An early UM statistical analysis

Submitted by tpilews on

Okay, so at first this diary started off as just another post at a different forum. But, one thing led to another, and here we are. The original post started off as a way to statistically justify why UMs defense was ranked #100 in the country. Without further ado, here we go.

 

These "rankings" are going to change. Especially when competition becomes tougher for the higher "ranked" defenses. For example, you've got a team like OSU sitting at #7 in total defense. They are a great defense, but their ranking is based on play against the #95 offense in Marshall, #65 offense in Miami, and #119 offense in Ohio. (rankings from ncaa.org)

On the flip side, UM faced the #57 offense in UConn, #24 in Notre Dame, and UMass, if placed in with the FBS schools, ranks #17 in the nation at 467 yds/game.

So, on average, UM faced the #33 offense in the nation, while OSU faced the #93 offense.

 

At this point, you're probably saying to yourself some of the same things I was questioning. Well, of course Notre Dame's offense is going to look good because they played against UMs defense. Well, just how much did UM effect those rankings?

 

ND would move from #24 to #48 without the UM game. UM held UMass under their season average. UMass would move from #17 to #15. UM held UConn to 50 less yards than their season average. They'd move from #57 to #41. So, UMs average offensive opponent taking out their UM game = #34. So, taking UM out of the equation pushed the rank of their opponents' offense from #33 to #34. Not much change. OSU was a different story.

Looking at OSU...

Marshall moves from #95 to #68
Miami has only played two games, but w/o OSU game move from #65 to #53
Ohio moves from #119 to #114.
OSU average opponents' offensive rank = #78. A move from #93.

So, when taking out the immediate matchup, UM was facing the #34 offense while OSU was facing the #78 offense. For comparison's sake, the #78 offense is Texas Tech at 345.67 yds/game. The #34 offense is Wake Forest at 430.67 yds/game.

How does this pertain to the rest of the schedule?

Based on the average of #34, UM will only face 3 more offenses better ranked than the average offense they've already played. (MSU, OSU, and Wisconsin at #28, #20, and #30, respectively)

 

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Pushing the analysis further, UM is holding their opponents to 100.68% of their average offense.

UConn - 343/417 = 82.25%
ND - 535/409.5 = 130.64%
UMass - 439/481.5 = 91.17%
Total - 439/436 = 100.68%


OSU is holding their opponents offense to 68% of their average offense.

Marshall - 199/371 = 53.63%
Miami (YTM) - 352/405 = 86.91%
Ohio - 158/257 = 61.47%
Totals - 236.33/344.33 = 68.635%

If we take those numbers and look at the UM vs. OSU matchup at the end of the season, we get this in terms of expected offensive output:

UM: 350 yds
OSU: 463 yds

Of course, this same argument can be implemented to UMs offense vs. their opponents' defense. Without taking UM stats away from their opponents average, UM is still putting up 135.28% more yards than their opponent's defense normally gives up.

So, let's take away UMs impact on their opponents' defensive stats.

UConn - gave up 525 yds in their two other games. UM put up 473 yards on them.            473/262.5 = 180.19%

ND - gave up 799 yards to their two other opponents. UM put up 532 yards.           532/399.5 = 133.16%

UMass - gave up 544 yards to their other two opponents. UM put up 525 yards.            525/272 = 193.01%

So, to this point, UMs offense is putting up 163.81% more yards than their opponent typically gives up in a game.

In terms, of what this means vs. OSU... Ohio States defense is only giving up 236 yds/game. Based on UMs offensive output, they should put up 387 yards against OSU.

 

EDIT: So, I took all individual games and plugged them into Excel and came up with a pretty un-scientific predictor.

It is interesting to note that based on my predictor, UM will only be outgained by one team, OSU. I think these stats will really start to reign in the right picture once UM is two games deep in Big10 play.

Football

Comments

Seth9

September 22nd, 2010 at 3:29 AM ^

1. The sample size at this point in the season is still rather small.

2. The only team we've played that doesn't have a significant portion of their stats boosted by an easy FCS team is Notre Dame, who throttled us offensively from a yardage standpoint.

3. Holding a FCS team to 91.17% of their usual yardage doesn't bode well for the rest of the season, no matter how you slice it.

There are more issues here, such as insinuating that the offenses we will face will largely be worse than what we've faced so far because UMass has such a good offense, but those are the big three, imo. Well...big four. Whatever, why am I even responding to this at 3:28 AM. It's way too depressing that I'm still doing Stats homework (ironically) right now.

Joined: 04/01/2009

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tpilews

September 22nd, 2010 at 10:21 AM ^

Yeah, I almost didn't even post the diary because of the small sample size. I wrote the whole thing and just sat there going back and forth on whether I should post it or not. I think the best data you can take from this is that UMs defense is allowing teams to gain just over 100% of their opponents usually yardage/game. I'm going to keep a running tally and see where this goes after the sample size increases. It will be really interesting when UM faces MSU, which has a better offense than what they've already played against. We'll know a hell of a lot more about this team after that game.

