The 1970 Cincinnati Bengals have been widely credited with bringing the West Coast offense to the N.F.L. The team’s coach, Paul Brown, and offensive coordinator (and future San Francisco 49ers coach), Bill Walsh, were faced with a challenge, as quarterback Virgil Carter was a smart player with a weak arm. Under Walsh’s tutelage, the Bengals operated a short-passing game that was effective in those run-heavy days. A year later, Carter led the N.F.L. in completion percentage.

But that 1970 Cincinnati team is famous for another reason: Of the 158 teams from 1970 to 2014 that started an N.F.L. season with a 1-5 record, it is the only one to make the playoffs. It actually began the season 1-6, before winning its final seven games to finish 8-6.

Now, 35 years later, the Kansas City Chiefs (at 5-5) are poised to join the Bengals. Fittingly enough, it’s a team with Walsh ties; Kansas City Coach Andy Reid worked for years in Green Bay under Mike Holmgren, who was Walsh’s quarterbacks coach for three seasons in San Francisco. The Chiefs also have a quarterback with a similar playing style.

Like Carter, Alex Smith is one of the game’s brightest quarterbacks, and is able to make plays with his legs. Their passing styles are similar, too. Entering Week 11, Alex Smith’s average pass had traveled just 6.08 yards from the line of scrimmage, by far the fewest in the league. But Smith’s conservative approach has its benefits: He has not thrown an interception since Week 3, and he has thrown a franchise-record 253 consecutive passes without an interception.