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Nornagest comments on Harry Potter and the Methods of Rationality discussion thread, February 2015, chapter 104 - Less Wrong Discussion
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If I remember right, Quiddich is scored in increments of ten, so if the current House Points score for one of the contenders isn't a multiple of that it's impossible to tie them based on Quiddich scores. I don't remember seeing anyone giving out one or two House Points at a time, but we've seen five.
I seem to recall many single points issued in academic settings, and I also seem to recall the conversion from Quirrell points to House points allowing single numbers.
I imagine it helps to have a Professor in on the scheme.