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The officiating crew led by Brad Rogers that worked Sunday's Vikings-49ers game at Levi's Stadium has called offensive holding at roughly the median rate for an NFL crew this season. According to NFLPenalties.com, Rogers' crew has called holding an average of 2.82 times per game, good for seventh most among 17 officiating crews.

Rogers' crew called three holding penalties Sunday: two on 49ers guard Laken Tomlinson and one on Vikings guard Oli Udoh. After the Vikings' 34-26 loss, though, coach Mike Zimmer said he'd spent much of the day talking to officials about how they should have called it more on the 49ers.

"I mean, these guys hold all the time," Zimmer said. "So they're grabbing us around the waist, grabbing our backs. The officials, they don't want to call it on every play, but until they start calling it on every play, they're not gonna stop doing it."

A year ago, NFL officials called holding an average of only 1.8 times per game — easily the lowest rate since the league moved the umpire from behind the defensive line to behind the offensive line in 2010.

But after the league emphasized a more balanced approach to holding during the offseason, the penalty was called 2.58 times per game during the first 11 weeks of the season, or roughly in line with the rate it's been called since the umpire positioning switch. And while no team has been called for holding more frequently than the Vikings (an average of 2.18 times per game), only five have benefited from more holding calls.

According to NFLPenalties.com, the Vikings have been the beneficiary of 1.64 holding calls per game, tied with Pittsburgh for the sixth-highest rate in the league. And when on the road, no team has benefited from more holding calls than the Vikings, who've drawn an average of 2.83 holding flags on opponents per game.

That might be due in part to a pass rush that's pressured opposing quarterbacks at one of the league's highest rates this season. But of the top 10 teams in pressure rates this season, only two (the Vikings and Bills) are among the league leaders in holding calls drawn against opponents. (The 49ers, for what it's worth, have seen holding called against opponents only 0.91 times per game, tied with Tampa Bay for the fifth-lowest average in the league. They've been called for it 1.27 times per game, which puts them 16th in the league.)

So what's the explanation? Holding, as is often said, happens more frequently than officials are likely to call it; they're inclined to throw flags for fouls that have a significant impact on a play. And while the NFL wants well-officiated games, there's also a balance between adjudicating every play and bogging down the game with calls that increase stoppages and have an adverse effect on scoring.

The Vikings might have had a case for one key hold that was missed early in the game: Zimmer grabbed his tablet during a TV timeout and walked a couple of yards onto the field to talk with down judge Kent Payne after Deebo Samuel's 20-yard touchdown run, where the Vikings wanted a penalty on George Kittle for holding Eric Kendricks as the linebacker tried to set the edge on Samuel's outside run.

Kendricks remained diplomatic about the officiating. "Shoot, it was a physical game [Sunday]," he said. "You know, refs let us play. Hats off to them, I respect them. [The 49ers] came with it and we knew their run game was really good."

Did he think Kittle should have been called for holding on the Samuel TD? "Refs let us play all day. So it is what it is," Kendricks said.

The 49ers ran for 208 yards on Sunday, and their success on the ground helped swing a game where quarterback Jimmy Garoppolo was shaky early. San Francisco held the ball for 37:07, and let the Vikings hold it for only 10:44 in the second half. Zimmer made his case for penalties he believed should have been called after a game where the 49ers might not have been able to win without an efficient ground game.

But holding calls, overall, are being made with relatively normal frequency after a dearth of penalties last year. On balance this season, those calls have hurt the Vikings more when they've gone against their own linemen than by how rarely they've gone against opponents.

TWO PLAYERS WHO STOOD OUT

Kene Nwangwu: He became the first NFL player since Cordarrelle Patterson in 2015 to return two kickoffs for touchdowns in the same year — and Nwangwu has only needed eight returns to do it. He showed his elite speed on his 99-yard TD, and got his first touch as a running back after Dalvin Cook left because of a dislocated shoulder. With Cook set for a MRI and possibly in line to miss time, Nwangwu could have a bigger role on offense; he's flashed the athletic ability to make that a tantalizing prospect.

