>Blackett's team made the logical recommendation that the armour be placed in the areas which were completely untouched by damage in the bombers which returned. They reasoned that the survey was biased, since it only included aircraft that returned to Britain. The areas untouched in returning aircraft were probably vital areas, which, if hit, would result in the loss of the aircraft.
https://en.wikipedia.org/wiki/Operations_research#Second_Wor...
The specific story of armoring an aircraft would be best completed by "...and the loss rate per mission was cut from x% to y% on the new planes". Unfortunately, that's one of the few examples that the section doesn't explicitly say demonstrated improvement.
It's not like they welded a piece of steel into a random place on the hull because they'd never seen it get hit before.
The complete absence of armor in the Mitsubishi Zero is often cited as one of the reasons why it became outclassed by American fighters later in WWII.