In the late World War II, the British and American air forces launched a strategic bombing of Germany. At the beginning of the bombing, the German anti-aircraft artillery fire caused great losses to the American and British air forces, and a large number of fighter planes were shot down. Therefore, the U.S. Department of Defense called Ward, a professor of statistics at Columbia University, and asked him to study the damage of fighter planes in order to improve the aircraft and reduce the probability of being shot down. Professor Ward inspected and studied the fighters who returned from the mission, and found that the wing of the aircraft was the most vulnerable part, while the tail was the least vulnerable part.

However, according to the aviation technology at that time, the armor of the fighter can only be partially strengthened to avoid being overweight. Then the problem is coming. Should we strengthen our wings or tail? At that time, the commander of the Air Force Command believed that since the wing of a fighter was the most vulnerable, it was of course necessary to strengthen the protection of the wing. However, Professor Ward's advice to the U.S. Department of Defense is just the opposite: we should strengthen the protection of fighter tail! Professor Ward believes that protection should be strengthened in the places where fighters are hit hardest, which is a wrong view.

Because, the bomber that successfully returns home has the most serious wing damage, that is to say, the wing can return safely after being hit many times, and bullet holes are rarely found in the tail, that is to say, once the tail is hit, the probability of its safe return is very, very low. Therefore, Professor Ward said, those invisible places are the most deadly. Later, this case has a very famous name, called: survivor bias! That is to say, when we analyze problems, when all or most of the information we rely on comes from important information, we seldom use irrelevant information, or we completely ignore silent information, so there may be a huge deviation between conclusions and facts.

As Professor Ward saw in the British and American Air Force, pilots who were killed or captured could not express their opinions, and there were serious errors in the source of bullet marks data. Second: experienced pilots, their professional opinions may not improve the quality of decision-making, because these pilots are survivors who were shot in the wing but not in the tail, and the dead pilots can't talk. Later, it turned out that Professor Ward's suggestion was correct. The rate at which allied bombers were shot down dropped sharply. The British military also collected some fighter wreckage that crashed in Germany by using spies behind enemy lines, and found that the parts hit by Ward were mainly concentrated in the engine position behind the fighter as expected. So the invisible bullet hole is the most deadly trap!