The Numbers Game: Schlabach Hate Week Continues!

I've got nothing personally against Mark Schlabach.  He's not my favorite college football writer, and he's not my least favorite either.  I've generally had no opinion on him.  Until this week.  This week he wrote one of the most asinine columns I've ever read.  I understand columnists often feel the need to stake out a contrarian viewpoint to the conventional wisdom in order to gain notoriety.  I suppose there's nothing wrong with this in theory, but that's only the case if the argument has some merit whatsoever.

For those who don't want to read through the entire thing because they prefer to not pull out all of their hair, here's a synopsis: Texas might not actually be good because no one in the Big 12 plays defense and thus SEC defenses are better and whichever team Texas plays in the national championship game will be better than the 7 teams Texas has played so far.  First of all, I'm not sure how you convince yourself it's a good idea to write an entire column in which the ultimate conclusion is that the team you play in the national championship game will probably be better than the teams you played in the regular season.

But leaving aside that ridiculously obvious point, are we really going down this "SEC defenses are obviously better than Big 12 defenses because OMG just look at the SEC's awesome defensive stats!" line of argument again?  Schlabach does deign to briefly mention the fact that Big 12 offenses are, you know, sorta good:

Entering this weekend, half the SEC's 12 teams were ranked in the top 20 nationally in total defense. Only three Big 12 defenses ranked in the top 40, and half the league's teams ranked 70th or worse.  Conversely, seven Big 12 teams were ranked in the top 30 nationally in total offense, including five of the top 11. Georgia was the only SEC team ranked in the top 35, and half the league's teams were ranked 74th or worse.

Let's recap:

• Number of Big 12 teams in the top 40 defensively: 3
• Number of SEC teams in the top 35 offensively: 1
• Number of Big 12 teams below top 70 defensively: 6
• Number of SEC teams below top 70 offensively: 6
• Conclusion:  SEC defenses are good and Big 12 defenses aren't.

The problem with coming to that conclusion based on that data is that there's a chicken/egg conundrum in terms of good offense/bad defense and vice versa.  It's hard to tell the extent to which the Big 12's good offenses make its defenses look bad and the extent to which the SEC's bad offenses make its defenses look good.  And what does Schlabach do to get himself out of this conundrum?  Well, he ignores it.  Doesn't mention it at all.  He just takes a conventionally-held belief (SEC defenses good!  Big 12 defenses bad!) and notices that the raw numbers support that notion and that's that.  Deadline: met!  Luckily, you all have me around to do for free all the work that Schlabach doesn't want to do for his salary.

After the jump, we look at some stats that might actually tell us something interesting about these offenses and defenses that can maybe work us out of this chicken/egg conundrum.

The first step is to stop talking about Total Defense and start talking about Scoring Defense.  The point of a defense isn't to allow fewer yards per game, it's to allow fewer points per game.  Yards allowed per game are a pretty good indicator of how good a defense is at preventing the other team from scoring, they are a means to an end, not an end in themselves.  There's so much more to it.

So let's take a look at the scoring defenses of the following 2008 teams, along with the 2005 Texas team, because it gives a us a championship comparison and also because I just want to prove Year2 wrong.  You're a smart guy, Year2, and a good commenter.  But I think you're wrong to say that the 2005 Texas defense was a lot better than this defense.  To the charts:

Well, that's a start.  But this chart tells us one thng and one thing only:  this is how many points each team has allowed per game against the particular opponents that they have faced this year (or 2005 in the case of the Fightin' VYs).  This doesn't come any closer to solving the chicken/egg conundrum.  To do that we'll need to see how well each of these teams is performing relative to other teams who have faced the same opposition.  Essentially, we need to see how many points Texas' opponents (for instance) are scoring per game against teams other than Texas and then compare that to how many they scored against Texas.  So let's add a column to that chart:

So this chart tells us a little bit more about these defenses, namely, how well they do at keeping opposing offenses from scoring relative to the other teams these opponents play.  You'll notice that Texas' seven 2008 opponents have scored an average of 33.86 points per game against teams other than Texas and only 17.57 points against Texas, for a 16.29 point difference.  That's the largest of this group, even larger than the 2005 Texas defense.  So, while the 2008 Longhorns are only ranked #4 among this group of 7 in terms of points allowed per game, they are playing such dominating offenses that the 17.57 points they're allowing per game is actually quite remarkable.

