Finding QB success rate is a bit iffy because I included the 2015 draft class, but I didn't want to exclude any up and comers. I used Pro-Football-Reference for all my information.
NOTE: This does not include UDFAs
From the 1991-2015 drafts we have had 302 QBs drafted in 25 years, roughly 12 a season.
We have seen 14 QBs taken with the #1 overall Pick
We have seen 20 QBs taken with picks 2-9
We have seen 86 QBs taken with pick 10-99
Leaving us with 182 QBs taken with picks beyond 100
During this time we have seen 40 QB start over 70% of their time in the NFL.
We have seen 11 QBs taken with the #1 Overall pick
We have seen 11 QBs taken with picks 2-9
We have seen 14 QBs taken with picks 10-99
We have seen 4 QBs taken with picks beyond 100
To further break down QB success, I broke this down to QBs with a 74+ PR. I used 74 because of era changes. Today, you won't be starting very long if you can't post mid 80s consistently. This only cuts 2 QBs off the list.
We have seen 10 QBs taken with the #1 overall pick
We have seen 10 QBs taken with picks 2-10
We have seen 14 QBs taken with picks 10-99
We have seen 4 QBs taken with picks beyond 100
So we know have somewhat of a risk % when looking for starting QBs.
#1 Overall Picks - 71.4% Success Rate
2-9 Picks - 50% Success Rate
10-99 Picks - 16.3% Success Rate
100+ Picks - 2.2% Success Rate
Overall - 12.6% Success Rate.
I actually found it somewhat shocking that #1 picks hit so often. That said I do have Winston counted as a hit, he started 100% of his career and had a 74+ PR, so he did qualify. The two bumped off the list for not having quality starts was 2007 #1 overall pick JaMarcuss Russell and 2002 3rd overall pick Joey Harrington.
Another note is that there have only been 38 starting quality QBs in the last 25 years... thats only enough to have 6 left over after giving each team one. QBs don't have 25 year long careers. Thats a crazy fact.
I did go a little further, and include probable backups in this list to see where perhaps QBs that didn't get enough starts over their career to meet the playing % requirement, but had enough quality starts to be considered a viable backup.
Excluding the starting quality QBs we have 43 viable backups that have a playing history greater than 0% season starts, and a 74+ passer rating.
We have seen 3 QBs taken with the #1 overall Pick
(Sam Bradford's 67% career starts throws him in the backup category, as does David Carr's 50%, and Michael Vick's 47%)
We have seen 2 QBs taken with picks 2-9
We have seen 20 QBs taken with pick 10-99
We have seen 18 QBs taken with picks beyond 100
So, if you consider finding even a backup quality QB a win you have a pretty good chance of finding one, in any round really. Obviously like any position if you have the top talent to chose from, as in earlier in the draft, you will hit more frequent. Below are the odds of hitting a roster quality QBs.
We have seen 13 QBs taken with the #1 overall Pick giving us a 92.9% chance of landing a quality QB.
We have seen 12 QBs taken with picks 2-9 giving us a 60% chance of landing a quality QB
We have seen 34 QBs taken with pick 10-99 giving us a 39.5% chance of landing a quality QB
We have seen 22 QBs taken with picks beyond 100 giving us a 12.1% chance of landing a quality QB.
You have a 26.8% chance of landing a roster quality QB.