It’s November 2016. Michigan Coach Jim Harbaugh is holding his hands a foot apart after that day’s game in Columbus, Ohio.

“That short,” Harbaugh said. By that much, he argued, Ohio State quarterback J. T. Barrett was short of a first down when he rushed on fourth-and-1 in the second overtime. The referees had ruled it a first down, though, and the No. 2 Buckeyes won on the next play, 30-27, holding off the No. 3 Wolverines — again.

Saturday’s game will also serve as a referendum on the tenures of Harbaugh, the former Wolverines quarterback who in his fourth season has yet to fulfill his big promises, and Ohio State’s Urban Meyer, who was suspended for the first three games of this season and has lately appeared to show symptoms of stress on the sideline.

On Saturday, in Columbus, the teams will meet for the 114th time. The stakes are again high: A victory would send either No. 4 Michigan (10-1) or No. 10 Ohio State (10-1) to the Big Ten championship game, where a win over No. 20 Northwestern (7-4) could mean a College Football Playoff spot.

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Plus, it is Ohio State-Michigan, one of sports’ greatest rivalries — at least it’s supposed to be. Ohio State has won 13 of the last 14 games.

“I never want to downplay what winning is against any individual opponent,” said Charles Woodson, a former Michigan cornerback and Heisman Trophy winner. “But there’s really only one game on the schedule, and that’s Ohio State.”

So over the course of this rivalry, which originated in the 19th century, who has been better?

This is not quite a debate over which university has had the better program over all. Nor can this be the simple question of who has won more games in the series (Michigan) or during the last 10 or 20 years (Ohio State, in a wipeout). Rivalries are about more than that: They’re about identity and pride and expectations and broad historical sweep.

Image Ohio State Coach Urban Meyer has had a stressful season. It began with his suspension and has continued with his team’s lackluster performances, like last weekend’s overtime win over Maryland. Credit... Nick Wass/Associated Press

This rivalry is college football’s Yankees-Red Sox. Michigan is the Yankees, the front-runners who have monuments to their great players and a history of domination that they will not let you forget. Ohio State is the Boston Red Sox, who have four World Series titles in this century but a boulder-size chip forever in place on their proverbial shoulder.

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“Every year is its own chapter, but the story doesn’t really change,” said Ramzy Nasrallah, executive editor of the Ohio State site Eleven Warriors. “The story is that Ohio State’s aspiration is to be Michigan.”

U.S. News & World Report ranks Michigan as the fourth-best public university in the country. Ohio State is 17th.

John U. Bacon, who has written several books about Wolverines football, has his own way of making a similar point. “Almost everything Ohio State does — academically, athletically, or otherwise — they compare to Michigan,” he said. “Michigan almost never does that.”

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But, Bacon added, noting the 21st-century slump Michigan has endured, “Michigan needs to hold up its end of the deal to keep it a rivalry.”

Scoreboard

It’s 1902. Ohio State has just lost to Michigan, 86-0. It is the most extreme version of how the rivalry went in its first years. Michigan had a varsity football team before Ohio State did. For roughly the first quarter of the 20th century, Michigan’s coach was the brilliant Fielding Yost. Ohio State scored no points until the sixth game of the series, in 1904, and did not win until the 16th, in 1919.

Those early years enabled the Wolverines to build an insurmountable lead (so far) in the overall series, in which Michigan is in front, 58-49, with six ties.

“If we go to the record, Michigan’s ahead by nine,” said Glenn Schembechler III, who is the son of the beloved former Michigan coach Bo Schembechler and who co-hosts a podcast about the rivalry.

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Image Jim Harbaugh has a stingy defense but also a good quarterback in Shea Patterson. Credit... Tony Ding/Associated Press

But if you date the rivalry to 1918, when it became an annual affair as part of Big Ten play, Ohio State leads, 49-46, with four ties.

Then again, Michigan won more games in every decade until the 1960s, and did so again in the ’80s and the ’90s.

If you had to decide whom to root for, knowing you would be dropped into the rivalry at some unknown point in time, you could argue that Michigan is the wiser choice, though the trend line does not point that way.

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‘A Brutal Century’

It’s November 2006. Michigan is having its best season in a decade, and enters Columbus ranked No. 2. But Ohio State is No. 1. The game is close, but quarterback Troy Smith, who is from Cleveland and will go on to hoist the Heisman Trophy, leads the Buckeyes to a 42-39 win, clinching a trip to the national title game.

If Harbaugh’s patience for a slim margin of defeat seemed thin in 2016, that might be because in recent years the rivalry has been decidedly lopsided.

Ohio State has won the last six games and 15 of the last 17. Over that period, the Buckeyes claimed two national titles and qualified for three more national playoffs, while the Wolverines split one Big Ten title.

“It has been a brutal century for Michigan,” Bacon said.

What happened? The last time Michigan was as good as Ohio State is all the time now offers a hint. It was 1997. Michigan again entered undefeated — and won, 20-14, on the way to its only national title since the 1940s. Woodson caught a long pass on a Michigan scoring drive and returned a punt for a touchdown. A cornerback, he became the only primarily defensive player to win the Heisman.

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But Woodson is from Ohio. So is Michigan’s previous Heisman winner, Desmond Howard. So were Michigan tight end Jim Mandich and Michigan safety Tom Curtis, and Schembechler, who before coaching Michigan had been an assistant to the forever worshiped Woody Hayes. At Ohio State.

Image For 10 years, Woody Hayes’s Buckeyes and Bo Schembechler’s Wolverines reigned over the Big Ten and captivated the country. Credit... Associated Press

It’s highly likely that Michigan’s current woes trace back to its diminished ability to recruit effectively over the southern border in Ohio. The turn occurred after Ohio State hired Jim Tressel, an Ohio native and longtime Youngstown State head coach, before the 2001 season.

