I haven't done any statistical breakdowns to determine whether there is a general trend, but there are some very high profile players from the modern free agency period (1993-present) that suggest that it is not uncommon for a QB to have a break out season or two towards the end of his career. By this I mean a talented QB that has performed (statistcally at least) at an average or slightly above average pace during the bulk of his career but suddenly performs well above his previous performances near the end. Guys that fit this mold include John Elway, Chris Chandler, Randall Cunningham, Steve Beuerlein, and Rich Gannon.
Elway in particular was nothing special from a statistical standpoint until his eleventh year in the league.
Code:
Passing Rushing
Year Team G Att Comp Yards TD Int Rating
1983 Denver 11 259 123 1663 7 14 54.9
1984 Denver 15 380 214 2598 18 15 76.8
1985 Denver 16 605 327 3891 22 23 70.2
1986 Denver 16 504 280 3485 19 13 79
1987 Denver 12 410 224 3198 19 12 83.4
1988 Denver 15 496 274 3309 17 19 71.4
1989 Denver 15 416 223 3051 18 18 73.7
1990 Denver 16 502 294 3526 15 14 78.5
1991 Denver 16 451 242 3253 13 12 75.4
1992 Denver 12 316 174 2242 10 17 65.7
1993 Denver 16 551 348 4030 25 10 92.8
1994 Denver 14 494 307 3490 16 10 85.7
1995 Denver 16 542 316 3970 26 14 86.4
1996 Denver 15 466 287 3328 26 14 89.2
1997 Denver 16 502 280 3635 27 11 87.5
1998 Denver 13 356 210 2806 22 10 93
Car Ttl 234 7250 4123 51,475 300 226 79.9