So I was planning on putting up a post at the usual time and then I fell down the rabbit hole at the NCAA's new APR data-dump site, which happens to be a joint project with Michigan itself. After pounding at their online interface for a while, screaming "why?" the whole time, I just downloaded the whole dataset and set about doing stuff in Open Office's Excel clone.

First, a clear explanation of how the numbers are calculated from the site's Codebook:

A team’s APR cohort for a given year is composed of student-athletes who receive financial aid based on athletic ability; if a team does not offer athletics aid, then the cohort consists of  those student-athletes who are listed on the varsity roster on the first day of competition.  Each student-athlete in the APR cohort has the ability to earn two points for each regular academic term of full-time enrollment.   One point is awarded if the student-athlete is academically eligible to compete in the following regular academic term.   The other point is awarded if the student-athlete is retained by the institution (i.e., returns to school as a full-time student) in the next regular academic term.   Student-athletes who graduate are given both the eligibility and retention points for the term.  Squads can also earn a delayed graduation point if a student-athlete who left the institution without graduating returns to the institution and graduates.

At the start of each academic year, each Division I team's APR is calculated by adding all points earned by student-athletes in the team's cohorts in each of the previous four years, dividing that total by the number of possible points the student-athletes could have earned and multiplying by 1,000.  Thus, an APR of 950 means that the student-athletes in the cohort earned 95 percent of the eligibility and retention points that they could have earned. 

This answers a few questions I had before: walk-ons don't count, but walk-ons who pick up scholarships do. They even include a handy football example:

Example of APR Calculation for a Men’s Football Team (n=85 at start of year)

Semester 1 (Fall) Points Earned

75 student-athletes eligible and retained to next term (or graduate in that term)
75*(2 of 2) = 150 of 150
3 student-athletes are retained to next term but are academically  ineligible
3*(1 of 2) = 3 of 6
5 student-athletes leave the university while academically eligible
5*(1 of 2) = 5 of 10
2 student-athletes leave the university while academically  ineligible
2*(0 of 2) = 0 of 4

Semester Total 158 of 170 (929 APR)

There are also separate rates for eligibility and retention provided as part of the data set that only consider the appropriate halves of the equation. For example, the retention rate above is 78/85 or 918.

Also: it is super hard to get serious penalties. The 925 Mendoza line everyone has been throwing around is indeed the cutoff above which a player leaving ineligible does not hurt you, but falling below that line does not immediately bring penalties with it. It only hurts you if 1) you are below 925 and 2) you have a player leave ineligible. The punishment is an inability to use that player's scholarship the next year. You have to get below 900 before the NCAA comes in with a stick looking for trouble. Only three schools (Temple, San Jose State, and UAB) fell below that line.

Nevermind The Panic

A drumroll for Michigan's exact numbers:

A couple oddities are immediately apparent:

• Michigan's 2008 APR is higher than either of their individual breakout scores, which should be mathematically impossible. This also happens in 2006.
• Squad sizes somehow range from 85—the theoretical maximum—to 99. Early departures from mid-year graduates and transfers could bring the numbers up somewhat if the second semester has a bunch of new faces, be they freshmen or walk-ons, but those numbers seem abnormally high.
• Lloyd Carr's last year: guh. Remember that picture where Mike Hart is staring down five Buckeyes? "889" is that in numerical form.

Also, the NCAA official numbers confirm my back-of-envelope doodling: despite the flood of transfers over the last few years, Michigan is nowhere near even the "contemporaneous penalties" cutoff line. It would take a 2009 APR of 863 or worse to get into trouble. This is actually four points more buffer than this site's previous estimate.

863 is spectacularly low. Only four teams have managed that over the past three years: SJSU, UAB, Temple, and Florida State(!). Those are three mid-major schools who specialize in the marginally eligible and a school that endured a massive institutional cheating scandal. Michigan is not in either situation. We can officially stop worrying about this. Not that you would have been worrying about it without my prompting.