Statistically Modelling Harbaugh’s Impact at Michigan


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.

The Background

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
2006 57.1
2007 68.16 11.06 89%
2008 75.2 7.04 78%
2009 81.61 6.41 76%
2010 100.91 19.3 98%

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.

The Process

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.

The Results

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
50% -0.92 70.23 5.63 51.08% 12.50% 0.42%
80% 7.42 78.57 7.41 79.64% 33.41% 1.90%
90% 10.74 81.89 8.20 87.48% 48.18% 4.93%
95% 13.79 84.94 8.78 92.56% 59.28% 7.77%
97.5% 16.43 87.58 9.26 95.50% 68.46% 11.58%
99% 19.50 90.65 9.77 97.72% 77.78% 17.11%

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.

NFL Playoff Simulation – Conference Championship Round

We’re getting down to the wire here, so I’m simulating things a bit differently. You are by now well aware of the odds that each team wins the NFC or AFC championships based on the spreads and moneylines in that game, so I’ll skip that.

Seattle Seahawks vs New England Patriots is the odds-on favorite to be the Super Bowl matchup, at a probability of about 50%. Since both of these teams have home field advantage (and are better on a neutral field than their opponents anyways) this should come as no surprise.

Winner Odds
Seattle Seahawks 38.19%
New England Patriots 34.03%
Indianapolis Colts 14.63%
Green Bay Packers 13.15%


Seahawks vs Colts is an interesting possiblilty – higher than some may have imagined. Last week I had mentioned some value in Vegas on +1650 for that outcome.


Matchup Odds
Seattle Seahawks vs. New England Patriots 49.04%
Seattle Seahawks vs. Indianapolis Colts 22.78%
Green Bay Packers vs. New England Patriots 19.20%
Green Bay Packers vs. Indianapolis Colts 8.99%


Now I’ve added a new possibility set, of all possible outcomes that could happen in the Super Bowl. Since we’ve got almost a 50% chance of the Seahawks vs Patriots matchup, those teams winning against each other are of course the two most likely results.


Result Odds
Seattle Seahawks def New England Patriots 25.40%
New England Patriots def Seattle Seahawks 23.64%
Seattle Seahawks def Indianapolis Colts 12.79%
New England Patriots def Green Bay Packers 10.39%
Indianapolis Colts def Seattle Seahawks 9.99%
Green Bay Packers def New England Patriots 8.80%
Indianapolis Colts def Green Bay Packers 4.64%
Green Bay Packers def Indianapolis Colts 4.35%



NFL Playoff Betting – Divisional Round

Based on the simulations, I’m taking a look at the odds out there to see if there are any good bets. It’s good to shop around because you can find better deals on each site. The three I’m using here are 5Dimes, Bet Online, and Sportsbook. I’ll show you which bets look like good deals and where you can find them.

These are all only ideas and are off the record so I won’t be making or tracking any of these bets. Just a fun analysis of where value may be in the market. It also confirmed my suspicions that 5Dimes is the absolute best at Monte Carlo simulations of these things.

NFC Champion

Seahawks +100 (Bet Online) – If you’re looking for a good one, you need to head over to Bet Online and grab this one. The other two sites are offering them at -130 and -138. I have them at 64.37%, while the odds offered here imply 50%. Even the -130 and -138 lines imply a 56.5% to 58% chance, but at +100 there’s so much value there.

NFC Champion Odds Best Line ROI Book
Seattle Seahawks 64.37% 100 28.73% BOL
Green Bay Packers 24.71% 290 -3.64%
Dallas Cowboys 8.99% 850 -14.63%
Carolina Panthers 1.94% 1,775 -63.63%

AFC Champion

No really good bets here. There’s some slight value in the Colts +850 (BOL) but that’s about it, and even so you’re splitting hairs with our odds of 11.59% vs their implied probability of 10.53%.

