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Since 1980, there have been 57 Pro-Bowl QB's drafted (Steve Young & Bernie Kosar were selected in the 1st-round of the supplemental draft in 1984 and 1985, respectively)

Excluding Young & Kosar,

25 (45.45%) were drafted in the 1st round.
7 (12.72%) were drafted in the 2nd round.
6 (10.90%) were drafted in the 3rd round.
2 (3.636%) were drafted in the 4th round.
1 (1.818%) was drafted in the 5th round.
7 (12.72%) were drafted in the 6th round.
1 (1.818%) was drafted in the 7th round.
3 (5.454%) were drafted in the 8th round.
1 (1.818%) was drafted in the 9th round.
1 (1.818%) was in the 10th round.
1 (1.818%) was in the 11th round.

In that time, there have been 64 QB's selected in the first round, so you have a 39% chance of going to at least 1 Pro-Bowl if you're chosen there.

The best multi-year Pro-Bowl QB's not selected in Round 1 have been:

Drew Brees - (4 Pro-Bowls), drafted 2001, Round 2, pick 32 (2nd QB taken)
Marc Bulger - (2 Pro-Bowls), drafted 2000, Round 6, pick 168 (6th QB taken)
Tom Brady - (5 Pro-Bowls), drafted 2000, Round 6, pick 199 (7th QB taken)
Matt Hasselbeck - (3 Pro-Bowls), drafted 1998, Round 6, pick 187 (7th QB taken)
Mark Brunell - (3 Pro-Bowls), drafted 1993, Round 5, pick 118 (4th QB taken)
Trent Green - (2 Pro-Bowls), drafted 1993, Round 8, pick 222 (8th QB taken)
Brad Johnson - (2 Pro-Bowls), drafted 1992, Round 9, pick 227 (13th QB taken)
Brett Favre - (11 Pro-Bowls), drafted 1991, Round 2, pick 33 (3rd QB taken)
Chris Chandler - (2 Pro-Bowls), drafted 1988, Round 3, pick 76 (2nd QB taken)
Rich Gannon - (4 Pro-Bowls), drafted 1987, Round 4, pick 98 (7th QB taken)
Mark Rypien - (2 Pro-Bowls), drafted 1986, Round 6, pick 146 (8th QB taken)
Randall Cunningham - (4 Pro-Bowls), drafted 1985, Round 2, pick 37 (1st QB taken)
Boomer Esiason - (4 Pro-Bowls), drafted 1984, Round 2, pick 38 (1st QB taken)
Neil Lomax - (2 Pro-Bowls), drafted 1981, Round 2, Pick 33 (2nd QB taken)