The aircraft armor example has been mentioned; I would like to add the “infantry helmet” story.
Back in the day (early WW I?) Infantry soldiers usually wore cloth caps in combat. As explosive artillery shells came more into use, lots of soldiers got head injuries, many of them fatal. The Wise Ones said “Let’s have our soldiers wear protective steel helmets to reduce head injuries in combat.”
After this, medical records indicated that a great many more head injuries were being treated. “Oh, No” said the Wise Ones. “Use of helmets increases the number of head injuries in combat.”
“No,” said the Very Wise One. “More soldiers are surviving head injuries and getting treatment because of helmets.”
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