Blue Moon, Redux

Submitted by MCalibur on August 24th, 2010 at 5:54 PM

[Ed: bump!]

Back in April, I wrote a diary called Blue Moon in my Eye in which I developed a regression model that could be used to develop a projected win total assuming that reasonable estimates had been used as inputs. At the time I thought that the team would be capable of winning at least seven, probably eight, and maybe even nine out of thirteen games this season. Since then, things have, uh, how do you say … changed. With the loss of Woolfolk, how do those numbers change?

The New Blue Moon

Gollum & the Ring Before I get to that, there’s a good reason to update the model. In April, I mentioned that turnover margin is meaningful factor in regard to outcomes, but I lacked enough data to break it out specifically and therefore decided to leave it as a lumped parameter; turnovers were doomed to fade into the ether that is Intercept. No more, the NCAA has finally included turnover data in its database and now there is enough data to mix into the model. The new model has an improved R-squared value (0.752 as improved from 0.675) using just three end-of-year factors: offensive yards per game, defensive yards per game, and total turnover margin. Last time I didn’t include the model because it was mine, my own, my … preciousss. That was incredibly lame and nerdy (both with holding the coefficients and referencing LOTR) but we’re talking stats here so no one should be surprised. Another reason for divulging the goods is, now that there are four dimensions, a chart would be useless. Behold, the Blue Moon Model coefficients:



Norm. Coefficients


Intercept 0.579253998 0.515607437 3.79693E-55
OffYds/G 0.001753298 0.107573121 7.5351E-118
DefYds/G -0.001981349 -0.112371575 2.1098E-122
TrnOvrMgn_Total 0.007973783 0.065213954 5.75637E-50
  • I left the P-Values in there for those who know what that is. For the rest of you, it suffices to say what I said last time: that ish be money, yo.
  • The second column (Normalized Coefficients) is there to demonstrate the relative importance of each factor; in short, defense is a skosh more influential than offense and turnover margin is a little over half as important as both.
  • The use of the model (first column) is simple, start with the intercept then multiply the other the coefficients with their interrogation values and add everything together.  Use it to gamble at your own peril. Until such a time as you can accurately predict end of year stats for these categories, the model is only good for using as a platform to base sophisticated guesses off of.
  • Probable influential factors that are embedded in the 25% of the variation not explained by the model (1 – R_squared) are:

    • Return Teams effectiveness. Good return teams will establish good field position thus reducing OffYds/G.
    • Coverage Teams effectiveness. Bad units will allow the other team to establish good field position thereby reducing DefYds/G.
    • Field Goal Kicking effectiveness. If you get into field goal position and miss, you’ll have a lot of yards but nothing to show for them.
    • Penalties. Penalty yardage will increase/decrease your production depending on if they’re called on you or them but doesn’t necessarily change how effective each team is at controlling field position.
  • In round terms, factor influence on winning percentage breaks down to 30% Offense, 30% Defense, 15% Turnover Margin, and 25% Other Things.

Shine Down on the Big Ten (and it’s self-absorbed neighbor)

Below is 2009 Big Ten Data and Blue Moon Model expectation (BMM Expect).

