## Defensive Bend-ex

Well, it could be worse...

So, remember when we were playing Missouri and the fans said that Missouri was a bend-don't-break defense?

Actually, I feel like almost everyone describes their system as bend-don't-break. Well, that got me thinking: what does a bend-don't-break (BDB) defense look like? Are those defenses good? Are BDB defenses better, on average, than their breaking counterparts?

I theorize that there should be a Defensive Bend-ex (Defensive Bend Index).

So I grabbed some data from cfbstats.com and went to work. I used the total defense and scoring defense stats, which meant I could extrapolate yards per point, plays per point, yards per game, etc. Then I played around with numbers and got a metric to give a scale of how bendy defenses are.

Turns out, this isn't exactly a trivial task, mostly because I don't exactly know what a bend-don't-break defense is. I think you could make cases that any of the following scenarios are classic bend-don't-break hallmarks:

• Give up a lot of yards in the orange zone (I made this term up) but stiffen up after that (say, force long field goals or short punts)
• Give an abnormally high number of field goals as opposed to touchdowns
• Give up less points than yards per game would suggest

Of these, I can't really test the first, because I don't have yards-to-go splits. I can, however, sort of test the second and third points. I ran a metric for each.

But first...

Unfortunately, this is more like us than the first image.

The Metric

So, I just wanted to make a really concise stat that can act as a cursory style of play reference. Like, "Is Missouri a bend-don't-break defense?" This should not necessarily give an insight into quality; really great defenses can be BDB, as can really terrible ones.

So, I tried a couple different score metrics out: yards per point (YPP Score), plays per point (the confusing PPP Score), FG/TD (FGTD Score), Adjusted YPP Score (adjYPP Score), and ExpPPG Score (ePPG Score).

To make the score, I averaged out the statistic in question (take yards per point) then reported a standard deviation (I just used the stdev function in Excel, because I forget which special things do what). I then found the difference in the value for a team by the average for all of CFB, then divided by the standard deviation. This tells you how many standard deviations a team is from the average.

This should be a normal distribution, so a simple scale is...

via i.imgur.com

For example, gaining 14.4 yards on Tennessee's defense results in one point (on average). The average defense allows 15 yards per point (standard deviation of 2.47 yards per point). Thus, our YPP Score would be:

(14.4-15)/(2.47) = -.25

This would imply that we're not a bend-don't-break defense (but, it essentially means nothing, and that we're in the big fat middle of yards per point).

Yards per point works OK, but I think it is dependent on special teams. Teams with a very high yards per point average are probably forcing long drives from kickoffs and punts. This is true for any of the metrics I'd use, however. Other issues are that the metrics don't always track with each other, especially the YPP or PPP metrics with the expPPG metric. I don't have realy concrete theories as to why that is.

Field Goals to Touchdown Ratio

Here's the thing: I don't like this metric. It turns out, defenses that are terrible allow more touchdowns than field goals. Obviously. But, theoretically you'd see bend-don't-break defenses on both the really high and really low ends of the total defense scale; that's not really the case with FGTD Score. Almost all of the good defenses are high on the list, while almost all of the bad ones are low on the list. We are -1 on this scale (we give up a lot of touchdowns compared to field goals).

When I put together the Yards Per Point metric, I noticed that teams with good defenses seemed to be higher on the YPP metric than other teams. This would imply that defenses that give up less points per game overall also tend to give up a higher amount of yards per game than you'd expect. That makes sense. However, that doesn't really answer my question.

Example: Florida State allowed 268.5 ypg and 10.7 ppg, which gives a YPP Score of 4.08 (which is ludicrously high, but this is college football, and there are lots of anomalies). But, if we see a general trend that defenses naturally allow more yards per point as they get better, is FSU's defense really more bend-don't-break than you'd expect?

To test that, I put together a graph of YPP Score vs. PPG:

via i.imgur.com

By taking the difference of the raw YPP Score from the expected YPP score (as a function of PPG), we can give the adjusted score (renormalized), which I actually like. Still, this weighted towards good defenses (which are usually bend don't break).

expPPG Score

To give another metric, I graphed YPG vs. PPG and made a YPG function:

via i.imgur.com

I then normalized the difference between what the regression would suggest a defense would give up (in PPG) as a function of YPG.

This metric actually was pretty scattered throughout good and bad defenses, which I wanted.

Missouri

By any of these metrics, Missouri is a bend-don't-break defense: 1.26 YPP Score, .77 PPP Score, .87 FGTD Score, 1.77 adjYPP Score, 1.94 expPPG Score. But, it's worth nothing that Missouri finished 71st in YPG (partially influenced by the Auburn Experienced), so they weren't exactly a good defense, either.

But that makes sense: this isn't supposed to tell you if a defense is good or not, it's supposed to give a sense of style.

Any tips or discussion is welcome.

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