AFC Champion Odds Best Line ROI Book
New England Patriots 50.02% 100 0.04% BOL
Denver Broncos 31.14% 220 -0.35%
Indianapolis Colts 11.59% 850 10.14% BOL
Baltimore Ravens 7.24% 865 -30.10%

Super Bowl Winners

Denver Broncos +700 (Sportsbook) – I have Denver at 16.22% to win, and most other books do too (+500 from BOL, +528 on 5D) but for some reason Sportsbook is offering +700. That’s an implied probability of 12.5%. Based on the payoff we’ve got an ROI of 29%.

Winner Odds Best Line ROI Book
Seattle Seahawks 33.78% 230 11.48% SB
New England Patriots 26.94% 310 10.45% BOL
Denver Broncos 16.22% 700 29.73% SB
Green Bay Packers 11.28% 575 -23.89%
Indianapolis Colts 5.28% 2,500 37.38% BOL
Dallas Cowboys 3.25% 1,280 -55.18%
Baltimore Ravens 2.86% 2,000 -39.90%
Carolina Panthers 0.39% 4,100 -83.54%

 Super Bowl Matchups

Seahawks vs Colts +1620 (Bet Online) – It’s rare that such “longshot” bets have value, but here it is. They’re implying a 5.81% chance of the matchup, but I have a 7.48% chance. Sportsbook was the only one who offered closer to what I expected at +1300.

Seahawks vs Patriots +260 (Bet Online) – Another steal. The other two books offering +180 and +190, but great deal from BOL at +260.

Seahawks vs Broncos +500 (Sportsbook) – The others are offering +406 to +450, and +425 is right around what I calculated so that makes sense. The +500 line has some value as it implies a 16.67% probability, compared to the 19.91% odds that I’ve got here.

Wow, I’m going to look like an idiot if the Seahawks lose. Sorry, that’s just where the value is showing up here.I’m only giving Seattle the standard 3.5 points here so I feel like I’m being pretty reasonable / conservative when it comes to them too.

Matchup Odds Best Line ROI Book
Seattle Seahawks vs. New England Patriots 32.29% 260 16.24% BOL
Seattle Seahawks vs. Denver Broncos 19.91% 500 19.46% SB
Green Bay Packers vs. New England Patriots 12.19% 600 -14.64%
Green Bay Packers vs. Denver Broncos 7.79% 1,300 9.12% SB
Seattle Seahawks vs. Indianapolis Colts 7.48% 1,620 28.72% BOL
Seattle Seahawks vs. Baltimore Ravens 4.68% 1,565 -22.04%
Dallas Cowboys vs. New England Patriots 4.53% 1,475 -28.68%
Green Bay Packers vs. Indianapolis Colts 2.91% 3,400 1.99% SB
Dallas Cowboys vs. Denver Broncos 2.86% 2,270 -32.17%
Green Bay Packers vs. Baltimore Ravens 1.81% 3,400 -36.79%
Carolina Panthers vs. New England Patriots 1.01% 3,725 -61.37%
Dallas Cowboys vs. Indianapolis Colts 0.97% 6,000 -41.07%
Dallas Cowboys vs. Baltimore Ravens 0.63% 5,500 -64.72%
Carolina Panthers vs. Denver Broncos 0.57% 5,650 -67.00%
Carolina Panthers vs. Indianapolis Colts 0.23% 12,500 -71.02%
Carolina Panthers vs. Baltimore Ravens 0.13% 16,000 -79.71%

NFL Playoff Simulation – Divisional Round

If you know me, you know I love simulations. For the divisional round we’re taking a look at the odds of each team making it to the super bowl, and winning it all.

Winner Odds
Seattle Seahawks 33.78%
New England Patriots 26.94%
Denver Broncos 16.22%
Green Bay Packers 11.28%
Indianapolis Colts 5.28%
Dallas Cowboys 3.25%
Baltimore Ravens 2.86%
Carolina Panthers 0.39%

The Seahawks and Patriots are the clear favorites (surprise surprise). Seeing the Colts at 5.28% seems low until you realize that Vegas actually has them even lower. It’s no secret that home field advantage plays a huge role in the playoffs (especially for the Seahawks) and we’ll find out this week if any road teams can pull off the upset.

