Why didn't they use randomized and scrambled serial numbers?
Because it happened 80 years ago, when German army (or any other) did not understand statistics as well as they do today.
It was a groundbreaking achievement by allies.
They did know about encryption and developed the Enigma machine.
I don't think you need deep statistics knowledge to know that if the enemy captured Serial # 0020, 0120, 0439, 1293 and 1356; they would at least have some hint that the lower bound is 1356 tanks.
Sure, but as the article points out, that's not a great bound—and you really care about the expected number of tanks (or the upper bound), rather than the lower. The Allies had drastically overestimated this, by about fivefold.
Furthermore, the interesting part isn't just the number of tanks or planes—though that has obvious strategic uses too— but the insight it gives you into their industrial production. What's the limiting factor in getting a tank to the front--machining the parts? assembly? fuel? Which of our raids affected that?
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Because it happened 80 years ago, when German army (or any other) did not understand statistics as well as they do today. It was a groundbreaking achievement by allies.
They did know about encryption and developed the Enigma machine.
I don't think you need deep statistics knowledge to know that if the enemy captured Serial # 0020, 0120, 0439, 1293 and 1356; they would at least have some hint that the lower bound is 1356 tanks.
Sure, but as the article points out, that's not a great bound—and you really care about the expected number of tanks (or the upper bound), rather than the lower. The Allies had drastically overestimated this, by about fivefold.
Furthermore, the interesting part isn't just the number of tanks or planes—though that has obvious strategic uses too— but the insight it gives you into their industrial production. What's the limiting factor in getting a tank to the front--machining the parts? assembly? fuel? Which of our raids affected that?