Drop rate is supposed to tell us something about the true talent of a receivers hands. I don't know exactly how a pass is categorized as catchable or an incompletion categorized a drop. However, I suspect that there is a subtle bias depending on the quarterback, maybe because of how they throw the ball or because of who they are. Like park factor in baseball - I'd like to tease out this correlation if it exists. The analysis presented here is not park factor analysis, nor is it complete - it's just a preliminary exploration to see if I should spend more time on this question. In particular, this investigation was motivated when looking at Wes Welker's drop rates - and thinking about how Brady and Manning throw the ball differently.
Receivers thrown the ball by Peyton Manning have had a 5.9% drop rate from 2008-2012. In that same period, receivers thrown the ball by Tom Brady had a 6.9% drop rate. The league average was 6.3% during this period. One QB with a very low average drop rate was Philip Rivers with a 4.8% drop rate and one with a high rate is Aaron Rogers at 7.7%. Do quarterbacks correlate with drop rates?
To answer this question a little deeper I decided to look at receivers playing with different quarterbacks. For example, Reggie Wayne is famous for his great hands, he also had Peyton Manning throwing to him most of his career. So, did Wayne's drop rate change with Andrew Luck throwing him the ball?
Reggie Wayne had a drop rate of 6.1% with Peyton from 2008-2010. Last year Wayne dropped over 8.6% of the passes thrown by luck. Brandon Lloyd played with Brady and other QBs between 2010 and 2012. Lloyd had a drop rate of 8.6% with Brady last year, whereas Lloyd had a drop rate of only 7.5% on 159 targets over the previous two years in Denver and St. Louis. Wes Welker had a drop rate of 9.5% from 2009-2012 with Brady, whereas in 2008 (without Brady) Welker posted a drop rate of only 6.0% on 116 targets. That said, Welker accounts for a significant amount of drops from Brady without which Brady's drop rate is much better. So we can say both that Welker and Lloyd dropped fewer passes with other quarterbacks but also that Welker dropped passes at a higher rate than Brady's other receivers.
As of now I'd take most of this with a grain of salt. I'm planning to try to look at all receivers that played with different QBs over 2008-2012 to normalize "drop rate factors" for the QBs. But based on preliminary work it does appear that drop/catchable categorizations may not be completely un-bias when it comes to the QB throwing the ball. They may be somewhat biased based on the type of throw (slot, deep) or style of throw. There also appears to be a very slight correlation with number of targets - but I think I will find this to be mostly noise.
As it relates to Welker? who knows - maybe his 9% drop rates will return to his 5-6% drop rates earlier in his career. Or maybe just come a little closer to Manning's 5.9% receiver average drop rates...