New Stat: Adjusted uAYA (Part I: Offensive uAYA)

One of my continual frustrations with Football Outsiders and their advanced metrics is the lack of applicability or what you could call user-friendliness.  There is no doubt in my mind that FO is the best at analyzing the game of college football, I just wish it was easier to understand or explain.  By the way, if you still haven't perused their website, I highly recommend you become familiar with their data.
 
For example, look at this year's Football Outsiders offensive metrics, Off. S&P+, OFEI, and Off. F/+ developed by Bill Connelly and Brian Fremeau (comparing the best vs. FSU):
 
Auburn (ranked 1st) had an Off. S&P+ of 153.6, while FSU (ranked 8th) had an OFF. S&P+ of 127.9
 
Auburn (1st) had an OFF. FEI of 0.805, while FSU (8th) had an OFF. FEI of 0.434
 
Auburn (1st) had an OFF. F/+ of +25%, while FSU (7th) had and OFF. F/+ of +13.9%
 
Care to try and decipher those?  Yes, Auburn was better than FSU.  But how much better? OFEI and Off. F/+ seem to say that Auburn was almost twice as good as FSU.  If you use Off. S&P+ they much more closely matched.  

Obviously, there is no ideal way to measure team performance, especially if you want the numbers to be usable by the masses.  But is there a way to have a statistic that is both useful in examining team strength and understandable?
 
After the jump I'll share my attempt to solve this problem.

 

Note for readers who plan on skimming the next section, or those who gloss over when statistics are used:  In summary, what I've gathered here is a ranking of the 120 FBS teams by an offensive stat that, in essence, measures the yards each team gains every time they snap the ball.  This number is adjusted for touchdowns and turnovers.  It is also an opponent adjusted number, but does not exclude garbage time (i.e. yards gained when the game is out of hand).

 

uAYA - Ultimate Adjusted Yards per Attempt

Piggybacking off a concept used in my recent article 'QB Efficiency and Success - Analysis and Projection', I decided to look at overall offensive and defensive efficiency using the same equation that I used for QB efficiency - uAYA (Ultimate Adjusted Yards per Attempt)
 
In the previous article I examined uAYA for yards only the quarterback was responsible for.  Today, instead of looking just at numbers contributed by the QB, I used the uAYA equation to look at an overall efficiency.
 
uAYA = (Total Yards + PassTD*20 + RushTD*18 - Fumbles*25 - INTs*45)/Attempts
 
While not as complex as Bill Connelly's S&P+ or Brian Fremeau's FEI, uAYA does account for turnovers and touchdowns, punishing teams that have numerous turnovers and rewarding teams who protect the ball.  For example, Miami gained around 5.9 yards per play, but Jacory threw enough interceptions to drop their offensive uAYA a full point to 4.85 yards per play.  On the other hand, Stanford gained 6.7 yards per play, but because they had few turnovers, their offensive uAYA rose to 7.3 yards per play.

 
Thanks to cfbstats.com this was a quick calculation and I was able to determine both offensive and defensive uAYA (O-uAYA and D-uAYA) for all 120 FBS teams.
 
Examples:
 
FSU 2010
O-uAYA: 897 plays, 5338 yards, 24 PassTD, 27 RushTD, 13 INT, 24 Fumbles = 5.71 
D-uAYA: 1005 plays, 4952 yards, 17 PassTD, 12 RushTD, 15 INT, 23 Fumbles = 4.24


 

Strength of Schedule

 

O-uAYA and D-uAYA are purely performance metrics, meaning they in no way account for strength of schedule.
 
Thanks to the help of Neil Paine at Pro-Football-Reference.com (this is the site who came up with uAYA), I was able to use O-uAYA and D-uAYA to correct for strength of schedule.  

After determining each team's offensive and defensive uAYA, there are several steps in adjusting for SOS.

Step 1:

Here's the equation used in step one:

{[O-uAYA - (Opponents' D-uAYA - Opponents Opponents' O-uAYA + Avg. O-uAYA)] + Avg. O-uAYA}

To demonstrate what's happening in step 1, let's look at two examples of how we applied this equation.


1. FSU O-uAYA = 5.71
2. Opponents' D-uAYA = 4.46
3.  Opponents' Opponents' O-uAYA = 5.33
 
1. Maryland O-uAYA = 5.69
2. Opponents' D-uAYA = 4.93
3. Opponents' Opponents' O-uAYA = 5.23

#1 shows us that for overall O-uAYA there was not much difference between FSU and Maryland (5.71 and 5.69).  #2 shows us that FSU gained a similar O-uAYA against a stronger set of defenses.  And #3 shows us that not only did the defenses FSU faced have a better D-uAYA, they did so against a stronger set of offenses.   

