Wouldn't mind seeing results against the spread (ATS). Thanks for the OP.

Thanks OP this is a neat analysis. one thing to note - the better we are, the more often we are going to be a favorite. One  thing I remember regularly with Hoke and Rod was finding ourselves in dogfights with the likes of UConn, UMass, and Toledo - yes, we won 2 of those, so I'm sure it will appear as winning as a favorite. But the only time I remember something similar with Harbaugh was Army in 2019. (Also - losing to MSU was almost guaranteed under those 2, and it was rarely close - 2009 I think was the only close one)

Here's a real solid take: "Michigan is rarely an underdog, but when we are, it's a a guaranteed loss." 

Gee, confirmation of the obvious, rationalization of regression to the mean, acknowledgment that what we expect, frequently occurs when our perception is based on accurate understanding of clear win-loss opportunity.

The argument you are trying to make only emphasizes the fact that fans of every successful program expect to win more often than not, usually and virtually always when favored. This often happens whether we are paying attention to the details of probability or not especially in cases where fear of losing outweighs the expectation or unlikelihood of winning.

In 1969, there was scant chance that Michigan would beat Ohio State in a year when most football pundits considered the Buckeyes talented enough to play in the NFL. And yet, we won, cementing Bo Schembechler's career at Michigan. It was the greatest upset win in program history until another gateway win over the Buckeyes in 1997, the greatest win for me in my Michigan fandom. We subsequently won the Rose Bowl and a divided national championship.

The point is, it's glorious to win when you absolutely, positively shouldn't. It's fantastic when you pull the ultmate upset. But when you are favored most of the time, then achieve success on that level as a pedestrian response to expectation, it's only revealing when you don't win with attitude against that perception. Times change, things change, outcomes change, the world moves on from your past worldview. Evolve. Adapt. We are, deal with it. 

Thanks for doing this.   As others have pointed out, being a clear favorite in almost 2/3 of your games is not a given.   We like to think that anyone we would reasonably hire could get us to that point, but there is plenty of evidence both at Michigan and other schools that is not a given.

The MSU lost sucked, but I would argue that We are much closer to 201516 Harbaugh than we are to Harbaugh 2017 to 2020 Harbaugh.  2015 and 2016 Harbaugh was never a clear underdog.   Get to that point on a consistent basis and you solve the problem of never losing when you are a clear underdog.
 
Time will tell, but on the defensive side of the ball, I think Macdonald will improve.   I have much less confidence in Gattis, but I also think he is likely to move on after this season.  It is very clear that Harbaugh has taken away some of his responsibility and I can’t believe he is happy.

Well FYI its been true for 40 years.  Spreads are always higher for Michigan.. Mainly because we have a huge fanbase who bets stupidly.

The goal of the spread is to have equal amounts on each team.  It's not entirely predictive, nor is it the goal

Its just like the Yankees.  

Since you asked in the OP, The Prediction Tracker has archives of betting lines as well as dozens of different rating services for NCAA football games going back to 2001.

Great work! Agree that I'm fine with Harbaugh running it back

I suppose I'd have to think more about this, but it seems to match what I believe most of us see in Harbaugh: he recruits reasonably well, he prepares players to play fundamentally sound football, his teams execute fairly well, but he is not going outwit opponents with a creative gameplan or motivate his guys to play beyond themselves. So he's often favored and generally able to beat teams that lack Michigan's recruiting and player development, but he never stuns anyone. If you've got better players than him, you win (as is true for most coaches).

This is admittedly an account of a coach that many programs would love to be able to give of their head man. I am not for firing Harbaugh. But I think that he's going to have to upset OSU at some point.

Nice post OP.  I did some similar research a few years back also using OddShark looking at all the Power 5 conference teams, and while it's a bit dated, I think it's interesting so I'll share some of the data here.  