Now, if I were someone like Mark Schlabach, I might take these stats, which at face value seem to prove my point, and say, "See, Texas' defense is actually better than all of these defenses, including the SEC ones!  And Oklahoma State's defense is actually better than Alabama's and LSU's!"  But I'm not Mark Schlabach, so I'm going to point out the flaws in this statistic.

Let's take a hypothetical in which Defense A has faced opponents who have a 14.0 scoring average in games other than those against Team A.  Even if Defense A has shut out each and every opponent it has faced, the greatest "Difference" number they could put up in that chart is 14.0, making it look like Texas' 16.29 number is better.  But we all know that it's not necessarily better.  Now, would Defense A be shutting teams out if they were facing offenses scoring 33.86 points per game, as Texas is?  Probably not.  But that's not the point.  The point is that this example underscores the problem with this statistic, which is that it tends to favor defenses that go up against high scoring offenses.  If Defense A faces offenses averaging 50 points per game and holds them to 25 ppg, that's a difference of 25.  And if Defense B faces offenses averaging 30 points per game and holds them to 15, that's a difference of 15.  Defense A looks better than Defense B because 25>15, but they're both holding opposing offenses to half their total scoring on the season.  So let's add some columns onto the chart look at that percentage of total points allowed statistic:

The Season Totals ratio is the cumulative ratio of the average points allowed by a team versus average points scored by opponents against other teams (i.e. for Texas, it's 17.57 divided by 33.86).  Cumulatively on the season, Texas is allowing its opponents to score only 52% of the points their opponents score per game against all teams other than Texas.  The Per Game ratio is an average of the ratios for each individual game instead of the points over an entire season, which number can be and usually is different that the Season Totals ratio.

The Season Totals ratio has the advantage of not weighing outliers as much as the per game ratio because it's a cumulative statistic.  Having one really good game affects the per game ratio more than the season totals ratio.  The Per Game ratio has the advantage of perhaps being more true to life.  Wins and losses aren't determined by performance over the course of seasons; they're determined by games.  An average of how a team has done in each game is instructive.  Determining which is better isn't really important, but noting the differences are because they tell you what kind of team you're dealing with.  A team whose two ratios are very similar is a steady team.  You're likely to get something close to that percentage in an actual game.  A team with ratios that are significantly different (my guess is anything more than 2-3% is significantly different) is an erratic team that sometimes has good games and sometimes has bad games.

You'll notice that the 2008 Texas defense has better ratios than both the 2005 Texas defense and this year's Alabama defense and is barely off the pace set by this year's Florida defense.  You'll also notice that LSU's vaunted SEC defense kind of sucks.  Additionally, Texas has an incredibly stable defense.  You know what you're going to get from it week-in and week-out.  Texas' lowest game ratio is .22 (against Rice) and its highest is .72 (against OU).  That is, Texas hasn't held any team below 22% of their scoring average and hasn't allowed anyone to score more than 72% of their scoring average.  LSU, on the other hand, has a low of 16% and a high of 187%!  I think this might have a lot to do with why SEC teams lose to each other all the time: erratically performing defenses.  They look great one week and terrible the next.  They call it parity and strength 1-12 in the conference, but it's not.  Florida, for instance, held Miami to 8% of its scoring average 1 week, held Tennessee to 27% of its scoring average the next week, and then the following week allowed Ole Miss to score 113% of its scoring average, or 13% more than they scored against every other team they've played.  Florida's average ratio is phenomenal despite the Ole Miss game, the best in this sample.  But that doesn't make Ole Miss good.  It means that Florida totally crapped the bed that week.

Before we go on, I need to point out a slight flaw in this ratio statistic too.  Whereas the "Difference" statistic favors teams that face excellent opposing offenses, the "Ratio" statistic favors teams that face bad opposing offenses.  The effect isn't as great in the Ratio statistic as in the Difference statistic but it's still there.  For instance, if Defense A faces an offensive juggernaut that averages 49 ppg and gives up only 21, isn't that a better indicator of a good defensive performance than if Defense B faces an anemic offense averaging 7 points per game and only gives up 3?  I think so, but the ratios are exactly the same: .42857.  This is a minor flaw, but it exists.