“We studied their success,” Tressel said in an interview. “A lot of their success, in the ’80s as well, was they got a lot of great Ohio players.”

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In an alternate universe, maybe Troy Smith would have been Michigan’s quarterback in the 2006 game.

Higher Highs

It’s November 1968. Under Hayes, Ohio State has won three national championships and, undefeated, has a chance at another one if it can get past No. 4 Michigan in Columbus.

Michigan strikes first, and Ohio State leads by just 7 points at the half. But by the end of the game, the Buckeyes are blowing the Wolverines away. Ahead, 50-14, in the closing minutes, Hayes elects to go for a 2-point conversion (which fails). Asked why afterward, Hayes said, “Because they wouldn’t let me go for 3.”

By the end of his 28 seasons, Hayes (16-11-1) had joined Yost (16-3-1) as the coaches in the rivalry with the most wins.

Since the rivalry has been competitive, Ohio State, not Michigan, has had the more sustained highs. At one point, Hayes went 11-4. Last decade, Tressel went 9-1. Meyer is 6-0. Even Yost lost a few.

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The Victors Are the Spoilers

It’s November 1969. The Buckeyes, defending national champions, are still ranked No. 1, with a 22-game win streak. Victory in Ann Arbor will effectively clinch another national title. Michigan, meanwhile, is 7-2 in its first season under Schembechler. Oddsmakers set the line at 17 points for Ohio State. Michigan takes a 24-12 lead in the first half and shuts out the Buckeyes in the second to win.

For a program that styles itself as college football’s ultimate winner — with the most victories ever, 953, and a fight song called “The Victors” — Michigan has actually been the underdog on quite a few prominent occasions. And gone on to win anyway.

Image Michigan shut out Ohio State in Ann Arbor on Oct. 21, 1933. Credit... Associated Press

In 1939, unranked Michigan took down the Buckeyes by a touchdown during their best season to date.

In 1956, at the height of Hayes’s powers, unranked Michigan shut out the No. 12 Buckeyes, 12-0.

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In 1995 and 1996, Ohio State entered the game ranked No. 2 — and lost. The 1995 team, which entered the game 11-0, had stars like Terry Glenn and Mike Vrabel and a future Heisman winner in Eddie George. Michigan countered by handing the ball to running back Tim Biakabutuka 37 times for 313 yards.

Lloyd Carr, whose first of 12 seasons as Michigan’s coach came in 1995, said in an interview, “If you’re a big underdog, no matter which school you’re from, the idea that the odds — ‘this team is 17 points better’ — we all tell our teams, it doesn’t matter.”

On more prominent occasions, that has more often been true of the Wolverines.

Gold Pants

It’s October 1933. Michigan has shut out Ohio State for a second consecutive year, prompting Ohio State to fire its coach, Sam Willaman, despite five winning seasons. A few months later, it hires Francis Schmidt. Asked how he intends to defeat Michigan, Schmidt replies with what at the time was more of a novelty than a cliché: Michigan’s players, he says, put their pants on one leg at a time, same as Ohio State’s do.

Then Ohio State beats Michigan — the first of four straight shutouts. A local businessman is inspired to give little charms, gold pants, to the players. To this day, Ohio State’s players still get the charms if they beat Michigan, though under N.C.A.A. rules they now cannot be made of gold.

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Matt Finkes, a former Buckeyes offensive lineman who runs the organization that provides the gold pants, recalled addressing the team a couple years ago.

“I tried to explain to them, this doesn’t always happen,” he said to players who had three or four pants apiece.

There is no equivalent to the gold pants for Michigan players. Although given Ohio State’s winning record since they were introduced, perhaps there should be.

Image A pair of the famous pants that the Ohio State team members receive if they beat rival Michigan, though they are no longer gold, per N.C.A.A. rules. Credit... Fred Squillante/Columbus Dispatch, via Associated Press

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“Michigan does not want to be Ohio State,” Nasrallah, the Eleven Warriors editor, said, “because Michigan wants to be Michigan and still beat Ohio State.”

Back to the Future

It’s 2018. Michigan has college football’s stingiest defense and, for the first time under Harbaugh, a really good quarterback in the Mississippi transfer Shea Patterson. He has thrown 18 touchdowns and just four interceptions. Another good omen: Patterson was born in Toledo.

Ohio State quarterback Dwayne Haskins has been at least as good — the Buckeyes are averaging the most points per game in the Big Ten. But in recent weeks, hobbled by a leaky defense, the team has performed only fairly against inferior competition — beating Nebraska by 5 and Maryland, in overtime, by 1; and losing, 49-20, to Purdue, which is 4-3.

It is enough to make you think the Wolverines, the favorites by a slight margin, might win.

The Ohio State inferiority complex is as undeniable as it is unjustified. Even more than the Red Sox and the Yankees, the Buckeyes are the ancient Romans to Michigan’s ancient Greece — victors valiant, if you will, who superseded the civilization they conquered by imitating it.

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But college football’s future is murky. As the recent struggles of Texas, Florida, Nebraska and other blue bloods indicate, we may be departing an era in which pedigree and local recruiting matter most, and entering one in which superior management wins out, as with professional franchises. Who can tell which athletics program will excel in such a context?

The Wolverines’ sense of superiority can be off-putting. But it is grounded in history. And if they have frequently failed to live up to it, they have pleasantly surprised enough times to compensate.

It is likely that we are witnessing not Michigan’s rejuvenation but rather the latest stage of the elegantly managed decline of a great empire. Which, to be honest, seems rather in tune with the times.

Who has it better than Michigan? For now, no one. For how long? Maybe not very long at all.

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