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Around SBN: Relegation Simulation: Rewriting College Football History

Covariance Rankings (2005-11)

Babyfoot_tiny by Bill C. on in Stats You Need to Know

So we've talked about Covariance for a while now. The idea is both simple and intriguing: which teams play their best against the best competition, and which play best against the worst?

The simple 'math' definition of covariance is as follows:

Covariance provides a measure of the strength of the correlation between two or more sets of random variates.

We look at correlations a lot with football stats, and for obvious reasons. It allows us to figure out when our eyes are lying to us, it tells us how seriously we should be taking certain factors (returning talent, recruiting, etc.) when making projections, etc. We're going to use covariance to look at which teams tended to play well against good teams (play up to their level of competition) and which ones tended to only play well against bad ones. Were Florida State's defensive tendencies mentioned above rare? Let's see.

Within the frame of a given season, it can give you a glimpse at a team's personality. But what can it tell you about a team from year to year?

After the jump, you'll find 2005-11 Covariance rankings for all FBS teams. As you'll see, very few teams are consistently best against good teams or bad. Moving forward, I'm going to take a look at experience levels and compare it to covariance; I'm now developing a theory that a decent amount of year-to-year variation could be explained simply by how experienced a team may be. Then again, it could just be the personality of certain groups of personnel, too. Using my own Missouri Tigers as an example, Mizzou ranked 116th and 99th in 2007-08, Chase Daniel's final two seasons in Columbia, and have ranked 29th, 23rd and 12th the last three years.

But we'll look at this at a later date; it's making my head hurt at the moment. For now, you just get rankings, rankings, rankings.

Remember: the lower your Covariance rank (i.e. the closer to 120th you get), the more you tend to play better against the best competition. The higher your rank, the more you tend to most heavily dominate weaker competition.

Most Consistent
1. Tennessee (Std. Dev.: 13.8)
2. UL-Monroe (16.3)
3. Fresno State (16.4)
4. Central Michigan (16.5)
5. Florida International (16.7)
6. West Virginia (17.0)
7. Texas A&M (18.6)
8. Akron (19.9)
9. LSU (20.2)
10. Eastern Michigan (20.5)

That Tennessee is tops on the consistency list kind of blows my mind considering they have had three coaches in four years. But no matter what, they tend to finish between 14th and 33rd most years.

Least Consistent
1. Arizona State (Std. Dev.: 50.1)
2. South Florida (47.8)
3. Rutgers (47.0)
4. Pittsburgh (46.0)
5. Miami (44.2)
6. Nevada (43.5)
7. SMU (43.3)
8. Oklahoma State (42.9)
9. Hawaii (42.9)
10. New Mexico (42.8)

A Dennis Erickson team tops the "least consistent" list. I feel that makes quite a bit of sense. But seriously ... ASU has been kind of nuts. They ranked fourth twice, between 25th and 30th twice, and 99th or lower three times. In each of the last two years, they played quite well against good teams and let down their guard against lesser ones.

Most Consistently "Best Against Worst"
1. LSU (Average Rank: 22.1)
2. Mississippi State (25.0)
3. Tennessee (26.3)
4. UL-Monroe (27.4)
5. Penn State (29.1)
6. Florida (30.6)
7. Kentucky (33.1)
8. Connecticut (33.3)
9. Troy (33.4)
10. Ohio State (38.1)

I really don't know what to make of the fact that five of the top seven teams on this list are from the SEC.

Most Consistently "Best Against Best"
1. West Virginia (Average Rank: 95.6)
2. Maryland (94.1)
3. San Diego State (86.3)
4. UTEP (85.3)
5. SMU (85.1)
6. Stanford (84.9)
7. Cincinnati (84.3)
8. North Carolina (84.1)
9. USC (83.4)
10. East Carolina (81.4)

I was shocked that giant-killing Iowa State didn't make this list, though in fairness, they did rank 11th; at the same time, I did not expect Maryland to be that high on the list. USC and East Carolina do not surprise me, however.

Anyway, giant data table after the jump. Enjoy.

