[Ed: this marks the debut of the Mathlete in an official capcity for the site.]

I guess when I was born and my parents named me Brett they know that I wouldn’t ever mean it if I said I was retired. An unwillingness to stay out of the game comes with the birth certificate.

When I last left we had no coach, no momentum and the school formerly known as Ohio State was coming off a big win over the SEC after avoiding serious repercussins from a minor tattoo incident. Today Hoke-a-mania rules all, a probable top 5 recruiting class is just about wrapped up and Ohio is staring into a great unknown with a new QB and head coach.

When I ran down the prospects from a host of candidates in January, Brady Hoke provided two nice charts about which I had this to say about his time at Ball State:

Better than I expected, actually. Slow steady growth taking the program from terrible to average over four years and then a big leap forward. The team obviously fell apart in two years under Parrish. The good news is that the team progressed well over a long period of time, the bad news is that during all the period at the helm, Hoke only produced one above average team.

Then at San Diego State:

San Diego St has shown nice improvement during Hoke’s time there. The Aztecs have improved by over 7 points each of the last two seasons. The big jump has been repairing a terrible defense (-11 in two preceding years) and turning them into an above average group by year 2. The offense has improved as well, but the majority of change has been driven by the defense.

So we have a track record for Coach Hoke at turning bad teams into good teams, what do the first year prospects look like for a new coach inheriting a team with a season like Michigan just put in the books.

The Comparisons

The numbers you saw above and most you will see from me are based on my Points Above Normal (PAN) metric. It is a simple number that is exactly what the descriptor indicates; it tells you how many points above an average team a team or unit is. It adjusts for quality of opponent, excludes 1AA cupcake games and any plays where the lead is 17+ in the second half. +7 will probably get you in the top 25. +14 should put you in a BCS bowl and +21 is typically good enough for a title shot.

Last year Michigan finished +2 with a +10 on offense and a –6 on defense (the remaining gap comes from special teams). Because the offense/defense spread was the one of the ten biggest over the last 8 years, it will make more specific comparisons difficult and we’ll restrict the study to teams around +2 overall.

Since 2005, 18 BCS conference schools have undergone a coaching change after a season between +0 and +4.

Dennis Erickson, Gene Chizik, Jimbo Fisher and Brian Kelly all pushed their new teams ahead by at least five points in their first seasons while Dan Hawkins, Turner Gill, Ed Orgeron and Mike Gundy all saw their teams take the biggest dips in year one.

On average, teams regressed by about a point per game in the first year of a new coach versus the previous year under the departed coach.

In general, a new coach coming into a BCS program coming off a season similar to Michigan’s don’t trend toward major changes in either direction, but some big swings have come under similar situations.

The Offense and the Defense

Regression to the mean will be the friend and foe of Michigan this year. The offense will be hard pressed to maintain the high levels of success and the defense will almost certainly make a step forward. The question is how much in each direction.

In my database of the last 8 years, there have been 58 BCS teams that had defenses within 2 points of Michigan’s lowly –6 from last year. Across those teams, the following year saw teams improve on the defensive side by about 4 points. 21 of the 58 teams showed improvements of a touchdown or more.

The offensive side shows similar numbers. Only 35 teams over the timeframe were within two points of Michigan’s +10 last season. Of those 35, 8 improved from there and the other 27 declined. The average change mirrored the defense at 4 points to average. The teams who were able to buck the trend were truly elite offenses. Of the four teams to go from Michigan’s range and improve by more than 2 points, two were the 2005 finalists Texas and USC, Oklahoma’s basketball on grass of 2008 and Florida in Tebow’s Heisman winning season of 2007.

The Conclusion

Between a coaching change and where the offense and defense landed from last season, the strongest indicator that Michigan will move forward is in the success that Brady Hoke has had taking mid- and low-level programs, and consistently moving them forward. Beyond that, the optimistic scenario is ride the Hoke wave, Mattison gets a returner-heavy defense to make the leap and finding a combination of new and old on offense to hold on to all the success we can. A realistically optimistic outcome is probably a 5-point improvement generated on the back of the defense, a top 25 finish and the table set for 2012. The historical mean points to a worse offense, better defense but ultimately similar 7-8 wins.

The Post-“Script”

No team in my database history has lost a coach after the kind of season (+16) that Ohio had in 2010. Five schools have been at least +10 and gone through a coaching change.

Of those five, Chip Kelly is the only one to push the team forward. Les Miles was able to keep LSU at a very high level while the successors to Brian Kelly, Rich Rodriguez and Bobby Petrino all saw significant drops in their first seasons on the job. A quick look says Ohio is most likely to fall somewhere between Miles and the Big East schools.