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I'm going to use 1990 as my starting point for the modern NFL. Why? Because it seems like a good place to start and it gives us 26 NFL seasons to use. There have been 65 NFL QBs taken in the first round of the NFL draft since 1990 if you include the three guys taken in 2016. Below is a table showing how many games each of these guys started as an NFL rookie.
| Year Drafted | Pick | QB | Rookie Starts |
| 1990 | 1 | Jeff George | 12 |
| 1990 | 7 | Andre Ware | 1 |
| 1991 | 16 | Dan McGwire | 1 |
| 1991 | 24 | Todd Marinovich | 1 |
| 1992 | 6 | David Klingler | 4 |
| 1992 | 25 | Tommy Maddox | 4 |
| 1993 | 1 | Drew Bledsoe | 12 |
| 1993 | 2 | Rick Mirer | 16 |
| 1994 | 3 | Heath Shuler | 8 |
| 1994 | 6 | Trent Dilfer | 2 |
| 1995 | 3 | Steve McNair | 2 |
| 1995 | 5 | Kerry Collins | 13 |
| 1997 | 26 | Jim Druckenmiller | 1 |
| 1998 | 1 | Peyton Manning | 16 |
| 1998 | 2 | Ryan Leaf | 9 |
| 1999 | 1 | Tim Couch | 14 |
| 1999 | 2 | Donovan McNabb | 6 |
| 1999 | 3 | Akili Smith | 4 |
| 1999 | 11 | Daunte Culpepper | 0 |
| 1999 | 12 | Cade McNown | 6 |
| 2000 | 18 | Chad Pennington | 0 |
| 2001 | 1 | Michael Vick | 2 |
| 2002 | 1 | David Carr | 16 |
| 2002 | 3 | Joey Harrington | 12 |
| 2002 | 32 | Patrick Ramsey | 5 |
| 2003 | 1 | Carson Palmer | 13 |
| 2003 | 7 | Byron Leftwich | 13 |
| 2003 | 19 | Kyle Boller | 9 |
| 2003 | 22 | Rex Grossman | 3 |
| 2004 | 1 | Eli Manning | 7 |
| 2004 | 4 | Philip Rivers | 0 |
| 2004 | 11 | Ben Roethlisberger | 13 |
| 2004 | 22 | J.P. Losman | 0 |
| 2005 | 1 | Alex Smith | 7 |
| 2005 | 24 | Aaron Rodgers | 0 |
| 2005 | 25 | Jason Campbell | 7 |
| 2006 | 3 | Vince Young | 13 |
| 2006 | 10 | Matt Leinart | 11 |
| 2006 | 11 | Jay Cutler | 5 |
| 2007 | 1 | JaMarcus Russell | 1 |
| 2007 | 22 | Brady Quinn | 0 |
| 2008 | 3 | Matt Ryan | 16 |
| 2008 | 18 | Joe Flacco | 16 |
| 2009 | 1 | Matthew Stafford | 10 |
| 2009 | 5 | Mark Sanchez | 15 |
| 2009 | 17 | Josh Freeman | 9 |
| 2010 | 1 | Sam Bradford | 16 |
| 2010 | 25 | Tim Tebow | 3 |
| 2011 | 1 | Cam Newton | 16 |
| 2011 | 8 | Jake Locker | 0 |
| 2011 | 10 | Blaine Gabbert | 14 |
| 2011 | 12 | Christian Ponder | 10 |
| 2012 | 1 | Andrew Luck | 16 |
| 2012 | 2 | Robert Griffin | 15 |
| 2012 | 8 | Ryan Tannehill | 16 |
| 2012 | 22 | Brandon Weeden | 15 |
| 2013 | 16 | EJ Manuel | 10 |
| 2014 | 3 | Blake Bortles | 13 |
| 2014 | 22 | Johnny Manziel | 2 |
| 2014 | 32 | Teddy Bridgewater | 12 |
| 2015 | 1 | Jameis Winston | 16 |
| 2015 | 2 | Marcus Mariota | 12 |
The average number of rookie starts for a first round QB since 1990 is 8.4, you'll note that the trend in the past few years is to start them. This was not the case a quarter of a century ago. The current trend appears to be, that unless they are severely deficient and doomed to fail in the NFL (Jamarcus the Hutt, Quinn, Tebow, Locker and Manziel), they will start a good number of games as rookies.
It is even more interesting if you plot this data using the pick# as the X values and the rookie starts as the Y values :format(webp):no_upscale()/cdn.vox-cdn.com/uploads/chorus_asset/file/6710823/1st_rnd_QB_rookie_starts_1990-2015.0.png)