The Weekly Maths: One Man Band

Submitted by The Mathlete on November 1st, 2012 at 1:23 PM

Denard is Michigan and Michigan is Denard. The defense has stepped up to mitigate that statement on the team front, but it's more true than ever for the offense. More true than last year, definitely.

One fine gentleman on the internet, known only as @jemather prompted me to look into how true it was for Michigan and how the Wolverine reliance on Denard matched up against other one-man shows.

For methodology I looked at every player who has at least 50 combined rushes and passes this season, that got me a group of 313 players. I then compared what the EV (not opponent adjusted) was for each of the plays where they passed or carried the ball. That number was then compared to the per-play average for every play their team ran that they didn’t pass or rush. Based on this route, Dri Archer of Kent State is college football’s most valuable player on a per-play basis. On 71 plays, Archer averaged 0.54 pts/play while the rest of his teammates averaged 0.04 pts/play on other plays. Coming in second, Denard Xavier Robinson. With a significantly higher 247 plays, Denard has average 0.23 pts/play while the non-Denard portion is a mirrored –0.23 pts/play. The only other major conference player over 0.35 is Kansas State’s Collin Klein at a 0.42 difference.

The concept of team replacement value is probably more true when you combine the per play average with number of plays for a total points added. By this measure, Denard still comes in second to a small college player. This time its quarterback Kolton Browning from Louisiana -Monroe. Browning’s 385 plays push his total value to the Warhawks for the season to 129 points, followed by Robinson’s 114 point contribution to Michigan. Here is your major college top 10.

Rank Player Team Plays Value (Pts)
1 Denard Robinson Michigan 247 114
2 Collin Klein Kansas St 213 90
3 Nick Florence Baylor 259 90
4 Matt McGloin Penn St 318 86
5 Logan Thomas Virginia Tech 275 77
6 Matt Barkley USC 259 70
7 Taylor Kelly Arizona St 220 64
8 Tyler Wilson Arkansas 193 59
9 Tajh Boyd Clemson 300 52
10 Ryan Nassib Syracuse 299 51

All quarterbacks leading the way. In fact, the top 32 spots all go to quarterbacks, reinforcing my belief that running backs are overrated. Dri Archer is the top running back at 35 points above team average. Venric Mark is the top major college running back at +30 for Northwestern.

The bottom line is that so far this season no player has been more crucial to his team’s success than Denard Robinson. His play hasn’t been perfect but when one player is responsible for half of his team’s points, its probably better to have him in the lineup. I am not looking forward to next year. I am too scared to look at what the best seasons by true freshman quarterbacks have been, but that still might be better than the alternative.


The same concept of most valuable player can be flipped to look at least valuable players. [Ed-S: In baseball they call this the Neifi Perez Factor. e-fact!] These are the players who keeping the ball in their hand is doing the most damage to their own team. It’s not just theoretical, these are the players who on a per play basis are doing less than their teammates are.

Rank Player Team Plays Value (Pts)
1 James Vandenberg Iowa 232 -56
2 Keith Price Washington 239 -55
3 Zach Mettenberger LSU 173 -49
4 Bryn Renner North Carolina 294 -39
5 Dayne Crist Kansas 162 -38

Again, all quarterbacks. Hope you are enjoying the Vandenberg/Davis era Hawkeyes!

Game Recap


Biggest swing plays

+9%: Gibbons is good from 52 yards to put Michigan on the board

+11%: Martinez fumbles setting up Michigan with a chance for points before the half

+9%: Ojemudia intercepts Martinez

-8%: Martinez to Bell for the opening score

-22%: Bellomy intercepted by Smith and returned 53 yards

-10%: Maher hits from 51 yards

-8%: Bellomy intercepted by Stafford

-All the percents: Denard leaves the game

Game Scores

Denard Robinson: –1, +2%

Russell Bellomy: –12, –40%

Fitzgerald Toussaint: –3, –3%

Defense: +5, +18%

Wins Projection


Michigan went into Lincoln as the underdog so the loss doesn’t alter the 8-win most likely projection. The performance did knock the expected win chances for the next three games from the 80’s to the 70’s, along with making Ohio a longer shot. The net effect is that although eight wins is still most likely, the odds of hitting nine wins is greatly reduced and seven wins is very much in play. The model assumes Denard plays the rest of the season but there is a negative portion from the Nebraska game for the time he was out.

Dumb Punt

Norm Chow is considered an offensive genius but he is apparently still a conventional decision maker when it comes to fourth down. With about six and a half minutes left, Hawaii trailed Colorado State by 8 and faced fourth and six at the Colorado State 39. Rather than push the field position and try to tie the game, Chow elected to punt, ultimately gaining 26 yards of field position. The Rams would take three minutes off the clock and give the Warriors back the ball at their own eight. Hawaii would not go on to win the game. Norm Chow is your Ron Zook Memorial Dumb Punt of the Week Award Winner.

Honorable mention for the week in dumb game theory is a joint award for Charlie Weis and Mack Brown who were simultaneously trying to shoot themselves in the foot at the end of the Kansas’s failed upset bid over Texas.

