QBR for all rookie QBs with 3+ starts (since 2006 when stat was first kept) with special note if they started fewer than 8. Bold indicates team improved by >2 games, italics indicate team got worse by >1 game.

1. DeShaun Watson 83.5 (2017, -5 wins from 2016) - 6 starts
2. Dak Prescott 77.6 (2016, +9 wins from 2015)
3. Russell Wilson 72.7 (2012, +4 wins)
4. Robert Griffin III 69.4 (2012, +5 wins)
5. Matt Ryan 68.8 (2008, +7 wins)
6. Andrew Luck 65.6 (2012, +9 wins)
7. Justin Herbert 62.6 (2020, +2 wins)
8. Matt Leinart 60.5 (2006, +0 wins)
9. Kyler Murray 57.7 (2019, +2.5 wins)
10. Jameis Winston 57.2 (2015, +4 wins)
11. Cam Newton 56.6 (2011, +4 wins)
12. Vince Young 56.1 (2006, +4 wins)
13. Tim Tebow 56.0 (2010, -4 wins) - 3 starts
14. Daniel Jones 55.7 (2019, -1 win)
15. Mike Glennon 55.2 (2013, -3 wins)
16. Teddy Bridgewater 54.4 (2014, +1.5 wins)
17. Colt McCoy 52.8 (2010, +0 wins)
18. Mac Jones 51.3 (2021, +2.5 wins)
19. Baker Mayfield 51.2 (2018, +7.5 wins)
20. Nick Foles 51.2 (2012, -4 wins) - 6 starts
21. Drew Lock 50.2 (2019, +1 win) - 5 starts
22. Josh Allen 49.8 (2018, -3 wins)
23. Andy Dalton 49.5 (2011, +5 wins)
24. Joe Burrow 48.5 (2020, +2.5 wins)
25. Marcus Mariota 48.4 (2015, +1 win)
26. Ryan Tannehill 48.4 (2012, +1 win)
27. Joe Flacco 47.1 (2008, +6 wins)
28. Sam Bradford 46.9 (2010, +6 wins)
29. Carson Wentz 46.7 (2016, +0 wins)
30. Sam Darnold 45.9 (2018, -1 win)
31. Tua Tagovailoa 44.8 (2020, +5 wins)
32. Cody Kessler 43.4 (2016, -2 wins)
33. Lamar Jackson 42.6 (2018, +1 win) - 7 starts
34. Jay Cutler 41.9 (2006, -4 wins) - 5 starts
35. Geno Smith 41.0 (2013, +2 wins)
36. Derek Carr 40.1 (2014, -1 win)
37. EJ Manuel 38.2 (2013, +0 wins)
38. Matt Stafford 37.1 (2009, +2 wins)
39. Josh Freeman 37.0 (2009, -6 wins)
40. Trent Edwards 36.3 (2007, +0 wins)
41. Davis Mills 35.6 (2021, -0.5 wins)
42. CJ Beathard 35.4 (2017, +4 wins) - 5 starts
43. Brandon Weeden 33.9 (2012, +1 win)
44. Jalen Hurts 33.8 (2020, -4.5 wins) - 4 starts
45. Trevor Lawrence 33.6 (2021, +1.5 wins)
46. Mark Sanchez 32.8 (2009, +0 wins)
47. Jake Luton 32.8 (2020, -5 wins) - 3 starts
48. DeShone Kizer 32.6 (2017, -1 win)
49. Mitch Trubisky 32.4 (2017, +2 wins)
50. Christian Ponder 32.4 (2011, -3 wins)
51. Zach Mettenberger 30.8 (2014, -7 wins)
52. Zach Wilson 29.0 (2021, +1.5 wins)
53. Dwayne Haskins 28.0 (2019, -4 wins)
54. Blake Bortles 27.6 (2014, -1 win)
55. Justin Fields 26.0 (2021, -2.5 wins)
56. Josh Rosen 24.1 (2018, +1 win)
57. John Skelton 23.6 (2010, -5 wins) - 4 starts
58. Blaine Gabbert 22.2 (2011, -3 wins)
59. Jared Goff 18.3 (2016, -3 wins)
60. Jimmy Clausen 13.8 (2010, -6 wins)
61. John Beck 13.3 (2007, -5 wins) - 4 starts
62. Max Hall 8.8 (2010, -5 wins) - 3 starts

A few interesting takeaways

• It's pretty unusual for a QB to be as bad as Lawrence or ZW were this season and still have the team have a better year. Only rookie QBs with a QBR under 40 and team improvement are those 2, Josh Rosen, Mitch Trubisky, Brandon Weeden, and Matt Stafford
• Josh Allen is just an exception to everything - his rookie year had zero way of predicting any success
• #59 Jared Goff is by FAR the worst rookie season that kept getting opportunities (probably due to his high draft position, which bodes well for Lawrence, Wilson, and Fields).  The next lowest to get a meaningful second contract is #46 Mark Sanchez
• Guys with a rookie QBR over 70 all ended up studs. 60-70 were more likely to be successful than not (obvious caveats on Luck's retirement and RGIII injuries), but still basically a coin flip. 40-60 has a smattering of successful QBs and huge busts. Below 40 you've got Matt Stafford, Jared Goff and lots of ugliness
• Some of the best (Mahomes) and worst (Johnny Manziel, JaMarcus Russell) aren't included here since they started so few games

And finally, the best comps for each in this rookie class, based on this

• Trevor Lawrence: Brandon Weeden, Mitch Trubisky, Jalen Hurts, Mark Sanchez, Zach Wilson
• Zach Wilson: Mitch Trubisky, Josh Rosen, Mark Sanchez, Blake Bortles, Trevor Lawrence
• Justin Fields: Dwayne Haskins, Christian Ponder, Zach Wilson, Josh Rosen, Blaine Gabbert
• Mac Jones: Teddy Bridgewater, Andy Dalton, Joe Burrow
• Davis Mills: Trent Edwards, Brandon Weeden, Matt Stafford

Generally unexciting though it looks like Jones should be a placeholder, game-manager type QB at the least