Maybe it was the temperature — only in the upper 20s at game time. Or possibly Michigan’s anemic season.

Either way, the normally raucous scene that swirls around Ohio Stadium during the annual Ohio State-Michigan showdown seemed a bit subdued Saturday.

No. 10 Ohio State easily won the game 42-7.

‘‘It may be a factor that Michigan isn’t as competitive this year, but it’s also just cold as a beast,’’ said T-shirt vendor Richard Johnson of Miami.

Johnson said he normally makes about $1,500 on game day but would be lucky to clear $1,000 this time. He flies up from Florida each year to sell his T-shirts, only one of which could be described without the use of an expletive — ‘‘Beating Michigan.’’

The Buckeyes clinched a share of their fourth consecutive Big Ten title with the win. But Penn State’s 49-18 victory later Saturday over Michigan State means the Nittany Lions get the conference’s automatic Bowl Championship Series berth and are headed to the Rose Bowl in January.

Michigan’s woes this year — they are now 3-9 — appeared to be dampening enthusiasm for the game. They even lost to Toledo of the Mid-American Conference, sniffed Ohio State fan Andrew Frederick.

‘‘If it was going to be a tight game there’d be a lot more people out here, but they lost to Toledo,’’ said Frederick, 20, a junior at nearby Capital University. ‘‘How can you lose to a MAC team and have respect in the Big Ten?’’

Ohio State cautioned students about mistreating visiting Michigan fans — as the university does each year. But the warning seemed unnecessary, said at least one visiting Michigan student.

Meena Javuluri, a Michigan senior, stood out in the sea of scarlet and gray in her maize-and-blue scarf. But it all felt pretty tame.

‘‘It’s not been so bad this year, partly because I’m a girl and partly because our season hasn’t gone so well,’’ said Javuluri, 21, of St. Joseph, Mich.

But even before the game ended, police reported at least 41 arrests for alcohol-related crimes like underage drinking and open container violations.

Crowds at Hineygate, the overlapping and sometimes massive tailgating parties at businesses opposite the stadium, were reduced from years’ past.

That didn’t seem to spoil the experience of Rich Gerhardt of Columbus, who was enjoying the atmosphere outside the Varsity Club restaurant.

‘‘You drink enough, it doesn’t matter,’’ the 38-year-old Gerhardt observed. ‘‘It’s the biggest party of the year.’’

Still, it’s not like the parking lots and streets around campus were empty.

Scarlet-clad Buckeye students and fans still swarmed the neighborhoods around Ohio Stadium on Saturday, aware that anything can happen in an end-of-season game.

Buckeye fans braved frigid temperatures to tailgate early Saturday morning as temperatures hovered in the mid-teens in the Columbus area.

Police patrolled sidewalks and streets to head off a possible repeat of 2002, when fans rioted after Ohio State beat Michigan en route to the national championship.

Fans were much more subdued than in years past, with the stepped-up police presence and efforts at crowd control making a noticeable difference, jewelry vendor Dan Poel said.

‘‘I used to have guys try to grab my jewelry and run,’’ Poel said of his Buckeye-themed necklaces and bracelets. ‘‘Now, we feel a lot more safe doing business.’’