For Texas fans, the last month or so has been...well, what's like like a roller coaster, except one that rockets down but never comes back up? A plunging elevator?

A rollicking season-opening victory over the Fighting Irish promised a great season but quickly resolved into disappointment as Texas has lost in miserable fashion to mediocre team after mediocre team. Cal, Okie Lite, K Steak. Plus another L to the hated Sooners, which made my right-sided sunburn and $12 State Fair turkey leg a miserable consolation.

This, despite the fact that - without a trace of a doubt - the offensive curse that has befuddled the Longhorns since Colt McCoy graduated has ended. We've got a genuinely solid offense led by an All-Conference running back, an offensive line that's generally doing its job on any given snap for the first time in years, a revitalized receiving corps, and an impressively unflappable true freshman quarterback with a gift for sideline dime-dropping.

So what gives? The defense.

The reasons for this perplexing defensive disintegration have been discussed here and elsewhere at length. The ends pass rush OK sometimes but don't contain well. The linebackers are perpetually late to their run fits and wilt when blocked. The cornerbacks got so confused we not only whittled the playbook down to a notecard mid-season, we're also using QB wristbands to attach said notecard to everyone's forearm. The safeties and defensive tackles are the only ones dependably doing their jobs, and even with those units there's occasional reason to gripe.

Still, this is describing symptoms, not the disease. These players should be better than last year, just by sheer dint of playing in the same system twelve more months. Yet so far they're demonstrably worse as a unit than they were in 2015. Why?

Here's one idea: perhaps the coaching staff, when they committed to moving to a fast-paced Baylor-style offense in the offseason, failed to understand or appreciate that their defensive coaching style would need to change to both (a) fit the high-intensity repetition the offense requires in practice while (b) still giving their defensive charges the responsive instruction they need to continue learning their positions.

As it turns out, this theory is fairly easy to test. Pace is one of the few elements of gameplay that's almost exclusively a function of coaching tactics and strategy and can be easily adjusted for run-pass balance and competition. We can run simple correlations between adjusted pace and performance, and between changes in pace and changes in performance, and see what's up.

So...here's what's up:

Just for your edjamacation, here's how adjusted pace and adjusted offensive performance correlate in FBS since 2008.

Which is to say: they don't correlate. At all. There are fast-paced teams with great offenses, there are fast-paced teams with horrible offenses. There are slow teams with excellent offenses, there are slow teams with godawful offenses. The performance trendline actually goes down as pace goes up but the correlation itself is so weak that calling it "insignificant" is giving it too much credit. You might make a case that, if you squint, better offenses are more evenly distributed across the range of pace while crappy offenses tend to cluster a little closer around the average. Otherwise, this is almost a textbook example of what statistical independence looks like.

And here's a comparison between the change of pace from one year to the next and offensive performance:

Again, very little correlation between the amount of change and the positive/negative effect on offensive performance. If you're speeding up pace dramatically to improve your offensive effectiveness, that's a coin flip proposition, not a sure thing. Indeed, the Texas offense's improvement in 2016 is well above average in this regard. Not quite an outlier but nearly two standard deviations above the norm.

The main takeaway of this should be: increasing pace doesn't necessarily make your offense more effective. It's only guaranteed to give you more snaps. Some teams and coaches manage it very effectively but an equal number of them don't.

Now this is where things get interesting: change in pace vs. change in defensive performance:

This is what a real correlation of first derivatives looks like: teams that don't change much tend to cluster around the middle, but teams that speed up a lot tend to lose defensive efficiency while teams that slow down a lot tend to gain it. Of special note: teams that hurry up their average play by 4 seconds or more in a single season almost all lose defensive efficiency.

Texas' increase in pace this year? 3.84 seconds. And perhaps-not-coincidentally, we've somehow turned a bad defense even worse.

Here's the fastest-paced teams in the dataset (since 2008):

Out of 1471 seasons between 128 FBS teams, the Strong/Gilbert combo has given us the 25th fastest-paced.

Take Baylor out of this group and it's not especially impressive in terms of overall performance. And the reason why is obvious: look at the rightmost two columns. That's defensive S&P ranking and the change in ranking, respectively. Look at all that red. Precisely five of these teams have above-average defenses - two by Baylor, two by BYU. Meanwhile 40% are ranked 100th in defense or worse. And while the offenses have been generally good, they're not consistently good. Many are downright poor. Only 2 of 25 were considered top 25 S&P+ teams overall in their year.

Here's the fastest-paced teams in the current season:

Maybe it's time to recognize that Baylor is doing something impressively rare this year, I suppose? Nah.

Of the top 20 teams in pace, only four are playing considerably better overall (up 10 spots or more) than they did last year. Half are playing considerably worse. And some of the defensive performances on this list are galling - 12 of these teams are playing worse defense than Texas. And collectively, the tradeoff in offensive performance barely makes up for it. Of these 25 teams, despite the presence of a couple excellent squads, their overall record is exactly .500.

Let's compare this to the slowest 25 teams this year:

These teams are winning about 75% of their games and appear to be doing about as well offensively as the other group, and defensively they're blowing them out of the water.

So. Um.

Let me say, first and foremost, that this is not proof that high pace is "bad" and slow pace is "good".

In my opinion, what this data mostly shows is that, within typical ranges, both pace and changes in pace don't matter.

But at the extremes, a high speed offense, whether measured in terms of overall pace or the rate of change of pace from one year to the next, can make defensive performance hard to manage. Some coaches balance it reliably well. But many more are defensively inconsistent. And a handful don't even appear to be trying (howdy Kliff!).

The best part of this article, however, should be in comments. As time permits over the next couple of days, I'll be posting these stats for individual teams from 2008-2016 in the comment section. Several of them make for great case studies, and some will tell surprising stories.

I'll finish off with Texas' pace and S&P+ numbers:

We've been through two large upswings in pace before 2016, but those levels of pace were all within spitting distance of the global average. As I've said, those kinds of fluctuations don't seem to matter much. What seems to matter most is when you make a bigger jump, or jump to extremes. This year we're flirting with doing both.

Also: while none of us feel incredibly impressed with this year's overall performance so far, on paper it actually looks pretty good in relation to the field. We're up 27 spots in the overall rankings from last year. The problem isn't that the team is downright awful (it's not), it's that despite shoring up the offense, the head coach is utterly failing at his core competency and as a result we're flirting with missing bowl season yet again. And those two facts collectively kneecap the case for keeping Strong for another year.

If there's any other teams you want to see in comments, let me know. I'll be posting pretty much team/coach of obvious interest though.