Ranking Defenses Based on Difference Compared to Average

Submitted by Gameboy on October 31st, 2012 at 2:21 AM

Offense and defense rankings based on total numbers and straight averages can be misleading at times. If a team plays opponents with strong rush offense but weak pass offense, the team's pass defense stats might look better than what they really should be. This is something Michigan was being accused of due to the fact that much of our "bad" defensive games came against strong rushing teams (Alabama and Air Force).

One way to mitigate this "effect" would be to not look at the totals and average numbers, but compare the game output against the average output the opponent has produced against all opponents. This produces numbers that show you how good your performance was compared to all other team that your opponent has played. It is more useful comparative method than using just total numbers.

So, exactly how does it work?

Here are the stats for Michigan so far this year:

Opponents Rush Net Total Pass Yds Total Total Yds Pts Avg Rush Total Avg Pass Total Avg Total Offense Avg Scoring Offense
Alabama 232 199 431 41 214.38 222 436.38 40.63
Air Force 290 127 417 25 366.25 114.38 480.63 34.5
Massachusetts 112 147 259 13 101.375 169.125 270.5 11.25
Notre Dame 94 145 239 13 196.5 193.25 389.75 26.38
Purdue 56 162 218 13 161.25 220.25 381.5 30.88
Illinois 105 29 134 0 132.5 184.88 317.38 18
Michigan St. 112 192 304 10 131.22 229.11 360.33 19.22
Nebraska 160 166 326 23 264.13 225 489.13 39.25
Average All Opp 145.1 145.9 291.0 17.3 196.0 194.7 390.7 27.5

 

Opponents Avg Rush Off Diff Avg Pass Off Diff Avg Total Off Diff Avg Scoring Off Diff
Alabama 8% -10% -1% 1%
Air Force -21% 11% -13% -28%
Massachusetts 10% -13% -4% 16%
Notre Dame -52% -25% -39% -51%
Purdue -65% -26% -43% -58%
Illinois -21% -84% -58% -100%
Michigan St. -15% -16% -16% -48%
Nebraska -39% -26% -33% -41%
Average All Opp -24% -24% -26% -39%

The first four columns of stats represent the actual stats from the game played against Michigan. The second set (of four) columns are the average output of that team against all opponents this year. The last set (of four) columns second table are the differences in percentage of actual game stat versus the total year averages.

As you can see from the table, Alabama produced their average offensive output against Michigan while Purdue and Illinois barely produced about half of their normal offensive output.

By averaging all of the averages, we find that our defense is reducing our opponents' normal offensive output by about 25%, while only allowing only 61% of their normal scoring output.

Sounds pretty good, but how does that compare to rest of NCAA?

I didn't have enough time to calculate the differential averages for every team in NCAA, but I did the analysis for top 10 Pass/Rush/Total defensive teams and all of Big Ten (plus ND). I did not include stats against FCS opponents. Here it is ranked by total offense differential.

Rk School Avg Rush
Off Diff
Avg Pass
Off Diff
Avg Total
Off Diff
Avg Scoring
Off Diff
1 Alabama -64% -34% -49% -71%
2 LSU -50% -30% -37% -45%
3 Florida St. -34% -36% -36% -51%
4 BYU -45% -29% -31% -44%
5 Michigan St. -50% -15% -30% -46%
6 Michigan -24% -24% -26% -39%
7 Notre Dame -56% -15% -25% -65%
8 Connecticut -18% -24% -23% -24%
9 Wisconsin -29% -17% -21% -31%
10 Maryland -34% -11% -21% -11%
11 Bowling Green -32% -15% -18% -39%
12 Boise St. -15% -19% -16% -44%
13 Stanford -62% 3% -15% -37%
14 Oregon St. -39% 4% -15% -39%
15 Nebraska -1% -24% -14% -7%
16 Fresno St. -14% -18% -14% -24%
17 Arizona St. 5% -32% -14% -17%
18 Rutgers -41% -5% -13% -39%
19 Penn St. -39% 9% -13% -35%
20 Minnesota 16% -30% -9% -1%
21 Iowa -1% -17% -8% -20%
22 Illinois -12% -4% -6% 5%
23 Ohio St. -31% 9% -5% -20%
24 Vanderbilt 14% -16% -1% -18%
25 Northwestern -19% 13% 1% -13%
26 Purdue 14% 6% 11% 15%
27 Indiana 17% 17% 18% 19%

Few things that stand out:

  • Alabama, LSU, and Florida St defense stand above the rest
  • Michigan and Michigan St defenses stand above the rest of B1G
  • Michigan is pretty good at both run and pass defense
  • Ohio St pass defense is HORRIBLE!
  • BYU defense is much better than I thought
  • Many of the defenses highly ranked in one (pass or rush) only because they are so horrible at the other (I am looking at you Arizona St, Stanford, Nebraska and Oregon St!)
  • Notre Dame is living on borrowed time - their scoring differential is MUCH higher than what rest of the defensive differentials would indicate

I do believe converting straight up numbers to percentages makes it much easier to compare between pass/rush and between different teams. I hope most of you find this useful. If I get enough upvotes, I will do the same analysis for offense as well.

Comments

Finance-PhD

October 31st, 2012 at 4:12 AM ^

I am a math guy so I love to see these types of posts. Thank you for the work. I can't vote up or give points but I do hope others will.

