The Weekly Maths: Reality Check

The Weekly Maths: Reality Check

Submitted by The Mathlete on November 8th, 2012 at 4:09 PM

A win over Ohio, a BCS game win and a couple of killer recruiting classes have quickly escalated expectations of the Brady Hoke era. It’s time to put those expectations on ice. Not forever. But for another year or two it's safer to look at last season as the exception not the expectation.

This Year

The defense has been better than expected and I think this Greg Mattison thing is going to work out. They even have a fancy #7 ranking in total defense and a #13 scoring defense rank that’s not aided by fluck this time.

The offense has been a disappointment as Denard and Borges still seem further apart than ever, the offensive line has struggled and Toussaint hasn’t shown much when he does have a rare look at space.

I mentioned this in my season preview, but based on recruiting profiles and experience, this is the least talented Michigan team over the last 10 years [ed-S: I'm guessing attrition isn't taken into account?]. The Rodriguez recruiting bubble has arrived.

The other issue I was surprised to find this week is that Michigan is third nationally in a stat I call Garbage Points. For all of my analytics I exclude second half plays where the game is beyond two touchdowns, the approximate range at which teams deviate from their game plan and possibly individual effort in order to close out a less-competitive game. Garbage value has a pretty high correlation to team success because if you are good when it's close and in the first half you are having more drives in garbage time and probably having more success then, as well. Alabama and Kansas State are 1st and 2nd, Ohio cracks the top 10, but Michigan is the top team with a loss at #3 with a +57 EV during garage time. Lead extensions against UMass, Illinois and Minnesota all contributed to a Michigan spread that is one of the highest in the country. I have Michigan as the #28 in the country based on non-garbage time so a big spread between the two would likely indicate that Michigan has more of an issue with their official NCAA rankings being off due to extra time against over-matched teams.

Rank Team Garbage Points
1 Alabama 60
2 Kansas State 59
3 Michigan 57
4 Northern Illinois 56
5 LSU 56
6 Texas A&M 50
7 South Carolina 47
8 Florida State 45
9 Ohio State 43
10 Arizona State 41

Going Forward

Next year will be a first year starter at the most important position, which could be the newly popular Devin Gardner or five star Shane Morris. I’ll have more on this in the offseason but let’s just hope Gardner is able to win the job because the data on true freshman starting quarterbacks is emphatically troubling, even when they are elite recruits.

The defense should still continue on at a solid level, at this point the question with Mattison’s defenses is are they going to be good or great. A strong floor has been established.

Overall though, the talent/experience level isn’t going to be improved in 2013, in fact they may be worse. The upper classes will be Rodriguez’s final as well as the transition class. The elite classes will still be young enough that their contributions will likely be limited by playing time or play quality. By 2014, the team should be on par with the Carr-recruited, Rodriguez-coached teams in terms of talent and in 2015 back to the elite level of the late model Carr teams.

Michigan Talent/Experience Level By Season


Talent isn’t everything but it is certainly significant. At this point, the ability to overcome talent deficits seems more likely on defense than offense for Michigan, although the national trend is for talent to be more highly correlated to defensive success than offensive.

The other point of reference is that we aren’t talking about 2008-style drops, and especially in the current state of the Big TENNNNN! it could even mean conference championships. But don’t expect Michigan to make vast strides towards national elite until at least 2014.

Season Projection


Things keep coming back to eight wins. Northwestern is about 70%, Iowa 80% and Ohio 25% for the games remaining.

This week is probably Michigan’s last opening for the B1G Title game. If the Huskers survive a trip to Happy Valley visit from Penn St it’s hard to see them losing to Iowa or Minnesota.

Another little chart I put together shows who controlled their own destiny to the B1G title game by week.

Leaders division on top, Legends on bottom.

Dumb Punt of the Week

Not a lot of suspense for this one. Mark Dantonio was staring in the face victory and chose what any man with a strong jaw does. Hands the ability to win to the other team for 19 yards. It was fourth and 2 at the Nebraska 39. 1:27 on the clock and Nebraska out of timeouts. Hand it off to the best running back in the conference, watch him get 2 yards,  and that ices it. The WPA Calculator says that getting stopped gives Nebraska a 29% chance to win. A punt and touchback give Nebraska an 18% shot. Fourth and twos are successful 63% of the time, but even at 40% the return is positive. Even if you believe you can down them at the 1, going forward is at least neutral. Plus, Bell had just run five straight times in obvious running situations, gaining at least 2 yards on four of his five carries.