Team OffYds/G DefYds/G TrnOvrMgn_Tot 2009 Wins BMM Expect. Delta Wins
Ohio St. 364.8 262.5 17 11 11 0
Penn St. 412.5 277.1 6 11 10 1
Iowa 330.8 286.7 2 11 8 3
Wisconsin 415.8 310.4 3 10 9 1
Northwestern 386 344.3 4 8 8 0
Michigan St. 407.1 364.3 -6 6 7 -1
Minnesota 295.8 364.3 -1 6 5 1
Notre Dame 451.8 397.8 5 6 7 -1
Purdue 391.3 376.6 -5 5 6 -1
Michigan 384.5 393.3 -12 5 5 0
Indiana 365 401 7 4 6 -2
Illinois 393.5 403.3 -4 3 5 -2
The distribution of Delta Wins, Actual Wins minus BMM Expect, is shown in the chart above. Note Iowa 2009. I defy them to go +3 again. They were a good team, they weren’t a great team. In fact, Northwestern performed better over the course of the year and—what, what?—apparently the head to head match-up agrees! The Wildcats actually won that game. Surely, Iowa wouldn’t begrudge anyone who leverages a +3 (or better, ahem) turnover margin into a narrow victory, would they?
The chest thumping bit that Iowa fans have developed is unbecoming. Like them, I’ll take 11 wins by any ethical means. Celebrate good times, come on, and all that jazz. But, this notion that they’ll be there again is based on what happened last year. How have they improved for this year? Any improvement that can be reasonably expected will be incremental in nature do to player development. Meanwhile, they’ve lost some really excellent players to the NFL (Bulaga, Moeaki, Angerer, Spievey, Edds, Calloway); is Iowa suddenly a recruiting powerhouse? Do they have more first-four-round NFL prospects just waiting to step in without skipping a beat? Poppycock. They’re regressing, and if they’re unlucky, it might not be so pretty.
Oh my, I’ve digressed.
[How bad the Woolfolk thing is after the jump.]

The Dope with Turnovers

Turnovers are a bitch; most teams can deal with 1 or 2 especially since the opponent often returns the favor, but if they come in bunches, you’ve got a problem. Also, even 1 poorly timed turnover can obliterate an otherwise dominant performance. Most reasonable people would agree that luck is a factor, the disagreement occurs in regards to how big a factor it is.

There are people, many of them, who think that turnovers are highly, maybe even predominately, influenced by luck. Among those people is Phil Steele who includes an article entitled Turnovers = Turnaround in his popular annual football preview. Steele’s basic argument goes that turnovers are random enough that, if your turnover margin is low or high in a given year, chances are that the numbers will turn around the next year, and your win-loss totals will follow in kind. This idea applies the concept of mean reversion but in order for mean reversion to occur, there must be a clearly identifiable element of random variation / luck / football demigod malevolence in the data.

With that said, common football intuition would support the notion that players can take overt action to force the issue; players can cause turnovers. So, lady luck—hardnosed broad that makes you fight, for your right, to paaartay; or fickle, stone cold, heartless dame that takes out one of your 2 most critical players during preseason training on a freak, non-contact, season ending injury? Oh yeah, I was talking about turnovers, let’s see what we see.

Rosie and the Diva

To answer this question, I pulled data from the NCAA stats archives for all available teams for the 2000 – 2009 football season, almost 1200 data points. Let’s cut straight to the chase, see—go, go, gadget chart.

TurnOver Mean Regression

This chart shows lumped average (dark blue dots) as well as the number of observations (red circles) at each level of turnover margin. The average year-end total turnover margin is +0.3305, essentially zero, with an observed range of +25 to –26. Mean reversion is clear as day—the further from average you go, the more likely you are to go back the other way. HOWEVA, this is a classic “see what you want to see” situation. Allow myself to fisk myself—go, go, gadget different chart:

TurnOver Mean Regression Scatter

Schizophrenic statistics—what do they mean?

Like double rainbows and wingless helmets, schizophrenic statistics can be difficult to condense into meaning. Focusing on the lumped averages allows us to look past the variation and focus on central tendency for each level of proficiency. The high R-squared value for the y_lumped trend line indicates that the trend is not a fluke. At first blush it looks like the lumped averages are a cherry picked values, but it’s actually the exact opposite.

The R-squared value for the y_scatter trend line is half as large as for y_lumped where you collapse each column into a single point.  People who don’t thoroughly understand/remember what R-squared signifies might point to the lumping maneuver as a nefarious deed and say, “when you look at the actual data, there’s too much variation to determine what the real trend is.” This would be a fallacy that only a phallus would deploy; don’t buy it. A slope that large in relation to the magnitude of the independent variable is a real trend—it’s almost one-for-one.

The lumped average trend is our the best shot at synthesizing a projection if that’s your game. By considering all the values at a particular observation level we neutralize the observed variation. But, you can’t just ignore variation, especially when it’s that large (the observed range at the 0 point is –15 to +20!). Moreover, the fact that you might currently lack an explanation for said variation, doesn’t mean the variation is completely random.  You should do everything in your power to understand what might be causing the variation and use that information to improve your estimate.

