Because I’m curious by nature, and also because I already happen to have the entire pro-football-reference database ported into Access, I ran a quick breakdown on the entire database. It includes the stats for 7,245 individual games. So here’s the definitive answer to the question of how the passer rating is affected by number of attempts:
Attempts Games Complete Attempts Yards TDs Ints Rating
<20 1,730 8,826 15,602 57% 100,418 2,187 704 103.97
20-24 870 11,385 19,351 59% 140,433 937 622 84.10
25-29 1,310 20,876 35,474 59% 247,273 1,600 1,072 82.61
30-34 1,331 25,109 42,581 59% 293,336 1,748 1,241 81.47
35-39 985 21,271 36,264 59% 242,082 1,360 1,122 78.39
40-44 598 14,480 24,983 58% 162,906 861 815 75.45
45-49 266 7,282 12,395 59% 80,898 425 399 76.25
50+ 155 4,826 8,319 58% 52,664 259 274 73.46
All 7,245 114,055 194,969 58% 1,320,010 9,377 6,249 81.72
20+ 5,515 105,229 179,367 59% 1,219,592 7,190 5,545 79.78
25+ 4,645 93,844 160,016 59% 1,079,159 6,253 4,923 79.26
30+ 3,335 72,968 124,542 59% 831,886 4,653 3,851 78.31
35+ 2,004 47,859 81,961 58% 538,550 2,905 2,610 76.67
40+ 1,019 26,588 45,697 58% 296,468 1,545 1,488 75.30
50+ 421 12,108 20,714 58% 133,562 684 673 75.13
It does appear that the more one throws, the lower the passer rating will be.