For most of October, Sean Payton harped on his offense’s need to improve on third down.

The Broncos weren’t just struggling, they were flat-out bad.

Denver didn’t convert better than 36% of its attempts in any of its first seven games and entered Week 8 at No. 31 in the NFL, floating around a 26% conversion rate.

Over the past three weeks, though, the money down has been an entirely different story for Payton’s offense.

In a win against Carolina (11 of 17) and losses at Baltimore (6 of 14) and Kansas City (7 of 13), the Broncos offense was far from perfect, but really good on third down.

The team over that stretch has converted 24 of 44 chances for a rate of 54.5%.

“It’s probably a handful of things,” Payton said Friday.

“What we’re doing, who’s doing it, how are we protecting it? That kind of thing. We’re moving the pocket some. I would say, most importantly, though — take last week, for instance, we felt when we broke down the film that Kansas City defended so many third-and-6 to 10 or 10-plus.

“And so it was a little bit of, ‘Man, we have to be on schedule on first and second down’ to get to third (and manageable). If you look at what our third downs were, if I’m looking at (third-and-long), that’s not good. Two to three yards, everybody’s got the good ideas. Four to six, same way.

“Seven to 10, 11-plus, it’s crickets on the headset. Part of it is a product of first and second down.”

That’s true. Some of it, too, is the way rookie quarterback Bo Nix has been playing on third down recently.

Over the past three games, he’s 23 of 29 for 279 yards, three touchdowns and three sacks. He’s also picked up a series of first downs with his legs, though just one over the past two weeks.

Mostly, he’s been doing it with his arm.

Nix has thrown two third-down interceptions this year: Week 1 at Seattle and on Denver’s first possession in Week 6 against the Chargers.

Since that overthrow to Marvin Mims Jr., Nix has dropped back 52 times on third down without a turnover.

Take, for instance, the critical drive that melted 5 minutes, 56 seconds off the clock in the fourth quarter at Kansas City. Audric Estime churned for one first down, and on the other two conversions, Nix hit his top receiver, Courtland Sutton.

Sutton, though, isn’t Nix’s only reliable target on third down.

Over the past five weeks, rookie Devaughn Vele’s also been a conversion machine. Overall in that span, the seventh-round draft pick has caught 14 passes (19 targets) for 176 yards and, against the Chiefs, his first career touchdown.

Those aren’t monster numbers, but most of the catches came in critical situations. Vele has been targeted eight times on third and fourth down in that span and caught all eight for conversions.

“He’s been getting the opportunities and taking advantage of them,” offensive coordinator Joe Lombardi said Thursday.

“Any time you convert, it’s a team effort. Protection, quarterback making the right reads, (receivers) that aren’t getting the ball running their routes correctly and getting the spacing right. You never know where the ball’s going to go.

“He’s been taking advantage and completing the plays and taking advantage when he’s had the opportunity. It’s fun to see the rookies take advantage and get more confidence and everyone’s trust in them grows.”

Vele has quickly developed that trust from Nix and turned himself into a regular target in critical situations.

“It’s not even just that down; it’s any opportunity I get to step on that field, I just want to make sure I’m contributing the way I’m supposed to contribute,” Vele told The Post.

“So if they call a pass play for me or if I have to run block, anything I can do to help the team win, and it’s been effective on third down.

“I’m appreciative the coaches trust me with that and regardless of what happens, I’m always going to try my best to contribute where I can.”

Thanks in part to his contributions, third-down offense has turned from an area that looked bleak for the Broncos earlier in the season to a strength.

It’s also one Denver needs to take advantage of Sunday against Atlanta. The Falcons are No. 28 in the NFL in third-down defense, allowing a 45.5% conversion rate.

If the Broncos keep winning the down, they’ll find themselves in a good position Sunday and beyond.