Michigan is 58-51-6 vs Ohio State all-time.
Two things:
First, if this is what you mean by "win more than they lose" then it isn't quite as unreasonable as I was thinking. 58-51-6 is technically a winning record but the difference is roughly one game in 15 years. We've been talking here about 10 year timeframes and frankly coaching decisions are made on even shorter timeframes. If you were thinking that the expectation should be 6-4 in 10 years or 3-2 in five years, that is a much higher bar. Ignoring the ties because those are not possible anymore, this works out to roughly 8-7 in favor of Michigan every 15 years.
Technically that meets the definition of your stated expectation but if these had been evenly distributed (they weren't, more on that later) it would never have "felt like" Michigan was more than marginally better than tOSU as a program because we are only talking about a very slim advantage. On a ten year basis this works out to just over 5 wins for Michigan and just under 5 wins for Ohio State.
Second, all of Michigan's advantage was accumulated by guys who wore leather helmets or no helmets at all. That isn't an exaggeration, it is actually an understatement. Michigan has a seven game advantage today at 58-51-6. They first achieved a seven game advantage with their 6-0 win on October 20, 1906 which moved their all-time record against Ohio State up to 7-0-1. In the more than 110 years since then the series is even at 51-51-5.
- Michigan's advantage grew to 13 games at 13-0-2 in 1918 before Ohio State achieved their first victory in the series. Since then Ohio State leads 51-45-4
- Michigan's advantage grew to 16 games at 19-3-2 in 1927. Since then Ohio State leads 48-39-4.
To put this another way, according to the Census bureau there were approximately 331.5 million people living in the US as of 2020. Thelma Sutcliffe of Nebraska was born October 1, 1906 and is still living today. She is the ONLY living American in whose lifetime the Wolverines have a winning record against the Buckeyes. Their win on October 20, 1906 when she was just 20 days old is one of 52 for Michigan in her lifetime compared to 51 for Ohio State.
In more relevant time-periods:
- Ohio State leads 8-0 since 2012 when current recruits were roughly 10 years old.
- Ohio State leads 14-1 since 2004, roughly when current recruits were born.
- Ohio State leads 16-2 since firing Cooper after the 2000 loss.
- Ohio State leads 18-10-1 since Bo retired.
- Ohio State leads 25-19-2 since man last walked on the moon.
- Ohio State leads 24-19-1 since the Edmund Fitzgerald sank.
- Ohio State leads 23-16-1 since Woody was fired.
- Ohio State leads 27-21-2 since Bo was hired.
- Ohio State leads 27-21-2 since man first walked on the moon.
- Ohio State leads 31-23-2 since JFK was shot in Dallas.
- Ohio State leads 39-27-2 since Woody was hired.
- Ohio State leads 39-32-3 since the end of WWII.
- Ohio State leads 41-33-3 since 1942, the season of tOSU's first NC.
- Ohio State leads 41-33-3 since the Germans bombed Pearl Harbor.
- Ohio State leads 41-35-4 since the first TV broadcast of a CFB game.
- Ohio State leads 46-39-4 since the stock market crash of 1929 that precipitated the Great Depression.
- Ohio State leads 48-45-4 in the last 100 years.
- Ohio State leads 51-46-4 in conference games.
- Ohio State leads 51-46-4 since the Armistice that ended WWI.
- Ohio State leads 51-47-4 since the Titanic sank.
- Ohio State leads 51-50-5 since the Model T was introduced.