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More on Stuffs per rush against

By ricobert1

If you remember back to Monday's update piece on 2010 Stuffs and the original post from '09, we talked about how the NCAA's rushing yardage is all screwy because of their inclusion of sacks. And tackles-for-loss (TFLs) include all negative yardage plays, even though we know that a sack occurs on a pass play while a run stuff occurs (surprise) from a running play. My simple way around this was to remove sacks from TFLs to get a Stuff metric (i.e., TFLs - Sacks = Stuffs). This is nice because it allows for easy calculation and - using CFBStats.com - we can easily calculate conference and national numbers with the nimble use of copy/paste into an excel spreadsheet (note on execution: use "paste special" and choose Unicode Text).

For the 2010 season update, I took into account a per-rushing-play-against to try to gauge which teams were stopping opponents in the backfield for rushing plays only. That was the "Stuffs.pP" percentage, indicating on what percentage of plays did a particular defense stuff an opposing offense's running play.

The ACC results were interesting. The top 8 teams featured an above-average rate, with 4 teams in the national top 12: BC (4th), Miami (8th), NC State (11th), and Clemson (12th). Note that each team finished the season in the top 25 of S&P rush defenses as well (2nd, 19th, 23rd, and 6th, respectively). FSU was 9th in the conference, yet fielded a 40th ranked rush defense.

This begs the question: Is there any correlation between a defense's Stuff rate and their rush defense ranking? TN poster orinole stated this:

...what are your thoughts about actually using this as a metric to measure defense improvement? Or toward indicating the overall defensive prowess if you will? I'm not sure how many conclusions can be drawn on stuffs...

Along with Nolesos Locos' suggestion, I added FootballOutsiders' S&P rush defense ranking. Let's run some statistics using everyone's favorite open-source statistical software platform R.The data we'll be using for this analysis is located here. Note: You don't need to download it to run the software - we'll make an http call to the needed file. You can copy-and-paste the code in the shaded boxes below if you'd like to reproduce the analysis.

#Read in data to R and display

stuffs = read.csv("http://myweb.fsu.edu/reh3682/data/fun/Stuffs2010.csv",T); head(stuffs)

#Perform correlation test

cor.test( stuffs$Rush.D.Rk, stuffs$Stuffs.pP2)

    Pearson's product-moment correlation

data:  stuffs$Rush.D.Rk and stuffs$Stuffs.pP2
t = -4.9805, df = 118, p-value = 2.19e-06
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.5545874 -0.2567115
sample estimates:
       cor
-0.4167756

What we see here is a significant negative correlation between team S&P rush defense rank and Stuffs per rush against. That is, a team's S&P rush defense rank should be lower if they have a high Stuffs per rush against. That makes sense; maybe even obvious sense. But it's good to see that the relationship is there, and follows logic. (Note that Stuffs per rush against only explains about 17% of the total variance in a team's S&P rush defense rank, so it's not an end-all/be-all metric.)

What about the top 30 defenses? Do the higher ranked run-stopping defenses (adjusted) still demonstrate a proclivity toward stuffing opposing runners?

#Perform correlation test for top 30 defenses

cor.test( stuffs$Rush.D.Rk[stuffs$Rush.D.Rk<31], stuffs$Stuffs.pP2[stuffs$Rush.D.Rk<31])

    Pearson's product-moment correlation

data:  stuffs$Rush.D.Rk[stuffs$Rush.D.Rk < 31] and stuffs$Stuffs.pP2[stuffs$Rush.D.Rk < 31]
t = -2.3166, df = 28, p-value = 0.02806
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 -0.66520737 -0.04767016
sample estimates:
       cor
-0.4010517

In short: Yes. Generally, the best rushing defenses stuff opposing running games.

