B1G and National Statistical Rankings per Z-score method (Updated weekly)

[beorach]

I copy and paste figures from cfbstats.com and average z-scores for each team across nine categories (pass d, pass o, rush d, rush o, scoring d, scoring o, total d, total o, and turnover margin) to develop these rankings. There is no strength of schedule factor applied and I'm only considering games against FBS (WTH isn't it still called Division 1?) teams. I normalize figures, too, such that I'm not considering TD's scored but TD's per game instead, for example. I'll look at just the games between FBS Power 5 teams later but there aren't enough of them yet to bother with... For those not familiar with the Z-score, a number close to zero means that team's posted stats are average and the actual number corresponds to the average number of standard deviations difference from the means for all figures within the respective category. I've worked these up such that low numbers relate to positive Z-scores for defense (so it's consistent across all categories).

B1G Rankings Overall (with average Z-score for all stats across all categories)


Michigan 1.69
Ohio State 1.58
Nebraska 0.63
Iowa 0.55
Wisconsin 0.37
Minnesota 0.31
Maryland 0.25
Indiana 0.16
Northwestern 0.02
Penn State 0.01
Michigan State -0.31
Illinois -0.34
Purdue -0.76
Rutgers -1.29


BIG Rankings Defensively (with average Z-score for all stats across applicable categories)

Michigan 2.18
Ohio State 1.80
Wisconsin 1.22
Minnesota 0.92
Nebraska 0.77
Iowa 0.76
Maryland 0.60
Indiana 0.58
Penn State 0.10
Northwestern 0.03
Michigan State -0.23
Illinois -0.42
Purdue -0.96
Rutgers -1.18


BIG Rankings Offensively (with average Z-score for all stats across applicable categories)


Ohio State 1.51
Michigan 1.41
Nebraska 0.54
Iowa 0.28
Maryland 0.01
Northwestern 0.00
Penn State -0.01
Indiana -0.21
Purdue -0.37
Wisconsin -0.39
Michigan State -0.39
Minnesota -0.42
Illinois -0.55
Rutgers -1.55


National Top 25 Overall (with average Z-scores shared as before)

Michigan 1.69
Ohio State 1.58
Alabama 1.35
Louisville 1.34
Washington 1.30
Baylor 1.09
Western Michigan 1.02
Florida 0.94
Washington State 0.92
Army 0.88
Colorado 0.79
LSU 0.78
Houston 0.77
Memphis 0.72
Auburn 0.68
Virginia Tech 0.67
Toledo 0.65
Clemson 0.64
Nebraska 0.63
West Virginia 0.61
San Diego State 0.60
Troy 0.57
South Florida 0.56
Miami (Florida) 0.56
Iowa 0.55


National Top 25 Defensively (with average Z-scores shared as before)


Michigan 2.18
Florida 1.92
Ohio State 1.80
Alabama 1.65
Army 1.48
LSU 1.47
Wisconsin 1.22
Clemson 1.20
Virginia Tech 1.19
Miami (Florida) 1.12
Auburn 0.95
Baylor 0.93
Minnesota 0.92
Louisville 0.90
Washington 0.88
San Diego State 0.88
Tulane 0.86
Troy 0.86
UCLA 0.85
Western Michigan 0.82
North Carolina State 0.82
Boston College 0.81
Houston 0.81
Colorado 0.80
Washington State 0.77
Nebraska just misses out with another rounded score of 0.77 (lower than Wazzu's)


National Top 25 Offensively (with average Z-scores shared as before)

Louisville 2.17
Washington 1.65
Toledo 1.52
Ohio State 1.51
Michigan 1.41
South Florida 1.29
Alabama 1.29
Baylor 1.26
Texas Tech 1.25
Oklahoma 1.15
Western Michigan 1.08
Louisiana Tech 1.08
Washington State 0.99
Houston 0.99
California 0.93
Texas 0.91
Oregon 0.91
Pittsburgh 0.86
Texas A&M 0.79
Colorado 0.79
Mississippi 0.73
Middle Tennessee 0.72
Memphis 0.69
TCU 0.66
West Virginia 0.65
Nebraska is 29th with a rounded score of 0.54


p.s. - Here's everything on the home team (showing the stats this season's edition of the Corn has posted are above average in all categories I've tracked but rushing defense):

po pd ro rd to td sco scd to margin
Nebraska 0.17 0.87 0.72 0.26 0.46 0.70 0.83 1.26 0.43

p.p.s. - I've updated the post to reflect the stats as of today.

 

[beorach]

Bumping for week 5 stats having been analyzed... Just to add something besides that, here are the bottom ten Power 5 programs (per overall z-scores in ascending order):

Bottom 10 Power 5 Football Performances Statistically to Date (with the team possessing the worst stats at the top to confuse you)

Rutgers -1.29

Kansas -1.13

Purdue -0.76

Syracuse -0.48

Arizona -0.47

Iowa State -0.44

Oregon State -0.42

Arizona State -0.39

Kentucky -0.37

Oregon -0.35

p.s. - Only Bowling Green has statistics worse than those of Rutgers per this method.

p.p.s. - I updated to reflect current stats.

 

[beorach]

Bumping to bring this back to the surface for any who are interested...

 

[Nebfanatic]

So these are based 100% on statistics?

