I don't know the specific statistics, but franchise goalies are more commonly found in later rounds, are they not?
The most recent Vezina winners are:
Henrik Lundqvist - 205th overall
Tim Thomas - 217th overall
Ryan Miller - 138th overall
Martin Brodeur - 20th overall
Miikka Kiprusoff - 116th overall
Jose Theodore - 44th overall
Dominik Hasek - 199th overall
Out of those, only one was from the first round.
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