We have a winner. It was, as you all should have guessed

, the ever-inept Bungles.
The 1971 Bungles went 4-10 (a .286 win percentage), despite outscoring their opponents 284 to 265.
I actually know nothing about football prior to the AFL, other than the little Phil-Pitt Steagles and Card-Pitt stuff (which I think the funniest chapter in NFL history).