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Thinking about the odds some more and maybe not quite so small as I thought.
Let's say you accurately predicted for the 2007 tournament that there would be 11 games out of the 63 that would not be accurately predicted by the seeding. What then are the odds of you correctly picking the correct eleven games? Assuming upsets are randomly distributed (which they're not, 9 beating 8 is much more likely than 16 beating 1) you'd have a 1 in 615 trillion chance of being right on picking all 11 upsets. Still really small but 10,000 times better than treating everything like a coin flip.
Considering that the range in actual upsets seen is probably pretty consistent, adding in the need to correctly predict that it will be 11 upsets probably doesn't add more than a degree or two of magnitude. This would be counteracted by the fact that the upsets aren't randomly distributed across all 63 game.
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