Ron Rivera could have gone big. This was back in March, with NFL free agency about to start, and the new coach of the Washington Football Team had all the authority to spend owner Daniel Snyder’s money on expensive players with glowing records, men whose names would shout in boldface type and bring noise to a franchise that had slumped to irrelevance.

And while Rivera did try to lure Dallas Cowboys wide receiver Amari Cooper and Atlanta Falcons tight end Austin Hooper in free agency’s opening hours, neither attempt felt like the relentless refusal to hear “no” the way many of Washington’s free agent pursuits had in the past. Aside from bringing cornerback Kendall Fuller back from the Kansas City Chiefs on a deal worth $10 million per year, Rivera chose to go small. Really small.

The announcements that came over the next few days did not offer much hope for a team that had won just three games the previous season. Logan Thomas, a onetime quarterback, was not the tight end Washington fans wanted. Who had heard of Wes Schweitzer and Cornelius Lucas? Surely they weren’t the team’s solution for a fractured offensive line. Wide receiver turned running back J.D. McKissic didn’t sound like an upgrade for an offense that had done little the previous season.

But they came cheap and hungry.

“Prove it,” Rivera called their contracts, which mostly ran for one or two years and generally were worth between $3 million and $4 million each.

“A lot of these [players] come in and say, ‘Give me an opportunity to compete, prove myself and then we’ll see,’ which I think is great,” Rivera said in April when talking about the low-level players he had signed. “I love the fact these guys are betting on themselves and are going to come in and prove that they belong and they deserve an extensive contract.”

Some, such as safety Sean Davis — signed with the idea of starting beside Landon Collins — did not work out and were released. Many others, however, did. Now, as Washington begins the final month of the regular season, Rivera’s gamble on those gambles is working. The players who came to “prove it” are proving something.

Thomas, the tight end, has 34 catches for 328 yards and four touchdowns. McKissic, playing as a third-down back, has caught 46 passes for 338 yards and is averaging 4.5 yards on 50 carries. Schweitzer has helped solidify the offensive line, having started the past two months at left guard, and Pro Football Focus grades him as the NFL’s 17th-best interior lineman through 11 games. Lucas has played well, too, at times.

Perhaps at another time their seasons would be hopeful pins of light for a rebuilding team. A 4-7 record usually is not much to be excited about. But in this oddest of seasons, in an awful NFC East where 4-7 has you tied for first place, players such as Thomas, McKissic, Schweitzer and linebackers Jon Bostic (re-signed in the spring for two years and $5 million) and Kevin Pierre-Louis — who have had good moments — are helping to pull Washington toward the most improbable of division titles.

And without the pressure to use high-priced players such as Cooper or Hooper — or even running back Adrian Peterson (who was cut before the season) — Washington has been able to let players such as third-round draft pick Antonio Gibson grow into a potential star at running back and undrafted wide receivers Cam Sims and Isaiah Wright develop into usable options in games.

“You sit there and say, ‘Man, these guys are ready to have these kinds of years,’ ” Rivera said this week when asked about his offseason signings.

He and his staff believed McKissic would fit perfectly in the offense. They thought Pierre-Louis could help immediately. Tight ends coach Pete Hoener loved what he saw on game tape of Thomas, then with the Detroit Lions, and thought, “This guy was ready to ascend,” Rivera added.

“You look at these guys and think these are types of guys that you want,” Rivera said, pointing to the ability of many of those players to play different positions.

“Now, those guys may not be your starters, but they may be top-flight backups that are just as valuable to what you’re trying to do,” Rivera continued. “If you can keep those guys around for a period of time, now it takes the pressure off going into the draft. That’s the other thing that we have to think about. You look at the wide receiver position and go: ‘Man, do we need to draft another guy? Or do we have the makings of it? Is there a guy in free agency that you add into the mix of it and that guy’s a solid [addition]?’ ”

By not spending in the spring, Rivera can spend this winter. Overthecap.com projects Washington to have a little more than $50 million of salary cap space this offseason, though pinning down the NFL’s cap number after a year of lost ticket revenue during the coronavirus pandemic could be difficult. Washington might have less to spend — and will have to dedicate significant resources to re-sign guard Brandon Scherff, whose return seems to be a priority for Rivera.

Still, Washington is in line to have more cap space than all but four other teams, and it may already have key pieces at tight end, at running back and on the offensive line — while still hoping that tackle Saahdiq Charles and wide receiver Antonio Gandy-Golden, promising draft picks now on injured reserve, will be healthy next year. And if Washington decides to sign one or more high-priced free agents, the resources will be there to do so.

For a franchise with a long past of impulsive winters that have led to somber autumns, Rivera’s decision to go small in his first free agency might be the best bet he could have made.