What is a bad beat, really?

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I don't get it. You say a 2 outter (QQ hitting a Q) is not a bad beat, but perhaps a backdoor flush with an Ace is a bad beat? Do you realize that the second hand actually has more outs to beat KK?

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The difference being that QQ played the hand reasonably whereas the other hand did not.

Don't you need to know odds and pot sizes before determining whether it's a bad beat? to determine whether the player shouldn't legitimately have been in the hand in the first place?