When Matt Williams was hired as the sixth manager in Washington Nationals history two Octobers ago, there was no way to know anything substantive about his style and strategy. How would he act in the clubhouse? How would he run a game? We could ask questions, and he could answer, but until he rolled out his first lineup (remember that one, with Wilson Ramos hitting cleanup and Bryce Harper hitting sixth?) and began pushing buttons and pulling levers, certainty was impossible.

To an extent, that’s true with any first-time manager. So it would make sense, as the Nationals look for Williams’s replacement following his inevitable firing Monday, that they would veer the opposite direction, that they would hire someone with experience. It’s a typical response in sports: The defensive coach in football failed? Hire an offensive guy. Davey Johnson was too laissez faire with his players? Bring in the Big Marine.

So in considering who might be a good fit to be the Nats’ seventh manager, start there: experience.

“As we go through the laundry list of things that we look for in our manager, in the perfect leader of the ballclub on the field, leadership qualities, knowledge of the game, X’s and O’s are all important,” General Manager Mike Rizzo said in a conference call with reporters Monday afternoon. “Communication in the clubhouse, communication within the coaching staff is vital. Experience is always helpful. It always adds a layer of expertise to anybody’s resume

“We feel like where we are in our timetable … we certainly would lean toward someone who had some managerial experience, particularly at the major league level.”

So, experience. Do you call Jim Leyland? He turns 71 in December, has no connection to this franchise or the people who run it, and has burnt out more than once. But if you believe your roster is still ready to contend — and the Nationals do — then it’s worth the dime. Other than Tony La Russa and Bobby Cox, there’s no out-of-work manager with the combination of accomplishment and reputation Leyland would bring. (Plus, La Russa has a post-manager gig running the Diamondbacks, and Cox is 74 and settled into retirement.)

Okay, now, long shots aside: Bud Black. For eight-and-a-half seasons he managed the San Diego Padres, often at times when the club didn’t have the payroll clout or development system to compete against the powers in the National League West, the Dodgers and Giants. Yes, he had only two winning seasons. No, he never won a division title or even reached the postseason, the high-water mark coming in 2010, when the Padres won 90 games and finished two games behind the Giants.

But Black, who pitched in 398 big league games over a 15-year career, comes with two primary attributes that would be useful in Washington right now: a deep understanding of pitching and an ability to relate to his players. When Black was fired this season — a move made by new general manager A.J. Preller with San Diego standing 32-33 — longtime Padres spoke of their connection to a man they admired.

There are other potential candidates with managerial experience. Kansas City bench coach Don Wakamatsu managed the Mariners to a winning record in 2009 but was fired with the club at 42-70 the following season. Longtime Twins manager Ron Gardenhire wants another job after sitting out 2015 following his dismissal by Minnesota. But neither is as intriguing as Black.

The flip side of experience would be one Cal Ripken Jr. The Hall of Fame shortstop, who spent his entire career 40-something miles north in Baltimore, interviewed for the Nationals vacancy two years ago. To what extent he was a serious candidate, I’ve never been able to determine. He obviously brings credibility — just as Williams, hitter of 378 big league homers, did.

But bringing in Ripken would be doubling down on the Williams mistake. At least Williams had spent time in a major league dugout after his playing career. Ripken hasn’t. That one fact makes this the wrong place and time for the Iron Man.

Experience, though, can come in many forms. Bench coaches and minor league managers would carry some of the same questions with which Williams arrived, but tempered versions of them. And it sounds as though, while Rizzo understands his previous miscalculation, he’ll consider candidates from the last time around.

“Last time we brought in managing candidates with little or no managerial experience,” Rizzo said. “I think that we will have a greater pool of manager candidates this year, stemming from very experienced to limited experience.”

So, then, what about those who haven’t yet managed in the majors? A disclaimer: We would argue that serving as a bench coach — particularly a longtime bench coach under an established manager — and/or managing in the minor leagues over several seasons would give a candidate credentials the Nationals could accept. They could, rightly, argue that such a person is different than Williams, who served mostly as a third base coach and managed only five weeks in the minors.

Dave Martinez, who serves as the Cubs bench coach under Joe Maddon — and held the same position under Maddon in Tampa Bay — interviewed for the Washington job when it went to Williams. He impressed then, and his resume is only enhanced now because he has, in some way, helped Maddon pull the Cubs into the postseason during their first year in Chicago’s dugout.

With parts of 16 seasons in the majors as an outfielder and first baseman, Martinez brings the credibility of a player without the burden of being a star player. No, he hasn’t managed in the minors, but sitting at Maddon’s foot, seeing how he thinks, inherently means he has been exposed to the most creative, out-of-the-box theories — both about strategy and relating to players. In the modern game, there couldn’t be a better groomer.

Giants bench coach Ron Wotus would be intriguing as well, because not only has he seen Bruce Bochy expertly handle pitching staffs and personalities, but he managed in the minors for seven seasons. He understands the characteristics the 2010, ’12 and ’14 Giants — with lots of moving parts — shared, what it took to make them champions.

Martinez, of course, brings an interesting dynamic. The Nationals would essentially have to admit a major mistake and say, “We should have hired this guy two years ago.” But if they believe he is the right fit, they should own up to the gaffe. Williams’s dismissal, particularly after the club picked up his option for 2016, is already an admission of error. The franchise is still in good position to move forward — and reach the postseason in 2016 — so it shouldn’t let those optics get in the way.

In the clubhouse, all of this amounts to noise. There is one choice among longtime Nationals now, as there was when the club replaced Johnson two years ago. Randy Knorr has the deepest roots in the organization, predating its move to Washington, playing for the Expos. Since, he did whatever was asked, managing from Class A all the way to Class AAA, serving as the bullpen coach for the latter part of 2006 and again in 2009, then as bench coach for four seasons.

Knorr was let go Monday — along with Williams’s entire coaching staff. He interviewed for the big chair in the fall of 2013. Many saw him as the runner-up. Now, he could get another look.

“We have not ruled out Randy Knorr,” Rizzo said.

So that brings us to a list of checkpoints for which to watch as the search for Williams’s replacement begins: Will the Nationals reconsider candidates they rejected before? It appears likely. Could they value some continuity with the people who helped them grow from laughingstock to contender? Possibly. And what sort of resume will resonate, ultimately, for the man who becomes the Nationals’ seventh manager?

Welcome to the offseason.

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