Note: I have been asked why I cut it off at 2011 and why I didn't include beyond seven rounds, because in 1991 and 1992 there were more than seven rounds. On the first part, I cut it off at 2011 because it allowed ample time for the mid-late round picks to acquire starts and gave them three seasons in the league. Including 2012 and 2013 only adds in Russell Wilson to the equation, as Nick Foles only has 16 starts so far. They would not really effect the overall number, but would actually lower the percentage. There were seven quarterbacks drafted in 2012 beyond the first round with only Russell Wilson qualifying. There were nine quarterbacks drafted beyond the first round in 2013 with only Geno Smith and Mike Glennon getting notable playing time.
As for the rounds beyond the seventh, only two entries in the pool had that with the other 18 years limited to seven rounds. If you include all rounds the only addition is Brad Johnson with nine other quarterbacks missing the 20 start threshold.