Quote:
Originally Posted by AGPapa
I believe that it looks "shifted" due to ties and odd numbers of points. In reality very few teams get ties, but the normal distribution doesn't know this. I put 10 and 11 in the same bin so that there wouldn't be dips at every point. The actual distribution is also shifted down, (there are more really bad teams than really good teams). Again, the graph is just to get an idea of how the rule changes will affect things.
For the 10/11 bin I added the pdf of 10 with the pdf of 11; I'm not sure how this relates to a continuous function. I've attached the spreadsheet I used for you to look at. It's a little messy as I did not originally intend to upload it, however I added some labels and it should be clear enough.
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It was clear enough.
Here is the same histogram using the method I previously described. It has less than half of the variance of the other method, so it is likely a better fit. I also used a continuous integration of the normal distribution instead of using discrete points as an approximation. So that may also have had a small effect.