The Weekly Maths: Quarterback Progression Comment Count

The Mathlete September 13th, 2012 at 6:04 AM

2012 is Denard Robinson’s first real season of continuity. He enters his third season starting and as importantly, his second season with the same pass-oriented offensive coordinator. This week we’ll take a look at how quarterbacks progress and develop as they add years under their belt and how OC retention factors in, as well.

When looking at the data I don’t really have true class information. So rather than classifying players by Freshman, Senior, etc. they are grouped by years of experience. To classify as a year of experience, a quarterback must have at least six games with at least five pass attempts outside of garbage time (so Denard’s freshman season does not count). For four year players and quarterback’s who keep their jobs through their final season of eligibility the parallel is dead on, for players who lose the job, it can be artificially skewed.

Quarterback EV+ by Year of Experience and Total Years

EV+ of 1 of 2 of 3 of 4 All
Year 1 -2.5 -1.9 -0.8 -1.6 -1.8
Year 2   -1.3 -0.4 -0.2 -0.8
Year 3     0.4 0.8 0.6
Year 4       1.7 1.7

[More Maths and analysis after the jump]

The more experience you have, the better your EV+ is---not a big surprise. What isn’t clear is that whether the left to right increases are due to the fact that you are more likely to start at a younger age if you are actually better (selection bias) or if there are quarterback losing their jobs from the less experienced group that are driving the numbers down. Either way, the more you move to the right (eventual years of experience) or down (current year of experience) quality improves, with the only exception freshman starters who survive for four years at the helm. The exception is the good news/bad news about those advocating for Shane Morris in 2013.

When you look at the same chart but filter to only quarterbacks who are with a new OC (first year as OC for that team) the numbers don’t drop substantially, but for all data points but one, the new OC values are below average.

Quarterback EV+ by Year of Experience and Total Years for Players with a New OC

EV+ of 1 of 2 of 3 of 4 All
Year 1 -2.8 -2.6 -1.5 -3.0 -2.4
Year 2   -2.8 -1.6 0.3 -1.9
Year 3     0.4 0.1 0.3
Year 4       1.1 1.1

Of all the things that we don’t know about this team through a somewhere bizarre matchup of teams in the first two weeks of the season, one thing that seems most clear is that Denard has become a better passer. He’s still hasn’t kicked the occasional BRX (Bad Read Xtreme) label but his overall downfield success seems to be somewhere from good to very good, especially when coupled with his running ability.

Below is a chart showing how much returning quarterbacks improve year on year depending on how long the offensive coordinator has been in the position on campus. The good news for Michigan is that the largest average improvement in quarterback play comes in the second year of an offensive coordinator. The first year is behind and after more than 2 years, the improvement still happens but with diminishing returns.

Change in EV+ for Returning Quarterbacks by Years with OC at the school (as OC only)


61% of returning quarterbacks in their second year with the offensive coordinator improve and the total of all QBs is +1.0 EV+ gain. The biggest improvers under this situation were Mark Sanchez at USC, Brady Quinn at Notre Dame, Jay Cutler at Vanderbilt and Marcus Vick at Virginia Tech. Coming in at 9th overall is Ryan Lindley at San Diego St in his second year with Al Borges. Lindley went from –3.3 EV+ in the first season with Borges to +4.0 in his second. Last year Denard was +4 overall but only +1 as a passer. A gain of 7 like Lindley experienced would put Denard in contention for the best Big Ten season by a quarterback in the last 10 years. Probably a stretch to get to that level but a gain certainly seems likely based on the history of both Borges and returning quarterbacks with returning coordinators.

There are strong correlations between the situation Denard is in and quarterback passing improvement. Through two unusual opponents, the on-field evidence is starting to mount, as well. The only questions are can it be done with consistency and how high is the ceiling?

Weekly Notes

Game Chart

In-game win probabilities against Air Force.


Denard pushed the win probability over 60% on his first long TD run and even though the game stayed close throughout, it stayed above 60% for most of the first half and in the 70%’s for most of the second half until Air Force went into pass mode and Jake Ryan generated some big stops.

Game Scores

Denard Robinson: 39 plays, +20 EV (points added), +58% WPA (win pct added)

Fitzgerald Toussaint: 8 plays, –3, –6%

Devin Funchess: 4 plays, +8, +20%

Cody Getz: 26 plays, +10, +21%

Connor Dietz: 33 plays, +5, –5% (-4 and –25% on the final drive)



September 13th, 2012 at 8:22 AM ^

The "drive seasonality" of the win probability chart is hilarious. A dozen 8-yard Air Force runs slowly decrease the win probability, then Michigan gets possession and scores more quickly to "reset" the probability higher. Repeat.