This week’s Ron Zook Memorial Dumb Punt of the Week goes to the refs in the Michigan St-Nebraska game for making Sparty punt the ball away.

Game Chart


Biggest Plays

+15% Gardner to Dileo for Michigan’s opening score

+9% Kirkwood stopped on 4th and 1 at the Michigan 41

+7% Nelson’s pass falls incomplete, forces Gophers into attempting long field goal at end of first half

-8% Gardner is intercepted at the Michigan 49

-8% Minnesota is on the board first with an 8 yard TD pass

-5% Nelson to Engel is good for 32 yards on third down

Devin Gardner, +14 EV, +30% WPA

Fitzgerald Toussaint, +4 EV (all on final run), +1%

Defense, +12 EV, +20%

Jake Ryan now 17th nationally in defender rankings, 11th in BCS players, 4th in Big Ten


Northwestern has surprisingly turned into a slightly more defensive than offensive player this year. Venric Mark is one of the nation’s most valuable running backs and the biggest threat from the Wildcat’s offense. If Michigan’s defense is up to task, the offense should be able to generate enough for a decent win.

Michigan 24 Northwestern 14

The Weekly Maths: One Man Band

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

The Weekly Maths: Focused on Paul

The Weekly Maths: Focused on Paul

Submitted by The Mathlete on October 18th, 2012 at 8:09 AM

Dumb Punt of the Week

I’m tempted to award it to Iowa for punting on 4th and 2 from the MSU 39 last Saturday, but that wouldn’t be fair to Greg Davis whose call sheet’s only play listed for 4th and 2 says: Hail Mary.

This week’s dumb punt of the week goes to the Virginia Cavaliers. Trailing the Fighting Edsalls by 11 with 13 minutes and change left in the game, Virginia was facing 4th and 1 from their own 42. Giving up a precious possession near midfield down two scores in the fourth quarter for the chance to kick a 21 yard punt earns Mike London the Ron Zook Memorial Dumb Punt of the Week.

Game Chart


Not too much exciting on a game chart from a 45-0 nothing for a game that started as a 20+ point favorite. Robinson to Gallon provides the big jump in the first quarter and it was a slow burn off of Illini hope between then and early in the third quarter.

Game Scores

Due to a 17+ point lead in the second half, only first half plays are used to calculate numbers from Saturday’s game.

Rush Offense: +5 EV, +10% WPA

Pass Offense: +6, +15%

Rush Defense: +6, +12%

Pass Defense: +0, –2%

Denard Robinson: +13, +28%

Fitzgerald Toussaint: –2, –2%

Thomas Rawls: +1, 1%


A detailed breakdown of each unit and key contributors. All numbers are opponent adjusted except field position and special teams.

EV+, National Rank (leader), B1G Rank (leader)

Rush Offense

Michigan Offense: +3, 24th (Texas A&M), 3rd (Nebraska)

Michigan St Defense: +7, 1st, 1st

Denard Robinson: +4 (rush only), 7th among QB/RBs (Johnny Manziel), 2nd (Braxton Miller)

Fitzgerald Toussaint: –2

Thomas Rawls: -0

Pass Offense

Michigan Offense: +3, 27th (Baylor), 2nd (Nebraska)

Michigan St Defense: +5, 12th, 1st

Denard Robinson: +4 (pass only), 21st (Nick Florence), 2nd (Taylor Martinez)

Devin Funchess: +3, 83rd

Jeremy Gallon: +3, 118th

Devin Gardner: +2, 164th

Rush Defense

Michigan Defense: +2, 34th (MSU), 4th

Michigan St Offense: –2, 95th, 10th

Le’Veon Bell: -1

Pass Defense

Michigan Defense: +4, 23rd (Bama), 4th (MSU)

Michigan St Offense: +0, 59th, 6th

Andrew Maxwell: –2, 109th

Dion Sims: +4, 71st

Aaron Burbridge: +1

Field Position


2.04 expected points per drive (57th)

2.76 points per drive (30th)

135% conversion (26th)

Michigan St:

2.03 expected points per drive (63rd)

1.63 points per drive (99th)

80% conversion (100th)

Special Teams

Michigan: –1, 82nd (TCU), 7th (Iowa)

Michigan St: +0, 52nd, 6th

The defenses should have the upper hand. Michigan’s offense has clearly been better than Sparty’s but the model thinks that so far this year the Michigan State defense has been one of the best in the country. Michigan’s faced two other elite defenses and lost both times. This time they have the advantage of home field and a more defined identity. This is a game that Michigan could certainly lose, but directionally there seems to be much more upside for Michigan than for MSU. Dion Sims’ status could be huge as he is the only Spartan generated much offensive value. If the Denard/Borges fusion can have a good game Paul Bunyan should return to Ann Arbor on Saturday.

