The 1,371 touchdowns scored in the 2018 N.F.L. regular season were the most for a single season in the 99-year history of the league. Quarterbacks threw more touchdown passes than ever. For the first time, both teams in a regulation game scored 50 or more points. Dozens of individual and team offensive records fell as players raced up and down the field, apparently to the delight of fans, because the N.F.L.’s television ratings spiked substantially.

Fittingly, and not surprisingly, the four teams that remain in the hunt for a berth in the Super Bowl — the New Orleans Saints, the Kansas City Chiefs, the Los Angeles Rams and the New England Patriots — scored the most points this season.

But the recent offensive explosion in the N.F.L. didn’t just happen in the past year, nor did productive, pass-happy, fast-paced offensive schemes materialize in a vacuum. Instead, for roughly four decades (or the life span of Patriots quarterback Tom Brady), a series of innovations, minirevolutions, bold strategies from pioneering coaches and the purposeful rule changes by the N.F.L. led to the unprecedented 2018 season.

And it was on this path that the four starting quarterbacks in Sunday’s conference championships games — two in their 40s and two in their early 20s — were also shaped.