Turnover Reversion Drivers

So, what might the source of the very real variation we see in turnover reversion?

Offensive Driver-QB Play: In previous diaries I’ve discussed how a QB progresses depending on his recruiting profile and level of experience. There is a clear trend of improving interception rates. Previously charted for your viewing pleasure.

INT Rate

Offensive Driver-Improved Ball Security: From making QBs take hits in spring practice to coaching RBs to transfer the ball to their outside hand or clutching the ball higher on their torso (Tiki Barber), ball security is something that can be improved via coaching and drilling. No charts, just reasonable football intuition.

Defensive Driver-Ball Stripping: This is another technique that can be coached and drilled, but a forced fumble does not always equate to a turnover you need some luck for that to happen.

Defensive Driver – Be Good at Defense: This is the battle cry for the “residue of skill and preparation” crowd. It’s legit. Put pressure on the QB, cover receivers well, punish the ball carrier. The chart below shows Southern Cal’s positive turnover since 2000. The five-year run beginning in 2001 is the residue of skill and preparation.

USC Positive Turnover Chart

Plain Old Dumb Luck: It can’t be denied, being in the right spot when a pass deflects off of one (or six) players or having an oddly shaped ball bounce into your arms instead of your opponent’s has nothing to do with skill or preparation. The mean reversion chart shows this fact and it shows that the effect is strong. Specific teams might be able to resist the effect for several years, but sooner the talent disparity needed to sustain is something that few teams can and do achieve.

Shine Down on Michigan

Offensive Interrogation Point: Last time I figured that the Offense would improve to the 425 – 450 yards per game level. Regardless of whomever the QB is. Denard will not start unless he can displace a very good Tate Forcier. If someone gets injured we have a capable back up. The offensive line will be much better and can even sustain an injury or two without becoming a total disaster. The wide receivers are good and deep, and Stonum might even break out now that he can see. The only question mark is the running back situation, but the only reason its a question mark is because we don’t know who going to be the guy(s). I don’t think its appropriate to assume that we won’t be able to plug in one of our 4-5 talented recruits and pick up where Minor and Brown left off. We might even be better off if the new guys can stay healthier than Minor and Brown. I see no reason to modify my initial expectation.

angry_Michigan-hating_footbal_demi-godDefensive Interrogation Point: Here’s where things get dicey because of little baby predator’s angry-michigan-football-hating demigod’s desire to eliminate Woolfolk from Michigan’s 2010 roster. In April I surmised that its possible that Michigan’s defense undergo modest improvement from allowing 393 ypg to 375 – 350 ypg citing Northwestern, Minnesota, and Purdue from 2009 as proxies for the estimate; still bad, but better. With Woolfolk out a more thorough discussion is necessary.

The Defensive Line loses Brandon Graham, who will definitely be sorely missed. But, one guy is easier to neutralize than 3 (or 4). Martin, and Van Bergen will be better (incrementally at least) and Will Campbell should be available to contribute more than he did last year. Last year, teams could double or triple team Graham and let their other guys go up against talented but less mature competition. This year I think its more likely that the guys who don’t get doubled will be able to make more hay than they were able to make last year.

Linebackers, another area for concern based off of last season. Roh was great and should take a big step forward this season but, Mouton and Ezeh and the rest of the 2 deep were uninspiring and downright frightening at times. But is it reasonable to assume that Mouton and Ezeh will not be better at all? Even if they just get a little better due to being in the same system for the first time in their careers as starters, it’s still better than last year.

Defensive Backs, son of a bitch. It was bad when we lost Warren, now that we’ve lost Woolfolk also, it’s hella-bad. I have no delusions that this wont be the weakest link but how bad will they be?