Michigan 17 Michigan St 13

The Weekly Maths: An Offensive Bye Week

The Weekly Maths: An Offensive Bye Week

Submitted by The Mathlete on October 4th, 2012 at 4:23 PM

If you managed to watch any football with Michigan off last weekend, you probably saw a lot of offense. Unless, you were gritting your teeth and hoping for the Buckeyes to beat not lose to Michigan St. West Virginia and Baylor set a dramatic tone for the day with 133 points and 1507 yards between the two. The game nearly had two 600 yard passers and featured six different receivers go over 100 yards. Pretty much the kind of day you expect Andrew Maxwell to put up if his receivers had actual hands instead of giant clubs.

But the undercard also had some big days. Miami hit a last second deep ball to avoid overtime against NC st and win 44-37. As has been well documented here, Georgia out-gunned the Bray 51-44.  All in all teams in matchups between FBS teams averaged 423 yards per game, the most in the last ten years, and possibly of all time. The week narrowly edged out the bowl season of 2005 which averaged a fraction of a yard less per team per game.

In fact, 2012 has set a blistering pace for offensive output. Week 5 is ahead of week 3 and week 2 as the top three offensive outputs in terms of yardages of all time. 2012 is only five weeks old and already has the three best offensive weeks of the last decade. Even week 1, a traditionally low offensive output week, cracks the top 20 regular season weeks and is easily the best opening week of offensive in my database.

No matter what Nick Saban thinks about the pace, the trends hold up on a per play basis.

Yards/Play Through the First Five Weeks of a Season


After a gradual increase from 2003-2010, offensive output made a big jump in 2010 and appears to be on the verge of another jump in 2012. Beyond the video game type games like West Virginia/Baylor, this change in output fundamentally alters a lot of the nature of football. As has been discussed here many times, the fourth down calculus and even the onside kick decision process has to be accounted for. And as we’ve seen in the Alabama/LSU era, it puts a strange premium on defense. If no one else but you can play quality defense, it can be a major advantage.

[You want more maths, you JUMP for the maths]

The Weekly Maths: Writin’ Irish

The Weekly Maths: Writin’ Irish

Submitted by The Mathlete on September 20th, 2012 at 7:38 AM

Since Notre Dame is the first “real” opponent Michigan plays this year with any actual 2012 data, I’ll be forgoing a themed post and taking a deeper look at the Irish.

At this point in the season there aren’t quite enough results to truly adjust for opponents, but directionally, the strength of schedule is going to be relatively similar between the two programs. This should help offset the fact that until October, it’s difficult to do a quality strength of schedule offset.

Drive Results

Average points expected based on the offense’s starting field position vs actual points scored on those drives. Only drives non-half ending drives in the first half and second half drives within 14 points counted.

Michigan offense: 47 expected, 80 actual
Notre Dame offense: 55 expected, 61 actual
Michigan defense: 48 expected, 54 actual
Notre Dame defense: 51 expected, 23 actual

When Notre Dame has the ball, both sides have been pretty average. Both the Irish offense and the Michigan defense are less than a touchdown from the the expected output of a typical side. When Michigan has the ball both sides are decidedly non-average. Michigan is nearly doubling the expected output while the Notre Dame defense has allowed four fewer touchdowns than an average team would expect over the first three games.

In the last two weeks Notre Dame has pulled out wins while scoring a modest 20 points. I think Michigan will like their chances if Notre Dame only scores 20 this week. It will be interesting to see which matchup will be key in dictating the outcome, the highly publicized Michigan offense versus ND defense or the quieter matchup of the Irish offense against Michigan’s defense.

Run/Pass Splits

Early season results tend to skew to the offensive side of the ball. In a couple of weeks the opponent adjustment factor will take that but until then, you’ll see numbers that are a bit high and unadjusted.

