It'll be interesting to see whether your math or Brian's randomness assertion holds up.
2012 Turnover Analysis – Updated Thru UMass
Preseason Prediction: Michigan will end the year with a +8 Turnover Margin (TOM) or better (2011 was +7). The prediction for TOM for M for this year is based on the prediction that M will be a very good team again this year and is not based on the actual TOM of last year. (Very good teams will have a TOM of +5 or better.)
What The Heck Is Going On Out There?: The opponents have fumbled the ball 7 times (ranked #24) but Michigan has recovered just 2 for a paltry 29% recovery rate (ranked #92). This is far below the average 50% recovery rate and may appear to be just bad luck. But, a further look reveals that M has just forced 1 fumble (ranked #105) which they did recover. Of the 6 unforced fumbles, 3 occurred on punts in the UMass game (one of which was recovered by M), and three occurred in the backfield (all recovered by the player that fumbled the ball). Forced fumbles tend to occur with more M players around the ball and are more likely to be recovered. M's defense has zero interceptions (ranked #100) and the offense has thrown 5 picks (ranked #107). The result is a TOM of –3 (ranked #88).
Synopsis for Turnovers: Woooo! Taylor Lewan scored a touchdown recovering Denard's fumble in the end zone and Paul Gyarmati recovered a UMass fumbled punt. Other than that, I got pretty much nothin' here. M ended the game with a TOM of – 0 – . Denard threw another one – his interception ratio was 4% in this game and is now 5.2% overall (interception ratios of around 3% are "average" in FBS). (Note, this is just the interceptions thrown by DRob and excludes the one interception thrown by Bellomy.) I definitely expected Denard to improve this year and M to have a positive TOM for this game. Oh, well.
Synopsis for Expected Point (EP) Analysis: Just step away from the chart – nothing to see here. Each team had one TO but the EP gained by UMass was much larger because UMass returned the Denard interception for a TD.
(See the Section on Gory Details below for how the adjustment for Expected Points (EP) is calculated.)
National Rankings: Since M has a negative TOM overall, a game with a zero TOM improves the national rankings. All rankings include games between two FBS teams ONLY and are from TeamRankings except for forced fumbles which is from CFBStats. The four columns with *** show the best correlation to offense and defense (per Advanced NFL stats).
The Gory Details
Details for Turnovers: Here is overall summary for all games by player (data in yellow was affected by this week's game).
Expected Point (EP) Analysis: Basically, the probability of scoring depends on the line of scrimmage for the offense. Therefore, the impact of a TO also depends on the yard line where the TO is lost and the yard line where the TO is gained. Each turnover may result in an immediate lost opportunity for the team committing the TO and a potential gain in field position by the opponent. Both of these components can vary dramatically based upon the down when the TO occurred, the yards the TO is returned, and whether the TO was a fumble or an interception.
Here are the details for the game.
The analysis is a bit tricky because: (A) the TO may directly result in lost EP for the offense but (B) only modifies the EP for the team gaining the TO because the team gaining the TO would have gotten another possession even without the TO (due to a punt, KO after a TD, KO after a field goal, etc.). The Net EP Gain must take into account the potential EP gain without the TO. The EP gain without the turnover is based on where the field position would have been for the next possession if the TO had not occurred.
The expected point calculations are based on data from Brian Fremeau at BCFToys (he also posts at Football Outsiders). Fremeau's data reflects all offensive possessions played in 2007-2010 FBS vs. FBS games. I "smoothed" the actual data.
Here is a summary of the smoothed expected points.