If you follow me or more likely Brian on twitter, you know that the blog’s current pet peeve is not using your timeouts on defense when the other team is about to score late, even if you lead. Kansas was leading by 3 and Texas had 1st and Goal at the 3 with 1:16 left on the clock. Texas only had one timeout left so there were two possible outcomes, Texas scores or is stopped. If Texas is stopped, Kansas can run out the clock, there is no downside to Kansas keeping more time on the clock. If Texas scored, the time becomes valuable to Kansas, not Texas. With 1:16 left on the clock and one timeout. Texas has plenty of time to make whatever play calls they want and an incentive to burn the clock. Kansas responds to this situation by not using their timeouts, not after a first down rush and not after a second down rush. Texas responds by rushing to the line each time. The good news for Longhorn fans is they scored a touchdown with only 8 seconds left. The bad news is that they shouldn’t have had to rush, especially with a timeout in their pocket. Kansas should have received the ball with just under a minute left instead of 8 seconds. The good news is that Kanas had two timeouts to use when they took over at their own 27 with 8 seconds left.


A game that seemed like a laugher not that long ago is all of the sudden close enough to be nervous. What does Michigan get out of its quarterback? If it's anything close to regular Denard the offense should be fine this week. If not, then who knows. After losing two quarterbacks, Minnesota has found two solid starts from Phillip Nelson, the only Gopher QB to post two positive games this season. The Michigan defense controls the game but the offense is unable to blow the game open.

Michigan 21 Minnesota 15



November 1st, 2012 at 11:33 AM ^

Very interesting to see it in a chart form. I knew we depended on Denard, but I didn't know how much.

Any chance you can compare this to his 2010 and 2011 seasons? He was the impetus for the term "Omniback" and a Silver Football Award winner with his ridiculous 2010 numbers, and I'd bet he wasn't as vital in 2011 with a better Fitz (Molk?) and Hemingway. I just think it'd be interesting.

The Mathlete

November 1st, 2012 at 12:02 PM ^

Despite being only 8 games in, Denard is already more valuable than any previos year. In 2010 Denard was worth 99 points and last year that dropped to 48 points with a strong supporting cast. This year's weak non-Denard showing has eclipsed prior. Doesn't mean he wasn't used more previously, just that this year the difference between his production per play and everyone else's is substantially greater.


November 1st, 2012 at 12:39 PM ^

Ha - thanks for looking into this Brett. Its consistent with my thought that the "this is what happens when your team relies on one player" complaint is not a Michigan issue, but one faced by a number of teams, including some really succesful ones.

Its also interesting to see Mettenberger at the bottom given that the lay theory on LSU is that its a team designed to succeed in spite of its offense. I wonder where McCarron stands.


November 1st, 2012 at 12:52 PM ^

In 2010 the offense seemed like it was all Denard all the Time, but he's actually MORE valuable now. I think it has to do with the lack of talent/production around him more than anything... but anyone who has been saying he's not a fit for this offense or not our best option is just out of their mind. These numbers back that up. He IS this offense.

EDIT: also, you don't see any powerhouses up top because they have talent surrounding the QB. When you have a lot of good players, it's hard to have one SO much more valuable. I'd say Klein at KSU is the exception, but you won't see Bama or any other major top team up here.


November 1st, 2012 at 1:30 PM ^

That's also because he had Forcier there as a very reliable backup, if I understand the methodology correctly. I know these numbers arent opponent adjusted, but it would potentially be useful to standardize the numbers in some way. Given that we needed a lot more points to win games in 2010 compared to 2011 or 2012, a given point added is more valuable towards actual wins now than in 2010, presumably.


November 1st, 2012 at 1:34 PM ^

I'm curious about what these numbers are actually showing us.  If this is meant to measure the value of a particular player, are you saying that by the numbers, both Logan Thomas and Matt McGloin are more valuable than Matt Barkley?  Just want to know exactly what we're measuring because that doesn't really pass my sniff test.  (For the record I love these posts, just saying this seems a little dubious at first glance)

The Mathlete

November 1st, 2012 at 1:38 PM ^

Think of the replacement player concept, but localize it to one team. If Denard wasn't getting the plays, would we be better off? Compare Denard to AJ McCarron. Denard is +.23 and the rest of the team is -.23. If we take away plays from him the net result is -.46/play. McCarron is at 0.36 but his team is at 0.22. Even though McCarron's per play average is higher, he has more support behind him would still mean there is a good chance of similar production. Michigan doesn't have that luxury. Denard isn't the most productive this year, but losing him would be a bigger blow than any other team losing their best player.


November 1st, 2012 at 1:40 PM ^

a lot of good things as well, gnash our teeth and try not to think about what might have been last week. 


EDIT: Sorry. Whacking is for MOLES, not gophers. Forgot.


November 1st, 2012 at 1:54 PM ^

For what most of us predicted early this year, an 8-4 record.  Although the B1G is much weaker than I had originally thought, so I was hoping Michigan would finish 9-3 or 10-2. But now with Robinson health problems and the chance he may miss some games, I would not be surprised by 7-5 or even 6-6.


November 1st, 2012 at 2:03 PM ^

If you have watched the University of Hawaii this year, you know that Norm Chow is not an offensive genius, nor a genius of any kind.  It also makes it clear why despite his seemingly good to great resume he has never been a head coach prior to this year.


November 1st, 2012 at 2:27 PM ^

This is simply what happens when your coordinator is not able to use Denard's skills to open up opportunities for others.  All you need to look at is the severe dropoff in Roundtree's numbers the last two years to know that our the rest of our playmakers are not being put in the optimal position for their skills. 


November 1st, 2012 at 2:27 PM ^

deserve more than just an Honorable Mention in dumb game theory.  Their idiocy is epic compared to the Dumb Punt of the Week.  At least with the dumb punt, there is a net gain in yards and a possibility of pinning the other team near their goal line - this could be the smart play if the other team's offense if struggling.

There is no reasonable explanation for Weis and Brown's idiocy.  There's no need for complicated math.  It's extremely basic logic or common sense.  For any college football coach (especially those who make millions), this idiocy is inexcusable.