September 13th, 2012 at 8:23 AM ^

Also meant to ask: is it too early in the season for your process to have meaningful predictions for future games? How is the big ten stacking up? What's the matchup with ND looking like? Etc. thanks!


September 13th, 2012 at 9:06 AM ^

I know your numbers are averages but if I am reading this correctly:

ND is starting a freshman now (although may go back to Rees).  So that would be a -1.6.

MSU has Maxwell who is in year 1 of 2.  So that would be a -1.9.

Ohio has Miller who is in year 2 of 4.  So that would be a -.2.  Although Miller had an OC change which in his case was probably better.

This implies though that all of our rivals are held back by their QB.  And in MSU's case, it really wont get much better.  Miller should be a beast thought by his senior season.  As for ND, hard to tell with the carousel QB process they use.

What I dont understand is how can Denard only be worth +4?  Is that just +4 from average? 


September 13th, 2012 at 11:36 AM ^

AIUI, it implies that in an average situation, QBs would be holding those teams back. As you point out, at least one of those teams is not in an average situation (OSU replacing a divot with an offensive coordinator).

ND did seem to have some kind of issues with Purdue. I suppose it's possible that Purdue's defense has suddenly improved from meh to really good, and of course the QB wasn't the only change on offense, but I would think it reasonable to suggest that having a freshman QB is hurting ND.


September 13th, 2012 at 12:26 PM ^

Golson did ok, man; 21 of 31 for 289 yards with a TD and no interceptions. He ran for another TD but was sacked 5 times. On his 11 non-sack rushing attempts, he rushed for 28 yards. Whether or not those are scrambles, seems like ND's O-line is hurting them more than he is. Riddick only managed 53 yards on 15 carries.

Purdue tied the game at 17 after recovering a fumble on the ND 15 (sacked Golson). Even then, they had to go for the TD on 4th and 10. Score was much closer than the game actaully was.


September 13th, 2012 at 9:38 AM ^

Yeesh.  Looking at these numbers gets me thinking about next year.  We would have the following choices -

  • Year 1 (or 2 medical redshirt pending) of a 1 year starter Devin Gardner (-2.5) EV+
  • Year 1 (pending medical redshirt) of a 2 year starter Devin Gardner (-1.9) EV+
  • Year 1 of a 3 year starter (pending he can beat out Morris in remaining years) Russell Bellomy (-0.8) EV+
  • Year 1 of a 1 year starter (pending him getting beaten out by Morris in years following) Russell Bellomy (-2.5) EV+
  • Year 1 of a 4 year starter (pending Morris beating out Gardner and Bellomy) Shane Morris (-1.6) EV+

So that leaves us with the following situations moving forward -

  • If Bellomy will be surpassed by Morris in his second year, then Bellomy starting next year is the worst choice (-2.5) EV+
  • If Bellomy can retain the job for the next 3 years over Morris, then Bellomy starting next year is the best choice (-0.8) EV+
  • Devin Gardner starting will be either a (-2.5) or (-1.9) EV+ which is either the worst or second worst possibility.
  • Shane Morris starting and retaining the job for 4 years will be a (-1.6) EV+ which isn't the worst possibility, but not the even close to the best.

Of course these are only averages, but they are all fairly scary averages considering our choices next year will be not that great.  


September 13th, 2012 at 10:48 AM ^

Because the Bellomy/Gardner equations don't take into account whatever EV Gardner does or does not bring to the table as a WR. They might work in isoaltion, but at the end of the day we need to know which way will the team be better off, and unless I'm missing something, we don't see that there.


September 13th, 2012 at 12:18 PM ^

Sure, we want to field the best team, that is kind of the point of football.  I was only using the numbers to guess at who would be the best choice next year. Based on the averages presented in the first table, not figuring in any outside factors.  Saturating the numbers with outside factors that may or may not affect the performance in a positive or negative way, would be biased and unuseful.  In the end, all they are is numbers.  It was just food for thought.


September 13th, 2012 at 12:02 PM ^

These posts are great.  One question,and maybe I missed them, have you started doing pre-game matchups yet?  Are you waiting for 4-5 games in to provide meaningful picks?


September 13th, 2012 at 12:40 PM ^

The ESPN comments always amuse me.  In an article about how Denard is an improved passer, and very lethal from under center with Borges, we get this comment -


Denard is most lethal in space. What I've never understood is the hesitancy to mix up packages to feature him as a RB. Of course in doing so Denard would have to block and Michigan would require another QB threat, but it'd be an interesting formation to roll out with to confuse opponents and put Robinson in the best possible position to eviscerate opposing defenses.