Probably too late to use these in filling out your brackets, but these may be of interest:
Nate Silver’s advancement probabilities and bracket.
How to pick a winning bracket using analytics, from Laura McLay.
John Ezekowitz at the Harvard Sports Analysis Collective predicts the tournament and predicts the upsets.
And finally, Jordan Ellenberg’s math bracket, created by picking the school with the better math department to win.
Edited to add: a late breaking post from Laura McLay.
God plays dice 
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