Giants head coach Pat Shurmur looks on during a game against...

Giants head coach Pat Shurmur looks on during a game against the Eagles at MetLife Stadium on Sunday. Credit: Jim McIsaac

The Giants made news Monday with whom they canned . . . and whom they kept.

The team fired head coach Pat Shurmur, a move that became almost unavoidable after they won four games this season and nine in his two-year tenure with the organization. Co-owner John Mara called it a “gut instinct” to part ways with Shurmur, saying he felt the team should have won more games than it did and needed a new direction.

Based on the results, it’s hard to argue with that thinking. But the Giants stopped their semi-purge with Shurmur and retained Dave Gettleman as general manager, even though the two have identical records in their roles with the team and it was Gettleman who hired Shurmur in the first place.

“We want to give him a chance to finish what he has started,” Mara said of Gettleman, pointing to what he sees as significant upgrades in scouting, grading prospects and the use of analytics. “We believe it would be a mistake to pull the plug on that after two years .  .  . It’s not business as usual here with the Giants. We made a lot of changes, changes you don’t necessarily know about, and we felt like we needed to give it a chance to see if it’s going to succeed or not.”

Gettleman will address the media on Tuesday for the first time since the start of training camp.

Though he kept his job, he hardly got a pat on the back from ownership. Mara said he wants to see results. He noted that Gettleman needs to improve his “batting average” on free-agent signings.

“We need to win more games,” Mara said. “Dave knows that, and that’s going to be the challenge.”

Added co-owner Steve Tisch: “It’s been a very frustrating four years. Certainly the record indicates that. Those numbers don’t lie. And John and I want to make sure that those numbers change in the next season dramatically.”

While Gettleman is remaining as general manager, the job description for that position might change.

For decades, the Giants have had a power dynamic that gives the GM authority over the roster and the head coach the call for on-field matters. To lure a top head coach, Mara said he would consider adjusting that long-standing format.

“I’m always willing to look at whatever is going to improve the team,” he said. “If I thought there was somebody coming in here as a head coach who wanted a different role, if he could convince Steve and I that would make sense for our organization, we would certainly consider that.”

Mara also conceded that it is a “risk” to hire a new head coach this year and possibly have to fire the GM next year if Gettleman does not rise to the standards set by ownership.

“That’s certainly something we are aware of, but I happen to believe in Dave,” Mara said. “I happen to believe in the changes that he’s making here, and I think those are going to pay off.”

The Giants began the process of replacing Shurmur shortly after they announced his departure, with Mara and Gettleman leading the search.

They reached out to the Patriots to request permission to speak with offensive coordinator Josh McDaniels and to the Chiefs to speak with offensive coordinator Eric Bieniemy. Mara said he also will consider college coaches, with Baylor’s Matt Rhule considered a top prospect.

Shurmur was allowed to address the team on Monday morning and told them of the decision regarding his job.

Running back Saquon Barkley said it was “very hard” to hear the news.

“That’s your coach,” he said. “He’s one of the guys that believed in me, believed in DJ [Daniel Jones], for us to get here and live our dreams of playing in the NFL. You don’t want to see anybody go out like that.”

“It’s a tough deal, but everyone is responsible,” Jones said. “The players are very, very largely responsible for how this season has gone. I certainly feel responsible, and I think that’s the tough part. That’s the way we should feel.”

For Barkley and Jones, this will be their first coaching change. Their personal developments almost certainly will be one of the main topics discussed with candidates.

For others, this will be their second coaching search. Wide receiver Sterling Shepard was here under Ben McAdoo and Shurmur.

“Change is not always a bad thing,” Shepard said.

Now we’ll see if the Giants have employed enough of it.

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