It has become a rite of winter for the Giants: playing games at the start of a new year, at the end of an old, rotten season. There is a strong sense of finality, manifesting itself in very different ways depending on whether you are on the inside or the outside. 

There is a good-riddance vibe from fans who want out with the present and in with the new. There is hope for at least some continuity within the locker room from players who do not want to be cast aside. There is evidence — often sketchy — shared by the head coach that the situation is not as grim as the win-loss record reveals it to be and what is being built takes time. 

That the Giants (4-12) face Washington (6-10) on Sunday at MetLife Stadium will soon be a footnote to what happens next. Rain is expected and a damp chill is guaranteed, with those bothering to brave the elements and show up doing so to voice their displeasure about the Giants’ sad state of affairs. 

This will be the last game in a Giants uniform for many players, because who wants to keep together a roster proven to be lacking? This will be the last game for Dave Gettleman as the general manager, as his four-year stay, wholly unsuccessful, comes to an end, presumably on Monday. 

The main question: Will this be the last game for Joe Judge? The arrow seemed to be pointing upward when, as a 39-year-old rookie head coach, his team went 5-3 in the second half of the 2020 season to finish 6-10. The arrow is unquestionably all bent and tilted after a terrible second act for Judge, who is nearing the end of a dismal season devoid of much of the fight and competitiveness the Giants showed in his first year. 

There are no compelling reasons to keep Judge, who signed a five-year contract, other than the idea of giving him one more year because jettisoning him now would go against the promise co-owner John Mara made Jan. 8, 2020, the day Judge was introduced as the 19th head coach in franchise history. 

“It’s up to us to show a little more patience with this coach than perhaps we have over the last few years because he is a first-time head coach,’’ Mara said, cognizant that he and co-owner Steve Tisch fired Ben McAdoo 12 games into his second year and Pat Shurmur after two seasons. 

Keeping Judge would make good on the “little more patience’’ Mara said must happen. Has the season deteriorated so badly and Judge’s hold on his job slipped so clearly that Mara has reason to go back on his word? The Giants have been outscored 141-49 in their five-game losing streak, and Judge did not handle himself with much composure after last week’s 29-3 loss in Chicago, going off on an 11-minute rant to answer one single question: Why should fans believe he is the guy to turn this franchise around? 

“Everybody — the team, fans, all of New York — is obviously upset about how the season played out,’’ defensive lineman Leonard Williams said. “It’s easy to find the good things in a winning year, but it’s like in a down year like this, you get to find what is working for you. I think what’s working for the team is knowing that we have a lot of guys that are willing to fight all the way to the end — whether that’s the end of the game, end of the half, end of the season or whatever it is. I think having a lot of guys like that creates a good culture around.’’ 

It is debatable whether the Giants are fighting all the way to the end. On defense, a case can be made that they are. On offense, the production has been so feeble that it must be more a function of inferior talent and inadequate coaching and system, more so a lack of effort. 

“We’re trying to win games,’’ said safety Xavier McKinney, a bright spot in a dark season. “I think that’s the main goal. Nobody is trying to get anybody fired, nobody is trying to help anybody keep a job. We’re all just trying to win games at the end of the day. I think as players and as coaches, we know that, the coaches, they know that.’’