Using the equation:

FSU adjusted O-uAYA - 6.58
Maryland adjusted O-uAYA - 5.99


Step 2:
 
After all 120 FBS were assigned an adjusted O-uAYA and an adjusted D-uAYA, I recalculated each team's Opponents' D-uAYA and Opponents' O-uAYA.  For example, after accounting for the initial adjustment, FSU faced defenses that averaged a D-uAYA of 4.04 (instead of the initial 4.46 shown above)

Against those teams, FSU had an adjusted O-uAYA of 6.58, gaining 163% of what those teams allowed (adjusted opponent D-uAYA = 4.04).
 
Maryland had an adjusted O-uAYA of 5.99, gaining 129% of what their opponents allowed (adjusted opponent D-uAYA = 4.66)  
 
Step 3:

After getting that percentage, I calculated what each team's O-uAYA would have been had they faced the hardest set of defenses, which happened to be FSU - adjusted opponent D-uAYA = 4.04
FSU = 163% x 4.04 = 6.57
Maryland = 129% x 4.04 = 5.2
 
I did this for all 120 teams to determine the percentage they gained over their opponents, multiplied by the hardest set of defenses (FSU's) to get the final rankings.
 

Data Comparison

Because my goal was to come as close to Football Outsider's rankings as possible, I wanted to see how well my data correlated with F/+.  I made several charts to try and visualize how well my data matched up to theirs. 
 
This first set of graphs are simply comparisons of the numerical rankings of different systems. 

The first graph is Off. F/+ vs. O-uAYA (x-axis = F/+, y-axis = O-uAYA).  If my rankings matched perfectly the graph would be a straight line from point (1,1) to point (120,120), with auburn being 1st in both rankings, Buffalo being 120th in both rankings, and all the teams in between rankings matching identically between the two systems.

The second graph looks at Off. FEI vs. Off. S&P+ (the two components of Off. F/+) to demonstrate that even two highly complex systems will have discrepancies in where certain teams rank.

 

 

 

 

The second set of graphs look at the slopes of the individual ratings (O-uAYA and Off. F/+).  One thing you'll notice when looking at the actual data (not the ranking) is that offensive success is not evenly distributed.  For example, in Off. F/+ (whose data is presented as percentages), the absolute difference between #1 (Auburn-25%) and #5 (Arkansas-15.7%) is 9.3%.  That's almost the same difference we find between #5 (Arkansas-15.7%) and #31 (Michigan St.-6.2%) = 9.5%.



 

 

 

Points from these graphs:
- The rankings are fairly similar between Off. F/+ and O-uAYA, and surprisingly look like a closer match than FEI and S&P+.

- The slopes of the two lines look nearly identical.  The slope of these graphs demonstrate visually how offensive strength is distributed through college football.  This is how we need to think of offensively elite teams.  Not only are they better than everyone else, it isn't even close.  One more example of this... The difference in Adjusted O-uAYA between #1 and #10 (Auburn and Oregon) was 2.47 yards per play.  Then, if we start at #11 (Virginia Tech - Adj. O-uAYA = 6.02) and subtract that same 2.47 yards, we have to go all the way to #95 Arkansas State.

- Because the slopes of the two ranking systems match very well (and the rankings match decently), this tells us that, generally speaking, the difference in the yards per play measured by O-uAYA is similar to the difference in percentages seen in Offensive F/+.

 
 

O-uAYA Data


Now that I've hopefully convinced you that the data I've collected is useful and accurate regarding team offensive strength, let's look at the actual numbers to see if they are understandable.  In the graph below I've included several different measures, with the Final Ajusted O-uAYA represented in the blue column.
 
 
As a summary for those who skipped the above explanations, Adj.Fin O-uAYA represents an opponent-adjusted yard per play efficiency measure.   Remember that Adj. Final O-uAYA represents each team's offensive strength measured against the toughest set of defenses.

