EAST RUTHERFORD, N.J. — Given that the opponent was the New Orleans Saints, and the game was at home, on a crystalline autumn night, you can forgive the optimistic Giants fan for thinking this might be the Sunday to end what looks more and more like the N.F.L.’s most improbable streak.
For more than two years, the Giants have watched bitterly as teams like the Saints have put up eye-popping offensive statistics weekly, regularly surpassing — if not averaging — a threshold that has remained out of their own reach since Jan. 3, 2016: 30 points.
But the Saints defense was allowing an average of 34.3 points in its first three games, so the potential for another downfield shootout seemed reasonable on Sunday. Instead, with 6 minutes 47 seconds left at a lifeless MetLife Stadium, the Giants had barely reached double figures and trailed by two scores.
Despite some late energy that helped cut the New Orleans lead to 8 points with less than four minutes remaining, the Giants took their third loss of the season, 33-18, in humbling fashion, as Saints fans chanted “Who dat?” while the teams played out the final moments.
It was a gloomy end to a week that had started with the Giants buoyed by the simple fact that they were no longer winless.
“The water tastes sweeter, the air breathes cleaner,” Coach Pat Shurmur had said this week.
At least, they had ensured that history would not repeat, after going 0-5 to begin last season. What they could not avoid were the reminders of the offensive futility under the former coach Ben McAdoo, who, like Shurmur, arrived as a promising offensive coordinator.
And Shurmur, like McAdoo, might have a hard time pinpointing exactly what is holding the team back. There are flashes of its overpowering potential. The Giants scored a touchdown on their opening drive and mustered another impressive scoring drive late in the fourth quarter that narrowed the deficit to 26-18.
But on third-and-8 from the Saints’ 36, with 2:30 remaining, a pass-interference call on Giants cornerback Donte Deayon gave New Orleans (3-1) a backbreaking first down. Three plays later, Alvin Kamara broke through for a 49-yard scoring run, his third touchdown of the day, to seal the game.
Giants quarterback Eli Manning threw for 255 yards and no interceptions, Saquon Barkley rushed for a touchdown, and Sterling Shepard caught all 10 passes thrown his way. But Odell Beckham Jr. (seven catches for 60 yards) was conspicuously quiet for most of the game, and even left the field shortly before halftime to receive fluids intravenously, the team said.
It had been a strange first half, which hinged on a couple of referee reviews — both of which went against the Giants.
In the first one, Giants cornerback Janoris Jenkins had been flagged for a horse-collar tackling penalty on Kamara, even though replays appeared to show that Jenkins’s grip was on the shoulder, not the back of the neck. The call stood, however, costing the Giants 15 yards.
Later in the second quarter, Giants receiver Russell Shepard lost a fumble that was recovered and returned by the Saints’ Marshon Lattimore to the red zone. That play was also reviewed, confirming the fumble. The only reason Lattimore’s 37-yard return did not go for more was because of some extraordinary hustle by Manning, not known for his wheels, who shoved Lattimore out of bounds at the 11.
The Saints did not convert either of those plays into a touchdown. In fact, the Giants limited the league’s fourth-highest-scoring offense to four field goals on their first four trips to the red zone, and just one conversion on their first eight third downs.
Nonetheless, they went into the half trailing, 12-7, having scored only on their opening possession.
On that drive, Manning connected on six of his first seven passes. Barkley did what he usually does: make people miss. Tight end Rhett Ellison, filling in for the injured Evan Engram, found holes in the middle of the defense.
The 75-yard drive ended with a 2-yard touchdown pass to Sterling Shepard, and the offense appeared to be on its way to a breakthrough, as arbitrary as it might seem. The 30-point threshold should not matter as long as the Giants wind up with a win, which is what they had done in a 27-22 victory over Houston the week before.
This time, though, 30 points loomed overhead like an unbreakable ceiling.