  • Cornerbacks. Floyd should be better than last year however incremental his improvement might be. May not be faster though, so not a whole lot of consolation there. Cullen Christian should be better than Floyd ‘09, or anyone else who was trotted out there, and probably no worse than Cissoko.
  • Safeties. Why wont this sub-unit be better than last year (again, however incremental). There’s at least more athleticism available, and more familiarity with the scheme.
  • The scheme is designed to protect vulnerable secondaries, if only we give up fewer bombs…that’s a big improvement.
  • Proxies: Northwestern, Purdue, and Minnesota don’t recruit better than what Michigan has on its roster right now even after Woolfolk. Michigan State’s secondary was WORSE than Michigan’s last year, yet their overall defensive production was significantly better. A weak secondary is very unsettling but it’s only part of the defense, it doesn’t necessarily mean DOOM! Though, it could.

Having said all that, I’ll back off my range to 375 – 400; Why would the loss of Woolfolk legitimately make us worse than Illinois or Indiana or Notre Dame or Michigan from 2009? I’m really asking.

Lady Luck - Pin Up Turnovers: This is an area where Michigan should improve once more. There were reasons why Michigan ended up –12 on the year last year but not the ones I expected to find. In 2009 Michigan’s offense coughed up 28 turnover (13 fumbles, 15 interceptions), that’s only 4 above average. It was the defense that killed the turnover margin; Michigan’s D only generated 16 turnovers in 2009.

The average year end fumble total is 12.8, I’ll go with 13 since you can’t gain par of an interception. The average year end fumble total is 10.6, I’ll use 11.  All turnovers are zero sum, meaning that for every turnover lost by one team there is a turnover gained by its opponent; therefore, average fumbles gained and lost are the same number. Likewise for interceptions.

According to the regression above, Michigan should expect to come back to –2 in turnover margin, let’s see if we can reasonable explain why that would happen.

  • Interceptions Lost: Last year Michigan threw 15 interceptions with a true freshman passing the ball. Previous work has shown that we should expect that to improve (if Denard is throwing picks he wont be playing QB). Therefore, it’s reasonable to expect Michigan to return to average. Projection: –13.
  • Interceptions Gained: Last year Michigan had 11 interceptions, two less than average. We’re probably worse off in pass defense this year so, let’s leave that where it is, maybe even one lower. Projection: +10.5.
  • Fumbles lost. Last year Michigan lost 13 fumbles, two more than average. I subscribe to the notion that fumble recoveries are very random, so I think it’s safe to assume that Michigan will be an average team in this area. Projection: –11.
  • Fumbles Gained: This is where Michigan got killed last year, recovering just 5 fumbles versus an average of 11. Again, I say recoveries are random and we can expect to get back to average here. Projection: +11.

Doing the arithmetic yields an expected turnover margin of –2 or –3.

Acquiring target: Using the worst and best case estimates describe above, Michigan should still be able to make a bowl and end up with 6.6 to 7.9 wins out of 13 games. Heaven forbid we get a lucky break or two along the way.


Woolfolk’s injury hurts, but I don’t think its a death knell. In full disclosure, it would be reasonable to break the season into OOC and Big Ten play and re-project each portion, but I’ll leave that for others to do. Also, the estimates I’ve discussed above are just my own opinion, I’d love to hear where others think  I’ve been overly optimistic.

As usual comments and criticisms are welcome.


panthera leo fututio

August 24th, 2010 at 9:43 PM ^

It might also be cool to see an expanded take on your error bounds.  I.e. you give a range of predicted wins of 6.6 to 7.9 based on the best/worst case scenerios of yards/turnovers, but it'd be interesting to see you apply confidence intervals to both these scenerios based on the test variance from your initial regression.  This will better allow me to continue believing that we'll win 10 games.

Also, for you or others (or myself, if I weren't so lazy and inclined towards the more pornographic leisure time pursuits), I'd be real curious to see an analysis of just how autoregressive (i.e. dependent on past years' values) turnover margin is; I'm inclined to say a fair bit.  One good way to go about doing this would be to regress turnover margin on a number of likely factors (say, QB experience, run/pass ratio, sack total, etc.) and then run a test for autoregression, like a Durbin-Watson d test or something.