So what to make of this then?  You have to look at both the Difference and Ratio statistics in the above chart because both are somewhat flawed in different directions.  Put more stock in the Ratio than the Difference statistic though.  In looking at both, it seems like Texas' defense can hang with any other team on that list.  The only team they could reasonably be considered to be behind would be Florida (not even 2005 Texas, Year2!).  And yes, Schlabach, OU and OSU aren't showing championship caliber defenses, even considering the stellar offenses they are going against.  But LSU is a lot worse than either and they're one of the teams you list as being better than Texas has ever faced.

Regardless, so we know that Texas' defense is national championship elite, statistically.  And we also know that a few SEC teams have better defenses than the Big 12 teams Texas has faced/will face.  But what about offenses?  Say Alabama and Texas meet in the national championship game.  Their defenses are roughly equal, with Texas' probably being a little bit better, statistically speaking.  So how do their offenses stack up?  Let's look at the same chart, but modified to show the opponent's points allowed per game and the team's points scored per game:

First of all, note that in the offensive statistics, the Per Game ratio is much more subject to outliers than it is in the deffensive statistics (basically because there's an infinite number of points you can score more than your opponent allows per game on average, but there's a finite number of points you can give up below what your opponent is scoring per game).  Thus, the per game ratios are all a lot larger than the season total ratios and you get much bigger differences comparing the offensive ratios than comparing the defensive ratios.  But again, the closer the ratios are together, the more consistent that team is.

So first look at the Oklahoma per game ratio number.  OU is scoring 2.69 times more points per game against its opponenets than its opponents are giving up to other teams.  That's a lot better than even Texas' 2005 national championship team, which had one of the great offenses of all time.  But this is super-inflated by the fact that in two games (against Cincinnati and TCU), OU scored more than FOUR TIMES what those defenses give up per game to other teams.  That's why their season ratio is so much lower, almost identical to the 2005 Texas ratio.  That 2005 Texas team was much more consistently good.

The 2008 Longhorns have better ratios than every team on this list other than Oklahoma and the 2005 National Championship team.  Additionally, Texas has the smallest differential between the two ratios of any team on this list, meaning that they are very steady offensively, just as they are defensively.  What you get one game is very likely to be what you get the next.  Considering what Texas has done so far in its first seven games, I'd say that's a very good thing.  Also note that on both offense and defense, Oklahoma State is actually surprisingly mediocre in terms of the elite of these conferences.

But what about those SEC offenses?  Well, LSU isn't very good.  They're the worst of this group on both offense and defense, and it's not really very close in either category.  Alabama's a little below Oklahoma State--that is, mediocre for an elite team.  Florida is actually pretty good, just a little off of Texas' pace.

So what does it all mean?  Well, it seems to me that Texas' defensive stats are perhaps slightly behind Florida's but ahead of Alabama's, and Texas' offensive stats are slightly ahead of Florida's and well ahead of Alabama's.  Neither Florida nor Alabama is particularly erratic (the UF/Ole Miss debacle notwithstanding), but Texas is a pillar of consistency.  At least given the games that have been played so far, Texas has shown that they perform at pretty much the same relative level in every game, when you take into account their opponents.  That bodes well for the future, considering how well Texas has played so far this year.

As for Year2's assertion that this Texas team doesn't have an elite defense, well, I respectfully disagree my friend, and I hope the above has shown you that there is more than one way to skin a statistical cat, and some of those methods are better than others.  Perhaps you should have said that the 2008 Longhorns don't have as much offensive firepower as the 2005 team.  That would have been a lot closer to correct.

And as for you, Mr. Mark Schlabach, how about you go back to the drawing board writing table(?) and instead of writing an article about how we're not sure if Texas is good because they haven't played anyone with a defense, you write about how we're not sure Alabama's good yet because if they play Texas in the national championship game, they'll be going up against a defense that's seen the kitchen sink that Big 12 offenses throw out there and is still just as good as those SEC defenses, and they'll also be going up against an offense better than any they've seen this year.

That is, if you're into writing such prospective and meaningless articles.  Me?  I'd just like to beat Oklahoma State, Texas Tech, Baylor, Kansas, Texas A&M, and the Big 12 North champ first before we start thinking about things like that.  But I guess that's why I don't get paid to write about this stuff.  It's that vision thing...