Group: EV (points per game vs average-positive good, negative bad), National Rank

Michigan Offense: Rush: +8 (16), Pass: +7, (32)
Notre Dame Defense: Rush: +3 (24), +3 (28)
Michigan Defense: Rush: -6 (100), Pass: +0 (41)
Notre Dame Offense: Rush: +4 (49), Pass: +4 (43)

If you focus on the rankings instead of the absolute numbers you drr two pretty evenly matched teams. Michigan’s rush defense is the key outlier, but the Air Force game drives that to be a (hopefully) temporary outlier.

Defending Michigan’s run game will be a very different sort of challenge than Le’Veon Bell and the All-Two-Stars the Irish shut down last week. The personnel is in place for the Irish, so it could very well come down to an RPS contest between coordinators.

The Players

Player: EV (National Rank), Win percent added (National Rank)

Denard Robinson-All: +47 (1st), +93% (5th)
Denard Robinson-Pass: +21 (16th), +39% (20th)
Denard Robinson-Rush: +26 (1st), +54% (3rd)
Everett Golston: +9 (84th), +23% (64th)

Despite only logging two games worth of countable time, Denard checks in at first nationally in points created with 47, and points created on the ground (including running backs) with 26. His passing has even held up well with 21 points created, a number only bettered by 15 other quarterbacks. Golston hasn’t been bad but he hasn’t set the world on fire either.

I didn’t bother to post the running back numbers. Due to suspensions and slow starts, none of the three prominent backs in Saturday’s matchup have registered much on a national scale.

Devin Funchess: +13 (22nd), +30% (39th)
Jeremy Gallon: +7 (102nd), +5% (326th)
Drew Dileo: +6 (129th), +6% (326th)
Devin Gardner: +5 (158th), +12% (154th)
Tyler Eifert: +7 (90th), +18% (85th)
TJ Jones: +5 (170th), -10%
Davaris Daniels: +4 (211th), +10% (195th)
Robby Toma: +4 (213th), +38% (19th)
John Goodman: +4 (216th), +33% (31st)

Notre Dame has spread the wealth around to a variety of receivers, although most Michigan fans are thrilled that there are four guys to list for us, even if Roy Roundtree doesn’t even crack the list. Funchess is the headliner with 13 points created, good for 22nd nationally. What the Irish receiving corps lacks for points created they make up for in success in high leverage situations. Eifert, Toma and Goodman are all top-100 at this point, although the WPA stat can vary wildly at this point in the season.

The Prediction

At this point I have Michigan as a slightly better team but the home field swings the margin to the Irish. While I have been on board with Notre Dame having a strong season, I don’t see them as the favorite Vegas has installed them. This game is a coin flip and as noted above, could swing on a variety of factors. Can Notre Dame contain Denard on the ground without exposing their sparse secondary? Will Michigan push for the pass with the same game plan they’ve deployed in their last three losses? Will there be a breakout game for either the Irish offense or the Michigan defense?

Hopefully Michigan can make it four in a row. Another dramatic finish would be great but a blowout in South Bend would be better. Love Michigan and the points but straight up the numbers call for a narrow Irish win. Hopefully they’re just a little bit wrong.

Michigan 27, Notre Dame 28

UMass Game Notes

D. Robinson: 28 plays, +26, +38%
F. Toussaint: 11 plays, +3, +7%
M. Wegzyn: 24 plays, -2, -3%
M. Cox: 11 plays, -1, -3%

Game Chart


Pretty boring stuff this week, the kind of game you want as a 45 point favorite. I didn’t bother to add the adjustment based on spread because it just would have been a straight line across the top.

The Weekly Maths: Quarterback Progression

The Weekly Maths: Quarterback Progression

Submitted by The Mathlete on 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]

Stock Watch: Teams I’m Buying and Selling

Stock Watch: Teams I’m Buying and Selling

Submitted by The Mathlete on August 22nd, 2012 at 3:56 PM

[Ed: mathlete...




One I’m buying in 2012, the other I’m selling

After digesting a couple dozen previews, preseason rankings and countless team articles, there are still a handful of teams that my numbers just don’t mesh with the hive mind. For an overview of my numbers used to predict team success, open up your HTTV to the Technical Dossier (no, not about Cass Tech recruiting). The overview is that factors such as returning experience, returning coaching and level of recruits still on the roster are all weighted based on historical significance. The formula is driven by which factors have been most important over the years, not which ones best suit a given (Michigan) team.

CLICK THROUGH for the Mathlete's post.