Drew Brees made history on Monday night with a 62-yard touchdown pass that gave the New Orleans Saints quarterback the NFL record for most career passing yards. The same play also helps explain another groundbreaking trend in the league this year: a huge increase in scoring.

Brees’s record-setting completion to Tre’Quan Smith came on first down. That’s notable because, for the first time this year, NFL teams are passing the ball on first down more than they are running it. And that—along with some offense-friendly rule changes,...