That just about exhausts my one semester of econometrics.  Great work!

Edward Khil

August 24th, 2010 at 10:10 PM ^

I'm going to quibble about a few minor points made early on in the post.  You write,


Return Teams effectiveness. Good return teams will establish good field position thus reducing OffYds/G.

Coverage Teams effectiveness. Bad units will allow the other team to establish good field position thereby reducing DefYds/G.

I don't have any analysis to back this up.  But I don't know that yards per game will necessarily be affected considerably.  Certainly yards per drive would be impacted.  But there just might be more drives per game achieved by teams with good return units, and more drives per game allowed by teams with poor coverage units.  And, therefore, there would tend to be more yards per game.

However, I wouldn't be surprised if one of the premier minds at mgoblog has already investigated this issue.


August 24th, 2010 at 10:27 PM ^

I have played and or watched the game of football in depth for 21 years.  I love how mgoblog breaks down statistics like this, but there is so much more that goes into a football game in determining the results other then the stats you've used here.  You have to take into account the experience of being in the system an extra year, the defense finally has an additional year under its belt as well.  You also have to look at  the fact that ALL of our quarterbacks are very confident within the system (the same can't be said for last year).  In terms of depth this team is also much, much improved.  Couple all this with the fact that we are backed in the corner and pissed off with all of the bull shit that has happened and you've got a durastic turn around waiting to happen!!  I would put our likely win number between 7 and 9.  Great blog!  Keep up the good work.  GO BLUE 


August 24th, 2010 at 10:36 PM ^

1.) Team maturity. Overall the offensive starters have 1 to 2 years and some more, of being starters.

2.)  They have been exposed to the coaches and system now for over 1 year, some up to 3 years.

Both should lead to a reduction in turnovers by 30 percent which should result in two or more wins this season over 2009. I think this team is right on line for 7 wins.  The upside would be momentum. If DROB just explodes at QB this season and we start out with a long winning streak, I think we would have a chance to win against every team in the b10, may be not OSU...but it could be close in the horse shoe. How sweet would 11-1 be.  I hope we don't see that many injuries...but injuries would be the only reason we could under achieve this season.


August 26th, 2010 at 1:18 AM ^

I agree with that part. If we start out fast like last year and DR is awesome it will only bring our confidence level up with each victory. It sure would be nice to kick the shit out of those damn bucknuts this year, am I tired of their streak. It sure is nice having an OSU grad ask me "May I take your order..." when I walk into a Mickey D's though, isn't it?


August 25th, 2010 at 12:00 AM ^

I'm an English major, but the Vargas girls and the baby predator held my interest long enough to find the frickin' estimate.  6.9-7.6 sounds reasonable.  Depending on who are loses are against, we could have a decent season or a slightly improved apocalyptic meltdown. 


August 25th, 2010 at 2:09 AM ^

I sort of skimmed and thought I understood what was going on until this part:

HOWEVA, this is a classic “see what you want to see” situation. Allow myself to fisk myself—go, go, gadget different chart:

and then the chart and the whole "Schizophrenic statistics" section.

I need to read up on R2 but that's fine.  (I think I vaguely understand it's generally a measure of how much variation is explained by your model, yes?   Been way too long since I took undergrad stats.)  It's this lumping stuff for which I can't seem to find a good background reference.

Unfortunately, to me this is the most interesting part.   Sustainability of turnover margins from year to year is a topic that seems to drive a lot of heated discussions with fans convinced that their team's prowess in causing/not giving up TOs is being unfairly overlooked.

panthera leo fututio

August 25th, 2010 at 8:31 AM ^

As you correctly understand, R-squared is a measure of the portion of variance in the dependent variable (in this case, change in turnover margin) that the model is able to predict.  In other words, in this case, R-squared tells you how closely the points fall along the best fitting line when you graph out all the individual data points of change in turnover margin on the y and past year turnover margin on the x.

