EAST RUTHERFORD, N.J. — When the Giants (4-13) played the Washington Football Team (7-10) at MetLife Stadium on Sunday, both already having been eliminated from the N.F.L. playoffs, was it possible to find beauty and meaning — or, at least, warmth — in a game with so little at stake?

Pregame

Billy Price, the Giants center, tucked his cellphone into the padding around the goal post and started to stretch. On his headphones he listened to Def Leppard.

Other Giant linemen, with similar thigh-size triceps and waist-size thighs, stretched nearby. Korey Cunningham did so on his back while listening to gospel music. Steam rose from his head.

Above the empty MetLife Stadium stands, the sky was sludge-gray. The occasional plane slid overhead. For a moment it seemed that blue sky might break through the gray, but it did not. The punters, kickers and long snappers took to the field for their practice, then all the rest of the players. Fans filled the stadium (sort of). The game began.

First Quarter

The weather was bleak, and so was the Giants’ offense. Saquon Barkley, the star running back, kept getting stuffed. When he came to the sideline he wrapped himself in a blue cape. With all the Giants’ punting, that happened a lot. Cape on, cape off, cape on.

Second Quarter

Line judge Mark Stewart didn’t wear gloves (in the off-season he’s a rancher in Nebraska). He stared down the line of scrimmage, legs wide. Sometimes he shuffled sideways, sometimes he blew his whistle, or flipped the ball to the other game officials. His ears started to turn pink.

On the bench, the Giants’ offense huddled over tablet computers with their coaches. The bench was heated; rubber ducts shook and hummed behind it. The offense headed to the field, ran a couple of plays, punted, came back. Boos started to rain down. Rain started to rain down.

Halftime

Lunchtime! In Parking Lot G, sea gulls cleaned up after the tailgaters. Sometimes they took to the air and circled above the stadium (in Section 334 there may have been more birds than fans). Sea gulls are perfectly suited to Sunday’s weather, with feathers that keep the wet off, and efficient heat circulation. But enough about sea gulls! Back to the inaction on the field.

Third Quarter

The Giants quarterback was intercepted by the Washington safety, who returned the ball for a touchdown. Fans started making suggestions to the Giants, ones that can’t be printed here. Then the referee announced: “No. 79 is eligible.” He announced this again, and fans laughed. The eighth time he made the announcement, the crowd roared. It was the biggest cheer of the day:

A soggy day turned soggier. Dank, chilly. On the Washington sideline, fullback Alex Armah spun on a small stationary bike to keep his legs warm. Armah looked like a teenager on a tricycle. Then, quick, off the bike and back in the game.

Fourth Quarter

All day, Casey Kreiter had been perfect. Kreiter is the Giants’ long snapper, and one of the best in the N.F.L. In pregame he ran around the field with a kidlike smile on his face. During the game he was all business. Keeping his hands warm, peering back between his legs, zipping the ball with accuracy, then blocking. There’s a lot to be said for doing one thing well (as opposed to, say, the Giants’ general manager). His job done, he stood alone on the sideline.

The End

And then, with a sputter, the game was over. After one last Giants interception, the players from both teams gathered at midfield. While it was the end of a sorry season, there was real camaraderie here, and shared respect.

Kreiter, the long snapper, caught up with a Washington lineman. They played at Iowa together. As they gave each other thumping hugs, and headed back to their warm locker rooms, a lone piece of trash blew across the cold, hard turf.