General Manager Mike Rizzo, right, and Manager Matt Williams watch the Nationals together in spring training. (Jonathan Newton/The Washington Post)

The Washington Nationals’ 2015 season seesawed wildly for six months between head-shaking lows and historic highs. The penultimate day was a microcosm of the season: Before the first game of a doubleheader against the Mets, Manager Matt Williams, looking worn from a tumultuous week punctuated by a dugout fight, addressed questions about his murky future. Then, in the nightcap, Max Scherzer tossed his second no-hitter of the season, a moment he acknowledged as bittersweet given the team’s failure to make the playoffs.

What lies ahead after what General Manager Mike Rizzo called an “extremely disappointing” season is likely the most significant winter in the club’s 11-year history. Key players are likely to depart as free agents, leaving roster holes to fill, and the bullpen needs an overhaul as well. Chief among the areas to address, though, is Williams’s job status.

“The decisions we make this season are going to shape not only the 2016 season but beyond,” Rizzo said. “It’s going to be an exciting, busy, important offseason.”

Rizzo, who hand-picked Williams because of previous ties, has stood behind his manager amid criticism of his bullpen-handling and communication skills. But the Lerner family, keenly aware of the growing unrest, may have little choice but to part with Williams and start fresh, although Rizzo himself is believed to be safe.

Before Sunday’s game, Rizzo did not say whether Williams, who is under contract for 2016, would be back, instead offering a vague sign that changes are coming once the season is officially over.

“We’re going to make all the pertinent decisions: rosters, personnel from top to bottom,” he said. “We’ll have a decision down the road.”

Asked multiple times about Williams, Rizzo stuck to a variation of the same answer. But he made the timeline clear: The Nationals would charge ahead with the offseason plan starting on the 40-minute plane ride back to Washington from New York.

“We’re gonna be decisive and make decisions sooner rather than later about personnel both on the field, off the field and in the front office,” Rizzo said. “We’re not gonna let people twist in the wind. We want to make those decisions and move on and get moving to 2016.”

Rizzo said he has spoken with players about key personnel decisions, and ownership, which has been frustrated by the performances of Williams and his team, is very involved. “Baseball operations obviously is responsible for it, and ultimately I make the final choice,” Rizzo said.

Privately, Rizzo has told Williams he has been fighting for him, according to a person familiar with the situation. If Williams were to stay on, the coaching staff would undoubtedly be overhauled, but that would likely be the case under a new manager, too.

Williams and the other coaches haven’t always been on the same page. A prime example: Williams allowing closer Jonathan Papelbon to pitch after fighting star outfielder Bryce Harper. Two assistant coaches broke up the altercation, but neither informed the manager of the extent of the incident.

Washington Nationals owner Mark Lerner watches the final home game of the season. He’ll be heavily involved in any decision on Matt Williams. (Ricky Carioti/The Washington Post)

“I’m with [Rizzo] in that everything will be evaluated,” Williams said after Sunday’s finale. “So we’ll get home and evaluate everything.”

The roster will endure significant turnover this winter. None of the key free agents — Ian Desmond, Jordan Zimmermann, Denard Span and Doug Fister — are expected to return. All but Fister are expected to receive qualifying offers; all are expected to reject them. About $50 million from this year’s team-record $164 million payroll is likely to be cleared with the departure of about half a dozen free agents.

Under Rizzo, the Nationals have players poised to fill each of those voids: a potential combination of Yunel Escobar, Danny Espinosa and Trea Turner at shortstop; Tanner Roark and Joe Ross for the rotation, with prospects on the way; and Michael A. Taylor in center field. If oft-injured players such as 25-year-old Anthony Rendon and 31-year-old Ryan Zimmerman stay healthy, they could also pick up the slack.

“We’ve got a great young core of good, young players,” Rizzo said. “You look at the number of impactful players that we have that are under 25, 26 years old that we control for an extended period of time, it’s quite a group.”

The starting rotation, which underperformed, is expected to return ace Max Scherzer, Stephen Strasburg (who will be entering his free agent year), Gio Gonzalez and likely Ross and Roark. Prized prospect Lucas Giolito could also begin pushing toward the majors by midseason.

The bullpen will need the most work after relief undermined the team, especially in critical second-half games. Felipe Rivero, Blake Treinen and likely Craig Stammen, who should be ready for spring training after missing most of the season with forearm surgery, will make up part of next year’s relief corps. Drew Storen, who is eligible for free agency after 2016, might be needed next season but could benefit from a change of scenery.

The status of Jonathan Papelbon, who is owed $11 million next season, is the most uncertain. Could the Nationals really bring him back into the clubhouse after he attacked the best player on the team and the future of the franchise? Could the Nationals find a team to take him? Rizzo has a delicate issue to navigate.

“We’re gonna hopefully go about it and see what makes us better and makes us a team that clicks,” Harper said. “Rizzo does such a great job in the front office. . . . These guys might not be back here next year. The one thing we definitely need is another left-handed bat and hopefully a huge right-handed bat to hit behind me or in front of me. If we can do that, that would definitely help us out and put us up to the top.”

The outfield is set, although a proven backup beyond Matt den Dekker could be needed to help Werth, who will be 37 next May and played only 88 games this season. Catcher Wilson Ramos, under control for one more year, finally had a healthy season but struggled offensively, so the Nationals could upgrade there, too. Jose Lobaton, a little-used, defense-first back-up catcher, is under team control for two more years.

Another question is the exact composition of the infield. The Nationals need Zimmerman to stay healthy, but they found a good left-handed-hitting complement in 30-year-old rookie Clint Robinson. The Nationals want to return Rendon to third base, where his defense has best helped the team. So the Nationals could move Escobar, who is owed $7 million next season, to second base with proper coaching, return him to shortstop despite declining defensive skills or trade him after his finest offensive season. Espinosa, a superior defender who enjoyed a resurgence at the plate, could man the other middle-infield position until Turner gets more minor league seasoning.

Other, less obvious changes could be coming as well, and two minor front-office moves, in fact, were already made late last week. Bill Singer, one of the Nationals’ eight special assistants to the GM and a director of international scouting, was let go on Friday after nine years with the team, according to people familiar with the situation. Regular season advance scout Bob Johnson was also dismissed.

“We’ve got a lot of moving parts,” Rizzo said. “We’ve got a lot of free agents we need to decide upon. We need to decide upon how to get back into the championship conversation.

“Right now, we go into the offseason as being the team that is the chaser instead of being the chasee. We’re no longer the king of the National League East. We’re gonna chase down the Mets.”