Star-divide

Team 2005 2006 2007 2008 2009 2010 2011 Std. Dev
Air Force 84 106 29 21 64 111 92 35.9
Akron 85 49 45 68 22 44 49 19.9
Alabama 52 62 39 107 28 4 108 39.0
Arizona 110 38 86 52 103 50 91 28.6
Arizona State 99 25 4 30 4 109 114 50.1
Arkansas 24 53 82 91 77 60 100 25.9
Arkansas State 31 21 95 34 91 41 41 29.8
Army 55 79 96 67 108 71 3 33.9
Auburn 86 17 98 25 38 48 95 34.2
Ball State 18 72 16 109 92 57 21 37.9
Baylor 82 80 66 14 42 32 103 31.6
Boise State 29 118 2 61 110 47 86 42.6
Boston College 41 78 111 42 17 20 89 36.1
Bowling Green 98 114 62 87 32 105 26 35.4
Buffalo 109 30 42 77 60 95 51 28.7
BYU 53 69 106 95 94 13 43 33.5
California 56 85 110 11 13 7 22 41.0
Central Florida 111 70 23 23 7 87 46 38.2
Central Michigan 73 61 50 82 34 72 52 16.5
Cincinnati 66 90 113 86 113 54 68 23.1
Clemson 119 10 64 18 49 62 109 41.4
Colorado 5 115 40 55 102 70 33 38.9
Colorado State 65 54 52 85 78 34 113 25.9
Connecticut 11 55 17 36 66 12 36 21.5
Duke 38 105 63 60 100 40 31 29.8
Team 2005 2006 2007 2008 2009 2010 2011 Std. Dev
East Carolina 114 92 26 97 68 91 82 28.2
Eastern Michigan 40 82 46 45 85 36 44 20.5
Florida 13 13 10 106 56 1 15 37.6
Florida Atlantic 44 9 53 19 33 76 57 23.1
Florida International 70 67 43 24 47 56 67 16.7
Florida State 3 18 51 62 111 22 11 38.0
Fresno State 94 107 57 81 71 81 71 16.4
Georgia 71 96 112 53 69 2 34 37.1
Georgia Tech 74 104 25 118 81 43 37 35.2
Hawaii 21 103 118 39 88 8 85 42.9
Houston 104 108 7 79 93 49 76 35.5
Idaho 88 59 109 96 104 42 53 26.9
Illinois 33 100 76 93 90 67 23 30.1
Indiana 6 34 69 10 95 64 73 33.9
Iowa 23 91 24 78 118 89 83 35.7
Iowa State 116 45 61 105 44 79 117 32.1
Kansas 69 60 6 31 96 45 27 30.0
Kansas State 9 63 101 26 101 29 13 39.6
Kent State 117 50 41 98 89 14 40 37.4
Kentucky 101 58 47 1 1 16 8 37.4
Louisiana Tech 43 43 77 63 8 103 102 34.5
Louisville 35 77 94 90 52 15 106 33.7
LSU 8 8 55 8 43 28 5 20.2
Marshall 91 29 87 75 53 65 84 22.1
Maryland 107 101 104 115 107 9 116 37.9
Team 2005 2006 2007 2008 2009 2010 2011 Std. Dev
Memphis 75 42 59 89 70 46 24 22.2
Miami 60 95 14 9 106 88 120 44.2
Miami (Ohio)
 103 71 37 101 27 24 48 33.4
Michigan 16 83 20 32 39 94 16 32.5
Michigan State 17 94 54 16 30 100 4 38.8
Middle Tennessee 93 1 3 76 11 55 66 38.0
Minnesota 47 2 80 41 84 116 77 36.9
Mississippi State 10 73 35 5 18 27 7 23.8
Missouri 30 57 116 99 29 23 12 40.4
N.C. State 32 98 105 110 24 74 94 35.2
Navy 79 39 73 6 114 114 88 39.3
Nebraska 96 12 18 13 63 101 99 42.3
Nevada 72 14 103 12 35 112 14 43.5
New Mexico 105 116 9 48 105 99 32 42.8
New Mexico State 49 119 78 43 55 107 64 29.4
North Carolina 87 112 102 120 5 85 78 38.1
North Texas 68 44 19 83 54 58 28 22.3
Northern Illinois 76 66 34 22 74 52 107 28.5
Northwestern 64 28 79 56 117 84 119 32.7
Notre Dame 58 40 27 64 98 68 47 22.9
Ohio 26 32 13 70 97 61 110 36.7
Ohio State 25 97 93 17 12 5 18 39.3
Oklahoma 19 23 22 119 10 78 61 40.2
Oklahoma State 95 56 21 73 2 110 111 42.9
Ole Miss 63 102 119 2 109 82 79 39.2
Team 2005 2006 2007 2008 2009 2010 2011 Std. Dev
Oregon 34 48 67 94 23 33 54 24.2
Oregon State 50 7 108 92 112 97 70 37.6
Penn State 80 3 12 50 15 35 9 27.8
Pittsburgh 15 15 115 116 87 31 97 46.0
Purdue 22 89 48 104 86 53 17 34.0
Rice 62 22 89 44 73 83 59 23.2
Rutgers 106 109 1 4 79 18 72 47.0
San Diego State 100 35 90 72 116 117 74 28.9
San Jose State 78 99 15 59 41 21 63 30.2
SMU 118 65 71 114 119 108 1 43.3
South Carolina 20 87 74 58 50 113 69 29.3
South Florida 2 81 117 3 3 80 20 47.8
Southern Miss 51 11 70 71 75 69 80 23.8
Stanford 113 74 36 100 115 106 50 31.9
Syracuse 7 27 68 51 16 37 104 33.5
TCU 61 68 99 29 62 104 35 28.6
Temple 42 37 88 35 76 66 10 27.2
Tennessee 14 31 33 49 26 6 25 13.8
Texas 115 41 85 46 65 102 2 39.1
Texas A&M 54 76 75 33 72 38 42 18.6
Texas Tech 77 19 30 117 120 86 90 39.3
Toledo 83 84 38 20 36 39 93 29.4
Troy 39 16 8 15 9 51 96 32.0
Tulane 89 5 60 57 21 98 62 33.5
Tulsa 12 24 84 66 58 90 29 30.6
Team 2005 2006 2007 2008 2009 2010 2011 Std. Dev
UAB 97 51 72 65 46 92 118 26.2
UCLA 90 47 92 27 19 75 38 30.1
UL-Lafayette 36 20 49 38 59 96 65 24.6
UL-Monroe 45 6 44 28 37 26 6 16.3
UNLV 37 88 107 113 14 73 115 39.4
USC 108 113 100 74 25 59 105 32.4
Utah 102 33 65 103 82 3 101 38.9
Utah State 112 75 58 7 80 120 58 37.8
UTEP 81 111 114 88 51 77 75 21.8
Vanderbilt 48 86 5 80 6 10 56 34.9
Virginia 46 4 91 69 67 30 45 28.5
Virginia Tech 1 46 11 47 45 119 39 37.9
Wake Forest 59 117 97 112 57 25 30 37.9
Washington 27 110 56 108 20 11 81 41.5
Washington State 57 36 32 37 83 118 55 31.1
West Virginia 67 93 81 102 99 115 112 17.0
Western Kentucky 54 61 19 87 28.0
Western Michigan 92 52 28 84 31 17 19 30.9
Wisconsin 4 64 31 40 48 93 98 33.7
Wyoming 28 26 83 111 40 63 60 30.8