E80jo0

 

Here is a scatterplot of all 120 teams' S&P rush defense rank and Stuffs per rush against (as a percentage of plays): Note the 3 outliers on the right-most part of the plot. From top to bottom, they are: Miami (Ohio), Kent State, and Southern Mississippi. So Nolesos Locos' hunch pays off, to the benefit of the Stuffs ~ Rush D. relationship. We know these are smaller schools that aren't getting that great a talent. But then how are these teams getting such a high output on their Stuffs rate? Perhaps they are run-blitzing. The Dr.-turned-king suggested as much:

1zzriih_jpg

Let's add 10+ and 20+yard rushes to see if these or other teams are gambling with an aggressive scheme hoping to produce splash plays, but meanwhile giving up big plays. Ultimately, this could show who is gambling (all-or-nothing run coverages, below/average personnel) and who may have an incredible front 7 (vanilla run coverages, dominant personnel). Note that "10+pP" is the percentage of plays for which that defense gave up a run of 10 yards or more (and the same for "20+pP").

2010 Stuffs per rush against.
  Team Opp.Runs Stuffs Stuffs.pP Rush.D.Rk 10+pP 20+pP
1 Kent State 399 66 16.54% 61 11.28% 2.76%
2 Miami (Ohio) 413 67 16.22% 75 13.56% 4.84%
3 Southern Mississippi 379 61 16.09% 53 11.35% 4.49%
4 Boston College 381 60 15.75% 2 5.51% 1.57%
5 Mississippi State 409 64 15.65% 10 14.67% 2.20%
6 Arizona State 418 65 15.55% 8 10.77% 1.44%
7 Auburn 413 64 15.50% 21 12.59% 2.42%
8 Miami (Florida) 510 78 15.29% 19 15.69% 4.31%
9 Oklahoma 467 69 14.78% 12 15.85% 5.35%
10 Boise State 413 61 14.77% 4 11.14% 4.12%
11 North Carolina State 391 57 14.58% 23 12.02% 4.09%
12 Clemson 451 65 14.41% 6 14.63% 2.44%
13 Oregon 441 63 14.29% 22 13.15% 3.63%
14 Northern Illinois 429 61 14.22% 69 12.82% 3.96%
15 USC 389 55 14.14% 49 16.71% 4.88%
16 Purdue 428 60 14.02% 43 15.89% 1.64%
17 Rutgers 425 59 13.88% 54 14.12% 4.94%
18 Illinois 411 57 13.87% 9 10.95% 3.16%
19 Vanderbilt 499 69 13.83% 47 14.03% 4.01%
20 Northwestern 450 62 13.78% 111 15.78% 5.56%
21 San Diego State 494 67 13.56% 52 13.36% 3.24%
22 Florida 460 62 13.48% 24 12.83% 1.52%
23 Nevada 394 53 13.45% 85 12.94% 3.55%
24 UCF 419 56 13.37% 41 11.69% 2.15%
25 Mississippi 382 51 13.35% 55 15.45% 4.45%
26 Ohio State 382 51 13.35% 7 12.04% 1.83%
27 Connecticut 451 60 13.30% 64 14.19% 3.10%
28 South Florida 439 58 13.21% 36 11.39% 2.05%
29 TCU 364 48 13.19% 17 10.44% 2.75%
30 South Carolina 426 56 13.15% 3 10.80% 3.52%
31 Minnesota 428 54 12.62% 67 18.69% 6.31%
32 Virginia Tech 430 54 12.56% 48 16.98% 5.35%
33 Memphis 455 57 12.53% 77 15.16% 3.74%
34 UAB 409 51 12.47% 95 14.43% 4.16%
35 Texas A&M 452 56 12.39% 14 12.39% 3.10%
36 Idaho 462 57 12.34% 98 18.61% 6.28%
37 Western Kentucky 415 51 12.29% 118 17.83% 5.06%
38 Florida International 442 54 12.22% 103 15.61% 5.20%
39 Maryland 452 55 12.17% 28 11.95% 1.99%
40 LSU 444 54 12.16% 37 13.06% 3.38%
41 Arkansas 487 59 12.11% 26 13.76% 3.29%
42 BYU 438 52 11.87% 33 12.10% 4.11%
43 Troy 448 53 11.83% 100 16.29% 5.36%
44 Fresno State 415 49 11.81% 78 16.63% 6.02%
45 Alabama 408 48 11.76% 11 11.03% 3.19%
46 Florida Atlantic 519 61 11.75% 87 16.18% 3.47%
