One of the main talking points of college football next year will be the hire of Jim Harbaugh at Michigan. In fact, one sportsbook has already released the win total for next year’s Michigan football team (Over 8.5 -125, Under 8.5 -105). There is no doubt that Harbaugh will be held to a high standard due to his previous success. Luckily for him, he is coming in with a lot of resources already in place. In this article I attempt to quantify Harbaugh’s effect on Michigan for next season, as well as explain this attempt at quantifying something so subjective and difficult to predict.
Harbaugh’s tenure at Stanford is a perfect glance into what could be at Michigan. From 2007 to 2010, Harbaugh improved his team’s power rating by 43.81 points (Sagarin). What’s even more impressive is the consistency with which he did so. Harbaugh inherited a Stanford team that had finished the 2006 season with a 1-11 record and power rating of 57.10. They also ranked 113th in offensive S&P. Over the next four years, he improved their power ratings to 68.16, 75.20, 81.61, and 100.91 culminating in a dominating 42-10 Orange Bowl victory, while developing a quarterback who should have won the Heisman Trophy the following year. By the numbers, Harbaugh averaged an improvement of +10.95 power rating per year. His teams’ improvement were between the 76th to 98th percentile in each year at Stanford. So when we’re looking at how Harbaugh will see the team improve over his tenure, we should expect something in this range looking at his track record.
|Year||End Power Rating||Improvement||Improvement Percentile|
There’s no real question whether or not Harbaugh will fit the culture of Michigan. He is not only a Michigan man at heart, but his offensive philosophy is reminiscent of the old Michigan that we’ve seldom seen in the past decade. He also has Brady Hoke to thank for recruiting the perfect class for him. Next year, Michigan will be the only team in the Big Ten that returns all five offensive linemen, including freshman All-American OT Mason Cole. This is even more critical for a team running Harbaugh’s system, as it thrives on double-teaming defensive linemen to make it extremely difficult for opposing defenses to penetrate the line. He combines this with zone runs—which can be even more dangerous if the OL is able to penetrate into the linebackers’ zone—and short passes to tight ends and halfbacks/wingbacks, courtesy of easy reads created by the aggressive OL.
As an aside, I really hate it when people refer to his style as “hit ‘em in the mouth” / “smash mouth” football, or worse “old school football.” Harbaugh’s schemes, while physical, are actually quite sophisticated and unique. Commentators often speak of his teams as if they are perpetually in a 9-man goal-line formation punching the ball through on every play. That is so, so not what is going on here.
And when it comes to tight ends and backs, he is lucky to have some very large (and experienced) players: Jake Butt (TE 6’6” 249 lbs), A.J. Williams (TE 6’6”, 260 lbs), De’Veon Smoth (RB 5’11”, 220 lbs). With only 9 commitments on the 2015 roster and a few weeks left, Harbaugh has room to grow the class with a few possible freshmen at those positions as well, as long as they don’t keep telling these big guys that they aren’t smart enough to get in on their own. Hey, if they need any more size, maybe QB commit Zach Gentry (QB 6’6”, 230 lbs) can add an extra push.
Still, a complete overhaul in the way things are done holds its inherent risks. When TCU decided to change to its current run-and-shoot offense, things did not look pretty in the spring, to the point that they scored zero offensive points in spring practice. So it will be interesting to follow Michigan football as it progresses through an overhaul of their schemes through the spring and into the fall.
I ran multiple simulations of 30,000 seasons with the independent variable being the team’s improvement. This was done using the following:
- A table of each team’s expected improvement, and standard deviation, based on the current end of year power rating. For example, a team that finished with a rating of 90 will have an improvement of µ = -5.28 and σ = 7.63, while a team that finished with a rating of 50 will have an improvement of µ = +0.44 and σ = 9.23. As a general rule, power ratings equalize in future years, so teams finishing higher rated are likely to fall and vice-versa. There is also a higher standard deviation at lower power rating levels—which I believe is due to both the ceiling of ~100 for a team to hit on its power rating, as well as what we will call the “Alabama Effect” where teams with enough resources are often able to sustain a high level of success for long periods of time, which in turn leads to good recruits, a profitable athletic department, and a difficult cycle to break.
- Extra adjustments based on returning starters. While I am working on adding in more granular data for this, at this point I have only focused on the value of the quarterback, and the value of all non-QB players on average.
- When the QB is returning, we calculate the expected improvement based on the following formula: IMPR = -11.2885 + 0.91251 * (Returning Starters not including QB)
- When the QB is not returning, we calculate the expected improvement based on the following formula: IMPR = -13.7127 + 1.05 * (Returning Starters)
- These adjustments are added into the expected µ above to create µ-adj.
- These same adjustments are made for every team that Michigan will be playing in 2015 to adjust their power ratings as well.
- Based on µ-adj and σ, we use the NORMINV formula in excel. This creates a random percentile on a normal distribution, built from µ-adj and σ, and outputs the actual improvement (impr_act) for that season. The formula is as follows: =NORMINV(rand(),µ-adj, σ).
- This same process is done for each team. The impr_act for each team is added to the team’s previous power rating at the end of last season to give them their new power rating. We then take the difference between the power ratings, minus home field advantage, to calculate what the spread will be for each game. We can reference a matrix to convert these point spreads to a win probability for each team. “
- We then generate a random number for each game and determine the winner. For example:
- Michigan vs BYU spread: Michigan -7
- Odds of winning: Michigan 75%, BYU 25%
- For the winner, we use the excel formula =IF(rand()<75%,“Michigan”, “BYU”)
- We then count how many of the results from each of the 12 games are “Michigan” and paste the result, then run the simulation again and paste. Continue until a very large sample size is created.
- Finally, run the full simulation but input a different expected improvement for Michigan, holding all else equal.
Michigan finished last season with a power rating of 71.15 – we will base all improvement figures relative to this number. Since the standard deviation is based on this number as well, we will have the standard deviation set at σ = 8.3826.
|Improvement Percentile||Net Improvement||New Power Rating||Average Wins||6+ WINS||9+ WINS||Undefeated|
Now all of these scenarios are certainly possible. There’s also the less-probable outcome that Michigan actually does not improve, but let’s not even get into that. If Harbaugh does as he usually does (about 90th percentile), Michigan should expect about 8 wins – not a bad turnaround at all. Under those same circumstances they would have an 87% chance of going bowling, a 48% chance of hitting the 9-win mark, and a 4.93% chance of pulling off a beautiful undefeated regular season, culminating in a victory in Ann Arbor over the
undisputed national champion Ohio State Buckeyes, and put a reign to their street sign shenanigans (though we will probably never stop these street sign shenanigans). Those guys are the worst.