Pro Football Reference has a post up that's the flipside of an equilibrium concept that Chris Brown of Smart Football has pushed a couple times. Brown's idea is that you should pitch your playcalling so that you are gaining the same number of yards whether you pass or run*. If you've got a powerful run offense and a crappy pass offense, "balance" is running enough for your passing game to be an effective freak occurrence. Think Georgia Tech of late.

On defense, though, you aren't given the option of what to run. The equilibrium is forced on you by the opponent, and if you're just terrible at one thing you don't have the option of usually calling the other thing. This is most clear when teams have just terrible rush defenses, like Stanford a few years ago. This is interesting but not directly relevant until this section:

Defenses are like chains: they're only as strong as their weakest links (for the flip side to this argument, see Brian Burke's article that offenses are like chains). Picture an unbelievable run-D teamed with an awful pass defense. That defense isn't going to be very good, as almost every team in the league could pass on them all day long. Flip the script, and nearly every team could control the game with power football against a defense that can't stop the run. On defense, if you have a weakness, almost every opponent can exploit it.

What's this offensive flipside, then? There is math integral to the post that doesn't need to be repeated here, but let me reassure you that there was consideration and multiplication before Burke arrived at this point:

So, in a very simple way, a passing play is like two chains under strain. One chain is the pass protection, and the other is the pass defense. Each link is a player vs. player match-up, and it has its own probability of breaking based on the abilities of the respective players. The first chain to break loses.

Can you imagine a football team with a starting player who is a point-failure in nearly every play? He'd be a lineman who always gets beat by a pass-rusher or a defensive back who always gets beat by a receiver. It would be ugly. …

So far, I’ve left out the most important player. The quarterback has to see open receivers and throw accurately to make big plays. He has maneuver in the pocket, and scramble from pass rushers. The QB is a big wildcard in my chain analogy.

Sweet hot Jesus in a pickle bun.

While the above-pictured players are fine young men headed for productive lives, they share two traits: they were starters at Michigan and they were underclass walk-ons at the time. Sheridan was honorable mention all-conference in high school.  Kovacs had just rolled in from an open tryout and the defensive coordinator thought he was another anonymous walk-on. And the thing about Kovacs is that I'm not sure he's the guy pictured here if he's got a scholarship. If we cast away notions of who's going to school for free and who isn't, Mike Williams or JT Floyd or Boubacar Cissoko could just as easily been featured in the uncomplimentary photo.

The crotchety variety of Michigan fan—correction, all Michigan fans are crotchety these days: the crotchety and impatient variety of Michigan fan—likes to point to the recruiting classes under Carr as evidence that Rodriguez should be on the first trash barge out of town. What ho, a graph!

There is also a table in that post in which various teams finish a lot better than you'd expect based on their recruiting rankings because Illinois is five spots lower than they should be and Michigan is eight. Last year they were nine back. The charts strongly support the idea that recruiting rankings matter. This is a strong surface-level case for strapping Rodriguez to a donkey, putting the donkey in a catapult, putting the catapult into a rocket, putting the rocket into another really unbelievably large catapult, and firing the whole mess into the sun.

Anyone who's read this blog since the wheels fell off in the Utah game can probably recite counter-arguments to the whole catapult nesting doll idea in their sleep. Hell, MGoBaseballCorrespondent Formerlyanonymous provides a link to Misopogon's definitive study of Michigan attrition in the very comments of that post. If you were to revise the recruiting rankings by hacking out everyone who is no longer on the team and weighting the remaining players by age, Michigan would plummet.

Your personal agony is reminding you that they wouldn't dip to Indiana's level or explain the terrible in-conference numbers the past two years, and it's correct. Even a hypothetical attrition-and-youth adjusted recruiting ranking probably wouldn't see Michigan dip much farther than the middle of the pack. So Rodriguez should still be strapped to a donkey, catapult, etc, even accounting for the raw hand he's been dealt? Maybe, but Michigan had four to seven reasonable receivers last year. They had a decent backup or two on the offensive line. They went four to five deep at running back. A lot of the reason Michigan would be in the middle can't get on the field without other bits of it coming off.

Meanwhile in the secondary, they had two players who were anywhere near competent. This was because the roster had exactly four scholarship defensive backs who weren't freshmen after Boubacar Cissoko got the boot. Unless every single one of those players was good—and at least two were run of the mill three stars—Michigan was going to be facing down trouble. Since two of the scholarship players were really, really bad, Michigan had the mother of all weak links, and the defense collapsed. The year before Michigan had the mother of all weak links at quarterback, and the offense collapsed.

What pockets of hope still exist in the Michigan fanbase mostly rely on Rodriguez's stellar performance at West Virginia and struggle to understand how a guy who was so brilliant there can be so stupid here. By no measure has Rodriguez met even the modest tasks his supporters retroactively set after it was clear how ugly it was. And it's hard to see the defense improving when its three best players are off to the NFL.

This is the hope: last year's weak link was a disaster and 2008's weak link was a disaster and Rodriguez is bringing in three cornerbacks and three safeties and getting two redshirt freshman at his disposal and there's no spot on the roster that looks as utterly bereft of hope as quarterback in '08 or the secondary in '09. When Tate Forcier came in and played like an average freshman—which is to say not very well at all—the offense went from worst ever to passable.

Football is a game of weak links, and Michigan has had downright vaporous links at position groups the last two years. This is the tenuous hope: that no walk-ons play and no group is a white-hot nuclear Chernobyl. If that comes to pass Michigan will be at least mediocre; if it doesn't then it'll be an offseason of knives.

*(Passing gets a risk adjustment built in because turnovers are more common on passing plays, so you're actually aiming for a point where your YPA is about a yard or so better than your YPC.)