47 Indiana 392 46 11.73% 72 16.33% 4.85%
48 Wake Forest 469 55 11.73% 96 15.99% 4.26%
49 Cincinnati 439 51 11.62% 58 8.43% 2.28%
50 Arizona 448 52 11.61% 15 12.72% 2.01%
51 Tennessee 448 52 11.61% 73 13.39% 3.57%
52 Tulsa 405 47 11.60% 51 12.84% 3.46%
53 Penn State 466 54 11.59% 34 13.73% 2.79%
54 West Virginia 365 42 11.51% 5 9.86% 2.47%
55 Utah 422 48 11.37% 1 9.72% 2.37%
56 Middle Tennessee 556 63 11.33% 107 13.85% 5.22%
57 Houston 505 57 11.29% 101 15.84% 4.75%
58 Virginia 461 52 11.28% 109 15.40% 6.07%
59 Georgia 488 55 11.27% 39 13.52% 2.87%
60 Kentucky 482 54 11.20% 94 16.39% 3.73%
61 Washington 502 56 11.16% 82 13.75% 4.38%
62 Louisville 433 48 11.09% 68 14.55% 3.00%
63 Western Michigan 433 48 11.09% 71 15.01% 5.31%
64 Louisiana-Lafayette 429 47 10.96% 91 15.62% 4.66%
65 Buffalo 487 53 10.88% 59 11.91% 1.64%
66 Wisconsin 400 43 10.75% 35 13.50% 2.75%
67 Oregon State 476 51 10.71% 29 14.08% 2.52%
68 Texas 448 48 10.71% 38 12.28% 3.35%
69 Michigan State 431 46 10.67% 31 12.99% 1.86%
70 California 404 43 10.64% 32 13.37% 2.23%
71 Washington State 452 48 10.62% 110 17.70% 6.42%
72 Texas Tech 484 51 10.54% 44 11.78% 2.48%
73 Missouri 447 46 10.29% 56 11.63% 3.58%
74 Marshall 419 43 10.26% 50 14.56% 4.06%
75 Syracuse 461 46 9.98% 60 9.98% 3.04%
76 Army 401 40 9.98% 90 15.96% 3.74%
77 Ohio 434 43 9.91% 97 9.68% 2.53%
78 Central Michigan 435 43 9.89% 92 13.10% 3.68%
79 Florida State 480 47 9.79% 40 11.04% 2.50%
80 Michigan 536 52 9.70% 86 14.74% 3.36%
81 Colorado 392 38 9.69% 30 16.07% 4.59%
82 Colorado State 458 44 9.61% 105 17.25% 4.80%
83 Notre Dame 439 42 9.57% 13 12.07% 2.51%
84 Pittsburgh 409 39 9.54% 62 13.69% 2.44%
85 Toledo 409 39 9.54% 83 11.00% 3.18%
86 Tulane 441 42 9.52% 116 18.14% 4.99%
87 Stanford 370 35 9.46% 20 16.49% 3.78%
88 Baylor 487 46 9.45% 93 14.17% 3.49%
89 UCLA 448 42 9.38% 70 17.41% 5.13%
90 Iowa 386 36 9.33% 18 9.59% 1.30%
91 Eastern Michigan 443 41 9.26% 114 19.64% 5.64%
92 Hawai'i 494 45 9.11% 45 11.54% 1.82%
93 East Carolina 538 49 9.11% 108 17.10% 4.83%
94 Akron 440 40 9.09% 63 12.95% 3.86%
95 Bowling Green 457 41 8.97% 112 14.00% 3.06%
96 Air Force 536 48 8.96% 79 13.81% 2.99%
97 Louisiana-Monroe 414 37 8.94% 81 14.73% 4.35%
98 San Jose State 497 44 8.85% 104 14.69% 4.43%
99 Ball State 453 40 8.83% 115 14.57% 2.21%
100 Kansas 478 42 8.79% 99 15.90% 3.35%
101 North Carolina 411 36 8.76% 27 10.71% 2.19%
102 Georgia Tech 472 41 8.69% 76 13.56% 3.39%
103 Louisiana Tech 454 39 8.59% 80 12.56% 3.08%
104 Iowa State 501 43 8.58% 66 12.38% 1.40%
105 Temple 435 37 8.51% 74 9.20% 1.84%
106 SMU 521 44 8.45% 42 9.21% 1.34%
107 Oklahoma State 470 39 8.30% 16 11.28% 2.13%
108 Duke 507 41 8.09% 65 15.78% 3.35%
109 Arkansas State 526 42 7.98% 89 12.55% 2.85%
110 New Mexico 556 44 7.91% 117 15.47% 3.24%
111 New Mexico State 418 33 7.89% 119 17.46% 6.70%
112 Utah State 426 33 7.75% 106 17.14% 3.52%
113 Kansas State 487 37 7.60% 84 17.25% 6.37%
114 UTEP 479 36 7.52% 120 12.32% 2.30%
115 Wyoming 518 38 7.34% 102 13.51% 1.54%
116 Navy 452 33 7.30% 57 15.71% 3.54%
117 North Texas 455 32 7.03% 88 16.26% 3.96%
118 UNLV 542 36 6.64% 113 15.13% 3.14%
119 Rice 411 24 5.84% 46 11.92% 2.19%
120 Nebraska 519 29 5.59% 25 11.75% 3.47%

