"non-random" raffle on Empire..what are the odds

[AaronBrown]

It's not quite as bad as some people suggested.

The 90 runners-up seem to be a reasonably random selection of names. If we assume these are in fact random, then the 10 winners are all in the top 22 of the names by alphabetical order (AceBarber not only won, he was a runner-up as well). However, the 12 other names in the first 22 by alphabetical order averaged 54th place, what you would expect since they had to be between 11 and 100. The 78 names not in the top 22 seem to be randomly placed as well.

That suggests Empire drew 10 names at random out of the first 22% of the names in alphabetical order, then selected the runners-up at random. It's easy to see a programming mistake that could let that happen.

I'm ignoring the fact that the 9 winners second-place winners are in alphabetical order, they might have been listed that way after selection. The first-place winner is the first among the 10 in alphabetical order (although only second among the whole group).

If you put weight on that fact, an obvious hypothesis is the programmer considered the names in alphabetical order, then flipped a coin to decide whether or not they got a prize. He may not have used a computer at all. When he was up to 10, he could have tossed all the remaining names in a pile (plus AceBarber's) and picked 90 at random.

If you are picking names at random, the chance of picking 10 among the first 22 in alphabetical order is 1 in 26 million.

The flaw in your analysis is that you assume the 100 people were the only entrants. The 22% figure is not representative of the proportion of the sample (Aceberber - Caeser) in the entire population of names. According to research done by OP 13% is closer.

Even so, it's still a HUGE number.

[AaronBrown]

I didn't see OP's analysis but I wouldn't call my assumption a "flaw." I stated the assumption. It's one way of guessing the answer. It's true that the larger the number of people in the sample, the lower the percentage fraction, but also the less that fraction declines as you pick people. It doesn't make that much difference to the conclusion.