AFC Champion Odds
New England Patriots 50.02%
Denver Broncos 31.14%
Indianapolis Colts 11.59%
Baltimore Ravens 7.24%
NFC Champion Odds
Seattle Seahawks 64.37%
Green Bay Packers 24.71%
Dallas Cowboys 8.99%
Carolina Panthers 1.94%

The Seahawks find themselves in a league of their own in the NFC, while the Patriots and Broncos share space up at the top of the AFC. The NFC also has the Panthers, which Vegas more or less considers a deadweight (not a dig on them, but they have to win at Seattle), while the Ravens are expected to at least be a little more competitive.

Matchup Odds
Seattle Seahawks vs. New England Patriots 32.29%
Seattle Seahawks vs. Denver Broncos 19.91%
Green Bay Packers vs. New England Patriots 12.19%
Green Bay Packers vs. Denver Broncos 7.79%
Seattle Seahawks vs. Indianapolis Colts 7.48%
Seattle Seahawks vs. Baltimore Ravens 4.68%
Dallas Cowboys vs. New England Patriots 4.53%
Green Bay Packers vs. Indianapolis Colts 2.91%
Dallas Cowboys vs. Denver Broncos 2.86%
Green Bay Packers vs. Baltimore Ravens 1.81%
Carolina Panthers vs. New England Patriots 1.01%
Dallas Cowboys vs. Indianapolis Colts 0.97%
Dallas Cowboys vs. Baltimore Ravens 0.63%
Carolina Panthers vs. Denver Broncos 0.57%
Carolina Panthers vs. Indianapolis Colts 0.23%
Carolina Panthers vs. Baltimore Ravens 0.13%

Seahawks and Patriots fans, don’t start packing your bags for Phoenix just let – there’s still only a 32% chance the teams will meet. Still, it’s only one of three matchups that have greater than a 10% chance of happening (Seahawks vs Broncos, Packers vs Patriots).

YPP Stats by Conference – 2014

Each year I run numbers to compare each team’s yards per play efficiency. I look at not only their offensive and defensive YPP, but also break it down into yards per pass attempt and yards per rush attempt. This allows us to easily spot where a team’s weakness is, or which teams are more “complete” in the sense that they’re doing well on both sides of the ball, or in both the run and the pass game.

These are split up by conference for better comparison. Eventually the end goal is to turn this into something more meaningful by pulling each team’s season stat against all common opponents, and compare it to the game that occurred. For example, it would be very meaningful to look at the Big 12 and say “When Baylor played its opponents, they forced 11 of 13 teams to allow more YPP than that team’s average for the season” or “When TCU played its opponents, its defense held opposing offenses to have an output lower than their season average on 10 of 13 occasions, lowering their YPP output by 1.2 YPP on average.” These statistics become even more meaningful when narrowed down to round robin areas, like the Big 12 or a conference division.

For now, it’s nothing more than a visual aid to help bring out some stats that may get overlooked. I’ve also added two columns, YPP Percentile Score and Balance Percentile Score. YPP Percentile Score takes the average of a team’s offensive YPP and defensive YPP. It does not discriminate on run vs pass. Balance Percentile Score average of a team’s offensive YPP, defensive YPP, passing YPA, defensive passing YPA, offensive yards per rush, and defensive yards per rush. This is more in depth and can help identify a more well-rounded team, but also has its faults. If a team only passes 10% of the time, but is highly efficient at doing so since the opponent is so used to the run (see Navy Off YPA #26, Georgia Southern Off YPA #30), or if a team is terrible at the pass but never really passes anyways (Wisconsin Def YPA #104) then we shouldn’t be weighting this as high as other factors. For those reasons I’m presenting both percentiles side-by-side.


Miami comes in at the top. Is anyone surprised? I sure am. I’ll have to do more research as to what caused them to be so high yet register only a 75 power rating and a 6-7 season.