Adam Thielen: The Vikings offense has taken off with Justin Jefferson playing a bigger role in recent weeks, but Thielen delivered a day full of reminders why he remains such a complete receiver. His first touchdown catch was Cris Carter stuff — Thielen caught Kirk Cousins' pass in traffic and tapped his feet in the back of the end zone — and the receiver made a terrific adjustment to catch a back-shoulder throw away from safety Talanoa Hufanga for his second touchdown after Jefferson's shallow crossing route left the 49ers out of position. Thielen would have had an even bigger day if officials had ruled he made a fingertip catch while working back for the ball in the fourth quarter, but the Vikings lost a challenge when a review could not find conclusive evidence Thielen kept the ball from hitting the ground.

TWO AREAS OF CONCERN

Right guard: Udoh had the Vikings' only holding penalty on Sunday — his 10th of the season — and he had a rough day in pass protection on a day where the Vikings offensive line played fairly well overall. The Vikings gave Udoh the right guard job over veteran Dakota Dozier in training camp, but his struggles this season raise the question of whether he remains in the lineup because coaches are confident he'll turn things around, or because they don't feel any better about their other options. They again played Mason Cole over 2019 first-round pick Garrett Bradbury on Sunday, indicating they're not afraid to make changes, but they've shown no indication of putting third-round pick Wyatt Davis on the field after an injury-filled and underwhelming preseason. The Vikings could put Bradbury at guard, where he played in college, but they put Udoh at the spot in part because they wanted to get bigger along the offensive line. The Vikings might need to ride it out with Udoh and hope the third-year player — who converted from defensive line in college and shifted from tackle to guard — still has room to improve.

Clock management: Cousins angrily walked off the field at the end of the first half when he threw a pass out of bounds as time expired; the Vikings were trying to get into field-goal range with five seconds left in the half, and the quarterback was looking toward Jefferson before linebacker Fred Warner clipped Jefferson's heels while dropping into coverage and the receiver fell down. The bigger issue was the drive where the Vikings were trying to tie the game in the fourth quarter; they thought they had a good case on their challenge of Thielen's catch, but the fact Cousins mistakenly lined up under Udoh, not Cole, required them to burn a second timeout on the same drive. It's why, after the Vikings' last drive was stopped at the 49ers 38 when Cousins threw incomplete for Jefferson on fourth down, they had no recourse to try and get the ball back one more time.

ONE BIG QUESTION

A playoff spot is still right in front of the Vikings. Do they have enough left to grab it? Even after Sunday's loss, the Vikings woke up Monday in possession of the seventh and final playoff spot in the diluted NFC wild-card race. Washington would technically move ahead of the Vikings with a win over Seattle on Monday night, but the Vikings would be tied with three teams at 5-6, heading into a stretch of the schedule that looks easier than the one they just finished. They'll play at winless Detroit on Sunday, before facing a flagging Steelers team a week from Thursday and getting a mini-bye before the first of two games against the Bears. The Rams — the Vikings' Dec. 26 opponent — have lost three consecutive, and the Vikings have won two in a row against the Packers, whom they'll play on Jan. 2.

That's the good news. The bad news is a mounting list of defensive absences (Anthony Barr left with a hamstring injury on Sunday, and Dalvin Tomlinson would need to return from the COVID-19 list to play against the Lions), and the fact Cook's status is in question after his shoulder injury on Sunday. The Vikings have run for a combined 260 yards in their past three games, and 105 of those came on three carries for Cook in Baltimore. They're counting on their line to hold up, Cousins to play accurate and turnover-free football (he did neither on Sunday) and their defense to overcome the loss of up to five starters.

Winning four of their final six could get them in at 9-8, so beating the Lions, Steelers and the Bears twice might be enough for the Vikings to return to the postseason. But it's becoming clear just how thin a margin for error they have to get there.