Joined: 10/17/2008

MGoPoints: 3128

wolfman81

September 22nd, 2010 at 11:21 AM ^

1.  Of course the sample size is small, we'd like it to be bigger, but can't do much about it.  This might be an interesting statistical analysis to track for the next few weeks.

2.  Let's look closer at ND, especially since they have taken their annual tour of the Big 10.

vs. Purdue:   358 yds

vs. Michigan:  535 yds

at MSU:  461 yds.

This doesn't bode well.  Especially when you consider that they played for nearly a half with their backup QB.  However, you have to also consider game tempo...

 

vs. Purdue:   24:55

vs. Michigan:  25:51

at MSU:  25:36

Which doesn't really help (imagine trying to make a yards/minute stat...while yards/play would be better, # of plays isn't easy to find.)

So your point is taken, if using Notre Dame as the "canary in the mine" of the Michigan Defense, that canary is dead!

3.  Not all FCS teams are so bad...but I do think it borders on lunacy to simply rank UMass among the FBS teams using their yardage output against FCS teams.  Something interesting to try would be to look at the FCS teams who have played against FBS teams and compare yardage in the FBS game to the FCS game averages.  This way, you might be able to create a "conversion factor" that says if the FCS average is x YPG, then the equivalent FBS average would be x*f YPG.  People with databases could probably figure this out rather quickly [Mathlete, I'm looking at you!].  The point is to have a rule of thumb, and not a complicated regression conversion.

 

Lastly, I'd like to point out that YPG isn't the end-all be-all statistic we need to consider. Scoring defense is important.  Average number of turnovers caused is important (yes, recovering fumbles may be random, but causing them is the product of good tackling and aggressive play...things that a defense CAN control.  So on average better defenses should recover more fumbles too.)  I think the premise of the analysis of the OP has some merit, asking how far from the season's average did the opposing team do against your team, but this probably needs to be expanded to other statistical categories...and then you probably need to think about poisson distributions rather than normal distributions for a category like turnovers.  Or maybe some sort of cluster analysis might be useful.  I'm not quite sure how I'd go about doing it, but it would be an interesting problem to consider.

Joined: 12/17/2008

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NateVolk

September 22nd, 2010 at 8:23 AM ^

The UMASS stats are interesting.  I might let myself see that performance more positively if I saw the Minutemen have similar results moving the ball against another FBS team. I think their other two games were William & Mary and also Holy Cross.  

I do take heart that all the FBS schools we have remaining have played also played softer teams to date and only three of them could muster offenses with better rankings than two of the better teams we have already beaten.

Thanks a lot for this post. I'll definitely read it a couple more times after I loosen the cage and get more alert. Probably not seeing everything that is there right now.

Joined: 07/19/2010

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Tha Quiet Storm

September 22nd, 2010 at 11:13 AM ^

We have to play at least half of the season to get a good picture of where our defense will rank.  As another example, I heard that MSU has the #12 rush defense in the country.  That sounds great, but the teams that they played were WMU, FAU, and ND (whose coach is not a fan of running the ball despite having some good backs).  I can't speak for anyone else, but I'm not too worried about us being able to run the ball against MSU in a few weeks, despite their run D ranking.

Joined: 12/22/2008

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MGlobules

September 22nd, 2010 at 12:05 PM ^

must be taken with a grain of salt. Still, this is encouraging and productive analysis coaxed from an unpromising (because early) set of stats. And it serves to reinforce the perception that you get from looking at UM in the Sagarin ratings in comparison to upcoming opponents: despite a struggling D, Michigan has a serious chance in all of its remaining games. 

Joined: 11/17/2008

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UMfan21

September 22nd, 2010 at 12:27 PM ^

Is yardage really the best measure for a defense?  I would think number of series would be important.  Obviously turnovers are important.  Time of posession may be important when it comes to the 4th quarte/stamina. Points allowed would be the ultimate defensive stat since ultimately that is what decides the game.

I didn't know if someone has correlated yardage to "goodness" before to really validate that it's a good measure of how good a defense is.  Certainly "bend by don't break" is going to give up yards, but you hopefully force turnovers and settle for FGs instead of TDs.

Just my two cents.  It's really fun to compare Denards yardage too, but in the scheme of things, it doesn't matter as much as the points he puts up or the low turnovers he has.

Joined: 09/28/2009

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tpilews

September 22nd, 2010 at 3:35 PM ^

I agree that yardage is far from the end all, be all. However, another poster is doing a weekly update to TO margin, so I thought that you could combine that with my "analysis" and come up with a better picture.I'll update weekly and we'll see where it all ends up. If someone would like to do a weekly diary of "time of possession" or "pts scored/given up" then we would have a nice series of stats to look at weekly.

Joined: 10/17/2008

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Baceo Maston

September 22nd, 2010 at 2:46 PM ^

Wouldn't it be better to average statistics of the teams we have faced after pulling us out, and create a new rankings order based on that instead of averaging the actual ranking?

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