. Sluggish: Slow-moving or inactive. Used to describe how planes would perform if too much heavy armor were added.
3. Meticulously: In a way that shows great attention to detail; very carefully and precisely. The military “meticulously” mapped the bullet holes on the surviving planes.
4. Riddled with: Filled or permeated with something, especially something undesirable. The surviving planes were “riddled with” bullet holes in certain areas.
5. Counter-intuitive: Contrary to intuition or to common-sense expectation. Abraham Wald’s advice to armor the undamaged parts was “counter-intuitive.”
6. Profound in its simplicity: Deep and insightful, yet expressed in a very simple and clear way. Used to describe Wald’s brilliant and logical reasoning.
7. Inherently biased: Having a natural, built-in tendency to be unfair or skewed. Wald realized the data from only the surviving planes was “inherently biased.”
8. Inadvertently: Without intention; accidentally. Survivorship bias causes us to “inadvertently” overlook failures.
9. Viable path: A way of achieving something that is capable of working successfully. The passage mentions the mistaken idea that dropping out of college is a “viable path” to wealth.
10. Centenarians: People who are one hundred years old or more. Used as another example of survivorship bias, where we study the habits of “centenarians” to find the secret to long life.

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