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Part of the SEC ethos (and indeed, reputation for quality) is running up the score on bad teams to make you look better. Spurrier made fellow SEC coaches upset by doing it against them, but really, everyone’s been doing it against the Memphises and directional Louisiana schools forever.

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by Year2 on Feb 6, 2012 9:06 AM EST reply actions  

Excellent information

Any chance you could post the data file?

"I make love to pressure."
-- Stephen Jackson

by USCKB on Feb 6, 2012 11:26 AM EST reply actions  

That's certainly...

the Arizona State I know………sigh

You're a Bruin for 4 years, but you're a Trojan for life!

by DevilishTrojan21 on Feb 7, 2012 12:07 AM EST reply actions  

I'm curious

at what level this is “real” and what level it may reflect model design, noise and internal biases. Some of the league results seemed a bit odd: the SEC showed 5/10 “best against worst” compared to 0/10 “best against best”; the BIG had 2/10 and 0/10; and the Pac-12 and ACC showed 0/10 and 2/10.

I especially wouldn’t think that any specific league would tend to play its best football against the worst opponents, which is what the model appears to be strongly concluding about the SEC. I could certainly see a couple teams in a league doing that, but when almost half the league makes one extreme of the table and no one is on the other side, that seems questionable to me.

While that’s certainly a limited data set (top 25 would probably be better to draw conclusions against), to me that suggests the possibility of something odd going on in the model rather than necessarily being an accurate description of “best vs best compared to best vs worst”. My GUESS is that this reflects an over-valuation of big blowout wins against terrible non-conference opponents, since the SEC/BIG tend to have a lot of bodybag games, while the ACC/PAC tend to have much fewer.

Is it possible to have both you and Fremau calculate something like this using your own models and see how consistent the two sets of results are? That’s not perfect, but I think it ought to shed some light on how much of these results are model-specific and how much is a true reflection of what’s going on. I may take a stab at this as well if you don’t mind; IMO the idea is interesting, and may be worth investigating further.

by cfn_ms on Feb 7, 2012 1:00 PM EST reply actions  

SDSU

Interesting, would not have pegged the Aztecs for the Best vs Best before analysis; at least, not over that stretch given how rough the Chuck Long era was.

Twitter: @kensing45@saturdayblitz

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by Kyle Kensing on Feb 8, 2012 12:32 AM EST via mobile reply actions  

it may have

been more of a “everyone kicks their butts, but it’s WAY less bad when a good team does it than when a bad team does it” thing. Wild-ass guessing on my end though.

by cfn_ms on Feb 10, 2012 10:38 AM EST up reply actions  

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