 

I found the difference in Run vs Pass for ND interesting. Is it that the teams they play do not pass much and so there was not as much to take down or is it a weak secondary compare to the front 7?

burtcomma

October 31st, 2012 at 4:55 AM ^

Nice work, a definite upvote.  While looking at the data, I wondered about the effect both defensive turnovers created and turnover margin might have on the yardage stats as another way to say that good defenses force turnovers and how that might relate to the differences in terms of overall yardage pct. vs scoring diff pct.

I added the data here, I think this more likely explains what you refer to as ND living on borrowed time......

 

Rank School Avg Rush Off Diff Avg Pass Off Diff Avg Total Off Diff Avg Scoring Off Diff Avg Scoring Diff - Total Diff Def. T/O's Off. T/O's T/O Diff.
1 Alabama -64% -34% -49% -71% -22% 23 6 17
2 LSU -50% -30% -37% -45% -8% 21 12 9
3 Florida St. -34% -36% -36% -51% -15% 11 14 -3
4 BYU -45% -29% -31% -44% -13% 11 17 -6
5 Michigan St. -50% -15% -30% -46% -16% 11 10 1
6 Michigan -24% -24% -26% -39% -13% 13 17 -4
7 Notre Dame -56% -15% -25% -65% -40% 18 8 10
8 Connecticut -18% -24% -23% -24% -1% 11 18 -7
9 Wisconsin -29% -17% -21% -31% -10% 9 9 0
10 Maryland -34% -11% -21% -11% 10% 12 22 -10
11 Bowling Green -32% -15% -18% -39% -21% 17 11 6
12 Boise St. -15% -19% -16% -44% -28% 23 12 11
13 Stanford -62% 3% -15% -37% -22% 18 10 8
14 Oregon St. -39% 4% -15% -39% -24% 17 10 7
15 Nebraska -1% -24% -14% -7% 7% 12 20 -8
16 Fresno St. -14% -18% -14% -24% -10% 23 13 10
17 Arizona St. 5% -32% -14% -17% -3% 16 14 2
18 Rutgers -41% -5% -13% -39% -26% 22 13 9
19 Penn St. -39% 9% -13% -35% -22% 16 8 8
20 Minnesota 16% -30% -9% -1% 8% 11 14 -3
21 Iowa -1% -17% -8% -20% -12% 15 7 8
22 Illinois -12% -4% -6% 5% 11% 14 20 -6
23 Ohio St. -31% 9% -5% -20% -15% 15 14 1
24 Vanderbilt 14% -16% -1% -18% -17% 8 11 -3
25 N'Western -19% 13% 1% -13% -14% 15 9 6
26 Purdue 14% 6% 11% 15% 4% 18 17 1
27 Indiana 17% 17% 18% 19% 1% 8 5 3

 

 

 

Ziff72

October 31st, 2012 at 12:54 PM ^

I love the analysis.  I think it is a much better indicator of a defenses play than the straight numbers.

The only major caveat I see to the numbers is a problem in comparing any college football stats lately and that is the tempo of the team.   Arizona and Oregon are never going to have top defensive stats because they generate so many plays in a game they create more possessions.  More possessions= more yards and more points.    I know Ohio St was trying to be more up tempo this year, but I'm not sure if they have been successful in that, but that could be a factor in their horrid stats.

My solution would be taking the avg yards per play and then comparing it to their avg yards per play against the seasons average.  I think this would give you a more accurate number.   Something to think about.  Great work though I loved looking at your numbers.

Gameboy

October 31st, 2012 at 1:57 PM ^

Actually, I think your concern is exactly what this analysis is addressing. This model de-emphasizes actual amount of yards.

Take Oregon for example. They average something like 550 yards of offense every game. If Michigan played them and allowed 400 yards of total offense, our rank woud go up even though we just allowed double the number of yardages compared to Illinois since, percentage wise, we did little better than expected.

Gameboy

October 31st, 2012 at 10:02 PM ^

That is a good point.

Here are the percentages for Oregon:

  • Rush Defense Pct: 1%
  • Pass Defense Pct: -20%
  • Total Defense Pct: -8%
  • Scoring Defense Pct: -20%

If we believe Oregon D is at disadvantage because of additional snaps, I think we would see the biggest effect on the pass defense numbers as the opposing team would have to turn to the air after they fall behind. But that is not what we see here, Oregon's rush D is pretty awful. I don't care how many snaps Arkansas St gets, they should NEVER gain 226 yards on the ground when they barely average over 100 yards against all other opponents.

The Oregon's pass defense in contrast is one of the better ones in Pac 12.

I don't think we are seeing a very significant impact of added snaps on these percentages.

MaximumSam

October 31st, 2012 at 12:58 PM ^

I don't know that ND is living on borrowed time.  Total defense and scoring defense do not perfectly correlate.  ND consistently stops the run and forces teams to pass.  They play a pretty safe defense in the secondary, so they do give up some yards but do not give up a large number of big plays.  Their defense is kind of similar to OSU's 2002 defense, which also gave up a fair amount of passing yardage but overall was extremely good.

ebv

October 31st, 2012 at 10:24 PM ^

This is obviously better than the straight numbers, but the problem with this approach is that different teams schedules can have very different levels of difficulty. For example, if team A plays a very difficult schedule, they're not going to change those strong teams offensive output as much as team B, who plays nobody but cupcakes.

burtcomma

November 1st, 2012 at 3:41 AM ^

Models are made so we can review some data and have an intelligent discussion.  If you want to know everything and take everything into account including scheduling strength differences you can go see that kind of analysis with the numbers from USA Today and Sagarin.....