My research went from the 2008-2017 seasons, or the last 30 games dating back from the end of the 2017 season (the database wouldn't show more than that at that time for this search).  At that time Michigan was one of only four teams to not win single game as more than a 7 point underdog, and they went 0-12 in that span.  The others were Tennessee (0-30), Alabama (0-1, yup only a major underdog one time in 10 years!), and LSU (0-5).  So, the inability to win as big underdogs has been a problem going back through the last 3 coaches, not just Harbaugh.  Some records of note as being quite good as big underdogs were Ohio State (2-4), Michigan State (4-13), Minnesota (8-22) and Northwestern (11-19!).  

Michigan was good as big favorites, but terrible in toss up games (toss up defined the same way the OP did them).  They were 19-36 in toss up games, and I found a website that gave the likelihood of wins based on pre game spreads, so then calculated that Michigan was expected to win 27.54 of those 55 games (I had to divide up games into more specific spreads to get that number).  That 8.54 games under expectations was the worst of all Power 5 teams with only Virginia at 8.35 games under expectation coming close.  No other team was at more than 6 games under expectations.  I think there is something to Michigan fans altering betting lines with over optimism (I'm a fairly optimistic fan, but I don't get how people are willing to put money behind that!), but at the same time Vegas is not going to alter the spreads a crazy amount lest they get burnt. These data tell me it's pretty clear that Michigan football struggles against the weight of expectations has been a problem, and continues to be a problem under Harbaugh (duh doi!)  

I wanted to share another set of data as well since you mentioned comparing Harbaugh's record with Carr's.  It's not quite the same as spreads, but I looked at Harbaugh's record vs teams in certain ranking ranges vs. Carr's, and I thought it was quite enlightening.  I used Sports reference's postseason Simple Rating System to get the rankings.  Oh, also I did this after the 2019 season so this doesn't include the last two years: 

Carr was great against top 25 teams, but really struggled against the middle of the pack teams.  That was the frustrating part of his tenure - we would look great in knocking off a top team, then play tight in a game against inferior competition.  Harbaugh is pretty much the opposite.  Terrible against top teams, but very rarely do his teams lose to inferior competition (last year was the exception, but that was a weird year).  He's steady Eddie.  The problem for Harbaugh is the schedule has been so skewed to playing Top 10 teams, with him having to face over 3 of these teams a year.  I can't imagine any other team in the country has faced that many top ten teams without a single conference championship game or being in the playoffs. 

Okay, that's enough.  What I thought was going to take me 10 minutes to write out just took me an hour. Hopefully someone enjoys this data dump.  

As you note, the issue with using point spreads is that the goal of the spread is to get equal amounts bet on either side.  This introduces distortion when actively-betting fanbases are involved.

One way to recast the effects of the distortion is to compare them to the average W-L record for each "bucket" e.g. if Harbaugh wins 2/3rds of his +7 games and Michigan historically wins 2/3rds, but overall teams win 3/5 of their +7 games, that corrects a little for the effect of our fanbase.

I did not run the number rigorously, but five minutes and an envelope back tends to confirm what I think most of us believe:  Harbaugh is performing within historical norms, has definitely pulled us back from our "wilderness wandering" years, and has underachieved in rivalry games for reasons both in and out of his control.

That last is the sticking point, because if Michigan doesn't understand the reasons, any decision they make is less likely to get anyone where we all want to go.

Points spreads are fine as a rough proxy. They don't reflect the true win probability, but they usually aren't way off either.

As I recall, someone did an analysis based on recruited talent. Take a composite of your last 4 classes and the opponent's last 4 classes. It provides a good rough idea of who is the more talented team.

The results are similar. Harbaugh slaughters the opponents when Michigan is much more talented, and gets slaughtered the other way (mostly Ohio State). That much would be true of almost any coach.

But when the talent is comparable or only a modest advantage for Michigan, Harbaugh's teams don't carry their weight. This suggests what the other studies are saying. Harbaugh usually wins when there is a huge talent disparity in his favor. But he seldom wins by outcoaching or outsmarting his opponent.

Seems like we should win at least 50% of the toss ups and win the same percentage of the underdog games as we lose of the favorite games.   

I think Harbaugh is a good coach, but whether it is refs or luck, he doesn't seem to get a lot of breaks.