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Ha! Took me a second to understand. I was hoping to find a more definitive answer, but the more I get into these things the more I see judgment calls and the less I see definitive answers. Some times I wonder about the way probability is taught. Combinations, permutations, binomial...

Here's another interesting, related topic. Let's say our athlete makes 45/100 shots. They then hire a coach and make 55/100 shots. Each shot is independent, but the second 100 shots have a 55% chance, versus the first set that has a 45% chance. The chance of making 55 or more shots in a...

Short version: You have a series of binary events, presumed independent but not known for sure. A subset of these series show all successes or all failures. If the subset was the entire dataset, it would be statistically improbable (which would force us to revisit the assumption of the...