How do you solve a problem like McFadden, part II

WARNING: ERRONEOUS ZONE. LAWYER PLAYING WITH LOADED MATH.

This morning we looked at the fear that is running rampant through the hills of Tennessee this week concerning Darren McFadden's upcoming visit to Neyland Stadium. The fear's well-founded and based primarily on the following facts: (1) Arkansas' rushing offense is No. 2 in the nation; (2) McFadden and partner McFelix Jones hung 487 yards on Steve Spurrier last week; and (3) Tennessee's rush defense is ranked 74th in the nation.

But here's the thing. The rushing defenses of six of Arkansas' opponents this season are ranked 92nd or worse in the nation. Even allowing for the fact that part of the reason they're ranked so low is that they had to play Arkansas, that's still not very good. When Arkansas played Alabama (38th in rush defense) and Auburn (24th in rush defense), they lost. They also lost to the next worst rushing defense, Kentucky (92). So maybe, just maybe, that No. 2 ranking for rushing offense is a bit inflated.

ARKANSAS
DATE
OPPONENT
RESULT/TIME
RUN DEFENSE RANK
RUN DEFENSE YARDS (per game)
09/01 Troy 46-26
103
205.78
09/15 at Alabama 41-38
38
126.44
09/22 #21 Kentucky 42-29
92
192.67
09/29 N Texas 66-7
107
209.38
10/06 UT-Chatt 34-15
(I-AA)
(I-AA)
10/13 #22 Auburn 9-7
24
114
10/20 at Ole Miss 44-8
105
208
10/27 Fla Int'l 58-10
99
204.11
11/03 S Carolina 48-36
104
206.50

And what about Tennessee's national rank of 74th in rushing defense?

TENNESSEE
DATE OPPONENT RESULT/TIME RUN OFFENSE RANK RUN OFFENSE YARDS (per game)
09/01 at #12 California 45-31
T-50
166
09/08 So Miss 39-19
28
190.78
09/15 at #5 Florida 59-20
29
189.44
09/22 Arkansas St 48-27
37
175.33
10/06 #12 Georgia 35-14
40
173.67
10/13 at Miss St 33-21
66
149.78
10/20 at Alabama 41-17
62
153.33
10/27 #16 S Carolina 27-24
95
121.60
11/03 La Lafayette 59-7
8
241.56

Hmm. Again, we've done our part to make those stats what they are, certainly. But is it too far out of line to conclude that our poor run defense ranking is at least partially a result of playing against good running teams while Arkansas' exceptional run offense ranking is at least partially a product of playing against teams with a poor running defense? You tell me. I'm thinking that Arkansas is still an excellent running team -- the best we'll play this year, no doubt -- and that we're still not very good at stopping the run, but the numbers aren't as bad as they seem at first blush and the situation isn't as hopeless as it seemed earlier in the week.

Wouldn't it be wonderul if we could determine how many yards we should expect the Hogs to put up on us this week? That's what I thought. I figured it would be easy enough to look at the yards gained by the Hogs against their opponents and extrapolate the numbers to determine what we should expect the Hogs to gain against our No. 74 rush defense. Eventually, I figured out that I didn't want to "extrapolate" but "interpolate." No problem, I thought to myself, how hard can that be? Well . . .

Okay, then. Look, it's no great secret that lawyers chose law due to acute allergies to mathematics, so let's do the poor man's interpolation, where poor = "dumb at numbers".

Test Case! Tennessee's currently ranked (very!) roughly midway between Alabama and Kentucky in rush defense nationally. Alabama's giving up 126.44 yards per game and Kentucky's giving up 192.67 yards per game. So we should be giving up roughly, what, 166 yard per game? Checking . . . it's actually 167.67.

TEAM
RANK
YARDS
Best (Boston College) 1 58
AR opponent (Auburn) 24 114
AR opponent (Alabama) 38 126.44
Tennessee 74
in sealed envelope . . . 167.67, which is very close to 166 according to my calculator!
AR opponent (Kentucky) 92 192.67
AR opponent (Florida Int'l) 99 204.11
AR opponent (Troy) 103 205.78
AR opponent (South Carolina) 104 206.5
AR opponent (Ole Miss) 105 208
AR opponent (North Texas) 107 209.38
Worst (UAB) 119 248.7

Okay, so so far so good, and my, that's a lot of sos. But the system works sort of. So now for the real thing. Alabama gave up 301 yards to Arkansas, and Kentucky gave up 338. And boy am I glad that Kentucky didn't actually give up fewer yards than did Alabama or my head would have exploded and this post would have been entitled: Using Math to Paint Yourself Into a Corner.

Anyway, the magic number for the Vols this weekend appears to be . . . drumroll . . . about 318. As in yards the Razorbacks should get against our defense on the ground. Which is not good, but not entirely not good. The three teams that have rushed for the most yards against us are the Bears (230) (beatdown), the Gators (255) (blowout), and the Ragin' Cajuns (234) (blowout in the other direction). So although it's unlikely, Tennessee could win the game even if Arkansas gets 318 yards on the ground. Remember, Georgia is currently averaging 173.67 yards per game, and we held them to 69. Let's do that again, shall we?

Apologies to hooper, our resident nuclear engineering grad student, who must be banging his head against his monitor right now. Somebody get him some BC.

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