The 1970 Cincinnati Bengals have been widely credited with bringing the West Coast Offense to the NFL. The team’s head coach, Paul Brown, and offensive coordinator (and future San Francisco 49ers head 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 of the NFL. A year later, Carter led the NFL in completion percentage.

But that 1970 Cincinnati team is famous for another reason: Of the 158 teams from 1970 to 2014 that started an NFL 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 are poised to join them. 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) and a quarterback with a similar playing style.

Like Carter, Alex Smith is one of the game’s brightest quarterbacks, and is able to make some 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 has now thrown a franchise-record 253 consecutive passes without an interception.

Kansas City is just the fifth team since 1970 to start 1-5 and then win four consecutive games, joining the 2002 Rams, 2001 Redskins, 1988 Colts, and 1974 Oilers. Among the 158 teams, just 14 finished the season with a .500 record, and only four finished with a winning record. None won 10 games, but the Chiefs have a chance to be the first.

The Chiefs schedule was frontloaded; the team’s remaining six opponents have a 20-39 record this year. That’s one reason the Chiefs have about a 70 percent chance of making the playoffs according to The Upshot’s NFL Playoff Simulator. Another reason: an improved defense, that has allowed just 73 points over the team’s last six games, the fewest in the NFL over that stretch.

After an ugly start, it was easy to count out the Chiefs. But Kansas City is in the process of making NFL history, and proving the early doubters wrong.