Boston College does an insanely good job at both (#5 in Stuffs.pP, #1 in least 10+ yard rushes allowed rate). FSU is actually 17th in 10+ yard rushes allowed rate.

We've already shown that there is a nice correlation between a team's Stuffs rate and their S&P rushing defense rank. So let's see if, through the same statistical test, there's a relationship between a team's S&P rushing defense rank and their 10+ and 20+ yard rushes-allowed rate:

cor.test(stuffs$Rush.D.Rk,stuffs$Ten..pP2)

    Pearson's product-moment correlation

data:  stuffs$Rush.D.Rk and stuffs$Ten..pP2
t = 7.2059, df = 118, p-value = 5.895e-11
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.4146318 0.6660386
sample estimates:
      cor
0.5527903
cor.test(stuffs$Rush.D.Rk,stuffs$Twenty..pP2)

    Pearson's product-moment correlation

data:  stuffs$Rush.D.Rk and stuffs$Twenty..pP2
t = 5.8627, df = 118, p-value = 4.232e-08
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.3232234 0.6028675
sample estimates:
      cor
0.4749486

Assuming you're not asleep now, the above test isn't very mind-blowing: Good rushing defenses limit big plays against. The 2009 FSU Seminole defense proves the corollary to that relationship.

What now? Well, we have two covariates for which we know can help describe a team's rushing defense aptitude: Stuffs per rushing play against rate, and 10+ rushes allowed rate. Let's incorporate this into a multivariate model. From that, we can answer a question like: Which variable describes the change in a team's S&P rushing defense rank more strongly?

Maybe I'll demonstrate this model in the future, but I'm risking losing the rest of you; so I'll summarize the findings:

  • It turns out that, while Stuffs rate is important, the ability of a defense to lower the rate of 10+ yard rushes against is roughly 2.5 more times important toward a team's S&P rushing defense rank.

So it pays to stop the bleeding first by limiting the big rushes against. As FSU's defensive personnel increase in experience and girth, I would expect both of those covariates and their final S&P rushing defense rank to improve as well.

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