Clemson ranks #1 in defensive efficiency but #92 in offense, and none of us are really surprised by that. Similar statistics for Louisville.

Georgia Tech finished #112 in defensive efficiency, despite fielding a top 10 offense.

There were no true stinkers in the ACC, but Wake Forest brought up the rear with the #128 offense and a mediocre defense. Dave Clawson has had some serious offensive success at other programs so it’s sad to see him struggle. He’s a rebuilding expert though, and Wake needs to hang on to him. With a relatively young offense returning though, we’ll expect to see an improvement here next year.

Down the road is UNC, who fielded the #122 defense. That’s pretty depressing, but guess who’s coming to save the day! It’s Gene Chizik!  I’m a big fan of the anti-trendy hire (see Lane Kiffin, Manny Diaz). There’s a reason they were head coach for a reason, and often times SEC schools and similar-minded schools (like USC and Nebraska) are too quick to pull the trigger.

ACC Standings YPP Opp YPP YPP Margin Off Pass Off Rush Def Pass Def Rush YPP Percentile Score Balance Percentile Score
Miami (FL) 10 23 5 16 18 22 33 87% 84%
Boston Col 55 35 36 65 21 66 8 65% 67%
Clemson 92 1 17 54 106 3 5 64% 66%
Louisville 81 7 32 31 113 19 20 66% 65%
NC State 49 49 44 72 27 39 60 62% 61%
Florida St 22 72 28 19 75 93 50 63% 57%
Pittsburgh 31 90 51 26 21 80 88 53% 56%
GA Tech 10 112 49 12 5 107 98 52% 55%
Duke 74 49 62 113 40 28 69 52% 51%
Virginia 92 27 58 87 100 57 22 54% 50%
Syracuse 102 27 69 118 65 89 20 50% 45%
VA Tech 113 35 78 108 93 45 45 42% 43%
Wake Forest 128 49 126 125 128 32 75 31% 30%
N Carolina 55 122 105 53 86 125 112 31% 28%

Big 12


Big 12 Standings YPP Opp YPP YPP Margin Off Pass Off Rush Def Pass Def Rush YPP Percentile Score Avg. Percentile Score
TX Christian 8 15 4 21 13 57 2 91% 85%
Oklahoma 19 35 13 71 5 57 3 79% 75%
Baylor 19 49 16 8 49 103 14 73% 68%
Kansas St 28 61 32 4 101 54 55 65% 61%
W Virginia 43 72 51 31 65 45 75 55% 57%
Texas 102 7 49 102 89 6 39 57% 55%
Texas Tech 15 115 56 48 21 115 115 49% 44%
Oklahoma St 81 78 85 26 113 103 50 38% 41%
Kansas 123 106 123 90 121 66 123 11% 18%
Iowa State 102 117 122 113 93 97 123 14% 16%



Big Ten



Big Ten Standings YPP Opp YPP YPP Margin Off Pass Off Rush Def Pass Def Rush YPP Percentile Score Avg. Percentile Score
Ohio State 5 15 2 5 9 8 39 92% 89%
Michigan St 15 27 9 19 18 39 14 84% 83%
Wisconsin 6 23 3 104 1 54 28 89% 72%
Nebraska 28 49 26 31 16 12 93 70% 70%
Michigan 81 10 36 97 44 45 8 64% 63%
Iowa 62 35 39 61 75 10 81 62% 58%
Minnesota 66 61 69 54 40 19 98 50% 56%
Penn State 120 3 48 104 121 6 2 52% 54%
Rutgers 37 112 78 23 55 103 119 42% 42%
Maryland 92 61 78 65 106 54 81 40% 40%
Indiana 62 96 85 123 9 66 104 38% 40%
Purdue 102 78 97 127 34 66 88 30% 36%
Northwestern 120 53 103 118 113 32 69 32% 34%
Illinois 81 101 104 72 93 107 108 29% 27%