By taking the average changes in turnover margin at different values for the previous year's margin, you reduce a big range of points down to a single point.  Thus, assuming your originial model is good and the averaged point falls near the line it predicts, your R-squared will automatically go up quite a bit.  An analogy: say I devise a model that says that AMCBHG will smite 3 CBs per year.  If I take the exact data points of 1 last year, 5 this year, etc., my model does not predict terribly well.  But if I average those numbers, my model is perfect and I get an R-squared of 1.


August 25th, 2010 at 5:29 AM ^

Turnovers are critical and will ultimately determine which QB stays on the field.  I see and would hope to expect improvement in all aspects but I hope they are not modest improvements.  Modest improvements may not be enough when other teams are likely also making similar improvements to their game.   I expect substantial improvement. 



August 25th, 2010 at 6:31 AM ^

and I dig the breakdown. This is a great way to better understand and project any given teams' potential.

I usually tend to prefer the emotional factors in college football like confidence and momentum to the math (damn the Illinois game!), so this really helps me to start to understand the statistical justification for my viewpoints.


August 25th, 2010 at 8:10 AM ^

All of this number mumbo jumbo crap is great, yet hard to understand (man, you're too smart for your own good), but it doesn't mean a damn thing come game time. Emotions are what is going to make this year at least 8-4 (can you tell I'm an optimist?). Our boys are tired of getting their asses kicked. They are going to come out of that tunnel ready to tear a M.F.'s head off! Football is about emotions and wanting to punch a guy right in his mouth. It's about letting the guy across from you know that you are hungrier than he is and that you're going to pound the shit out of him play after play. I think RR will have 'em fired up come the 4th, you'll see...


August 26th, 2010 at 12:57 AM ^

No, I don't think our guys lacked emotion the last couple of years but I do think there was a lot of uncertainty and doubt as to what to do on the field and how good they were going to be. I think this year will be different because the guys understand the system better, will have to do less thinking on their feet, and will be able to play with more emotion on the field. The fact the guys are bigger, stronger, and smarter will give them more confidence on the field of play. It's hard to really get after a guy if you're out in right field...


August 25th, 2010 at 8:55 AM ^

I really wish I knew about this website when I took my stats class.  You really should be a stats professor.  Great breakdown and I think you're right about the impact of losing Woofolk.  It will hurt, but it won't be the utter disaster that we all fear.  Because, lets be honest, the secondary was going to be bad anyway. 


August 26th, 2010 at 1:04 AM ^

I don't believe it will be an utter disaster either, but to say our secondary was going to be bad anyway is B.S. If you have good athletes on the field you'll always have a chance. Besides, we can't assume our secondary will be bad because we haven't seen them play a down yet. Have a little faith, we'll be fine...


August 25th, 2010 at 10:00 AM ^

That is one impressive set of numbers you put together there calibur... Well done, and while I am not the most math proficient of the MaizeRage I at least was able to connect the dots enough to box and whisker my way to reason.

Undefeated dre…

August 25th, 2010 at 12:30 PM ^

I was just wondering to myself, if Michigan's offense is 10% better than last year and the defense the same, and turnover margin is 0, what would be our expected wins this year. Great stuff!

Some more implications:

  • Looking at the absolute coefficients, a one-yard reduction in Defensive Yards Allowed Per Game is the same as a .885 increase in Offensive Yards per game. Or in other words, all else being equal, improving your defense by a yard per game is 13% more effective than improving your offense by a yard per game. 
  • A turnover costs the same as about 4 yards of defense allowed per game -- assuming a 12 game season, a turnover is worth about 48 yards of defense (and about 55 yards of offense). Some neat implications here -- if you're a cornerback and can go for the pick or play it safe and go for the tackle, assuming a 50-50 chance of success of getting the pick, go for the pick as long as the play is expected to get no more than 24 additional yards than it would if you just went for the tackle.

One thing that puzzles me -- why isn't the constant 50%? Obviously it may be due to missing factors, but a model where the expected probability of winning is 50% if all else is equal would be more intuitive. Does the model include only 1-A teams but allows for their record vs. all other teams (meaning 1-AA teams aren't included as cases, but they are included in terms of won-loss, yardage, etc.).