 

[Nebfanatic]

Being in the top 20 overall statistically is pretty great. While the top teams have the best statistics it's not a clear indicator of talent or team ability to a degree. I would say being in the upper quarter of these rankings means you are a solid team that can compete with just about anybody

 

[beorach]

So these are based 100% on statistics?

That's correct. The z-score is just the average deviation from the means (calculated using national stats for every figure I could make sense of within those nine categories I listed), expressed in terms of a number of standard deviations. I changed signs so the negatives (talking about z-scores for things like total yards given up per game) on defense would read the same as the offensive ratings for exceptional performances on the "good" side of average.

What I'd like to be able to do is figure out how to apply strength of schedule. The best thing I'm doing, in that regard, is only consider games between two FBS opponents. Once enough games have been played, I'll do calculations based on games between P5 teams only.

p.s. - There are z-score to percentile calculators out there on the web. That's probably easier to imagine but having rankings and the numbers to show how far apart two teams are numerically is cool, too...

 

[Mierin]

I think you're explaining too... thoroughly. Let me see if I understand it.

If the average total offense for the entire country is 200/game, and Akron is averaging 200/game, Akron's total offense "score" would be a 0? So anyone with > 200 yards/game has a "score" of more than 0?

When you write "p.p.s. - I've updated the post to reflect the stats as of today." could you put a date on it? I can throw up a quit graph if you want.

 

[beorach]

Sorry I'm a little slow responding. I think you get it but I'll try and explain further and confuse you anyway.

I'm actually averaging the z-scores for every stat within a category...and then averaging those averages for the rankings.

My explanations are probably confusing and an example would do a better job so...

Rushing Offense

National average for rushing yards per carry: 4.33

National standard deviation for this stat: 0.93

National average for rushing yards per game: 174.78

National standard deviation for this stat: 55.03

National average for rushing touchdowns per game: 1.79

National standard deviation for this stat: 0.76

Nebraska's stats...

Rushing yards per carry: 4.69

Rushing yards per game: 220.50

Rushing touchdowns per game: 2.50

The z-score for a stat is the difference between that stat and the mean, divided by the standard deviation.

(4.69 - 4.33) / 0.93 = 0.39 for rushing yards per carry

Per your Akron example, you can see your understanding of the z-score is correct (because, had Nebraska matched the average, their z-score for this stat would be zero).

My rushing offense z-score is a composite, though. I'm calculating the other two z-scores and averaging to come up with Nebraska's 0.72. The details are below:

(220.5 - 174.78) / 55.03 = 0.83 for rushing yards per game

(2.5 - 1.79) / 0.76 = 0.93 for rushing touchdowns per game

We take the average of those three z-scores (and I chose rushing offense for an example because there are so few measurables relative to other categories) to get what I shared for Nebraska's z-score for the whole category:

(0.39 + 0.83 + 0.93) / 3 = 0.72

That figure gets lumped in with passing offense, scoring offense, and total offense for the purpose of finding the rank of Nebraska's offensive statistics relative to those of other FBS programs. It's the same for the defense except, again, I'm changing the signs to keep low yardage as a positive. Both defensive and offensive categories, plus the turnover margin one, factor into the "overall" ranking list.

I'll throw some dates up, too. I think I was hoping the post would show the date of the last edit but no dice...

 

[Mierin]

Sorry I'm a little slow responding. I think you get it but I'll try and explain further and confuse you anyway.

I'm actually averaging the z-scores for every stat within a category...and then averaging those averages for the rankings.

My explanations are probably confusing and an example would do a better job so...

Rushing Offense

National average for rushing yards per carry: 4.33

National standard deviation for this stat: 0.93

National average for rushing yards per game: 174.78

National standard deviation for this stat: 55.03

National average for rushing touchdowns per game: 1.79

National standard deviation for this stat: 0.76

Nebraska's stats...

Rushing yards per carry: 4.69

Rushing yards per game: 220.50

Rushing touchdowns per game: 2.50

The z-score for a stat is the difference between that stat and the mean, divided by the standard deviation.

(4.69 - 4.33) / 0.93 = 0.39 for rushing yards per carry

Per your Akron example, you can see your understanding of the z-score is correct (because, had Nebraska matched the average, their z-score for this stat would be zero).

My rushing offense z-score is a composite, though. I'm calculating the other two z-scores and averaging to come up with Nebraska's 0.72. The details are below:

(220.5 - 174.78) / 55.03 = 0.83 for rushing yards per game

(2.5 - 1.79) / 0.76 = 0.93 for rushing touchdowns per game

We take the average of those three z-scores (and I chose rushing offense for an example because there are so few measurables relative to other categories) to get what I shared for Nebraska's z-score for the whole category:

(0.39 + 0.83 + 0.93) / 3 = 0.72

That figure gets lumped in with passing offense, scoring offense, and total offense for the purpose of finding the rank of Nebraska's offensive statistics relative to those of other FBS programs. It's the same for the defense except, again, I'm changing the signs to keep low yardage as a positive. Both defensive and offensive categories, plus the turnover margin one, factor into the "overall" ranking list.

I'll throw some dates up, too. I think I was hoping the post would show the date of the last edit but no dice...

I think I get it.

There's an option somewhere where you can choose to let your posts have an "edited by" line and it will show the date. I think?

 

[Mierin]

 

[beorach]

That's very cool. Thanks for adding a touch of class in this joint. GBR!