 

 

Team

O-uAYA

D-uAYA

Opp. uAYA

Opp. D-uAYA

Adj. O-uAYA

Adj. D-uAYA

Adj.Fin O-uAYA

1

Auburn

7.95

5.07

5.74

4.69

8.79

4.3

8.59

2

Arkansas

6.93

4.63

5.61

4.65

7.8

4.05

7.64

3

Alabama

7.29

3.25

5.49

5.01

7.94

2.56

7.34

4

Stanford

7.31

4

5.19

5.1

7.72

3.73

6.78

5

Michigan

6.42

6.28

5.43

4.76

7.14

5.93

6.64

6

Florida State

5.71

4.24

5.1

4.46

6.58

3.95

6.63

7

Wisconsin

7.47

4.67

5.47

5.31

7.73

4.3

6.39

8

Oklahoma State

7.63

4.41

5.25

5.22

7.75

4.25

6.27

9

Boise State

8.04

2.8

5.29

5.47

8

2.69

6.14

10

Oregon

7.05

3.53

5.2

5.29

7.29

3.28

6.13

11

Virginia Tech

6.49

4.62

5.4

4.89

6.86

4.14

6.06

12

Baylor

6.5

5.76

5.32

4.94

6.91

5.6

5.95

13

Georgia

6.17

4.48

5.46

4.98

6.65

4.02

5.94

14

South Carolina

5.61

4.8

5.95

4.7

6.3

3.77

5.93

15

Nevada

7.27

5.02

4.89

5.37

7.4

5.37

5.87

16

Kentucky

6.31

5.63

5.29

5.07

6.64

5.26

5.77

17

North Carolina State

5.44

5.02

5.28

4.57

6.05

4.63

5.7

18

Iowa

6.47

4.13

5.47

5.18

6.75

3.69

5.65

19

Michigan State

6.16

4.58

5.55

5.04

6.56

4.13

5.65

20

LSU

4.84

3.54

5.51

4.59

5.7

2.93

5.64

21

Cincinnati

5.43

5.29

4.99

4.48

5.98

5.1

5.58

22

Washington

5.29

5.3

5.28

4.72

5.97

5.05

5.57

23

Oklahoma

5.62

4.06

5.38

4.74

6.17

3.6

5.55

24

USC

5.96

5.53

5.41

5.09

6.36

5.12

5.54

25

TCU

7.31

3.14

5.35

5.48

7.23

2.94

5.54

26

Oregon State

5.02

5.45

5.81

4.64

5.78

4.73

5.47

27

Ohio State

6.82

2.84

5.41

5.35

6.87

2.41

5.47

28

Hawaii

7.52

4.11

5.26

5.69

7.31

4.11

5.4

29

Mississippi

5.55

6.44

5.65

4.95

6.07

5.85

5.39

30

Pittsburgh

5.38

4.03

5.12

4.56

5.86

3.69

5.38

31

Miami

4.85

4.03

5.33

4.54

5.54

3.53

5.36

32

Northern Illinois

7.53

4.99

4.61

5.42

7.22

5.55

5.33

33

Utah

6.03

4.48

5.18

5.09

6.36

4.4

5.31

34

Tennessee

5.26

4.68

5.47

4.88

5.8

4.22

5.26

35

Maryland

5.69

3.8

5.06

4.93

5.99

3.56

5.23

36

Missouri

5.62

4

5.36

4.9

6.03

3.72

5.22

37

San Diego State

7.02

4.64

4.95

5.53

6.9

4.86

5.22

38

Florida

4.5

3.68

5.35

4.57

5.3

3.21

5.2

39

North Carolina

5.62

4.46

5.12

5.02

5.91

4.1

5.16

40

Kansas State

6.03

6.23

5.15

5.09

6.25

6.24

5.15

41

Texas A&M

5.05

3.93

5.53

4.72

5.67

3.39

5.15

42

Navy

6.44

5.41

5.34

5.3

6.49

5.25

5.15

43

Minnesota

5.12

6.71

5.84

4.77

5.71

6.13

5.12

44

Texas Tech

5.64

5.37

5.29

5.02

6.01

5.2

5.1

45

Arizona State

5.3

4.8

5.57

5.03

5.75

4.23

5.07

46

Penn State

5.03

5.09

5.64

4.76

5.61

4.51

5.06

47

Air Force

6.24

4.64

5.22

5.26

6.31

4.6

5.01

48

Mississippi State

5.59

4.75

5.96

5.15

5.89

3.77

4.99

49

Louisville

5.79

4.66

4.98

4.98

5.93

4.55

4.98

50

Notre Dame

5.05

4.41

5.66

4.8

5.55

3.81

4.92

51

West Virginia

5

3.14

4.84

4.71

5.4

3.03

4.85

52

Tulsa

6.88

5.68

5.48

5.6

6.63

5.61

4.81

53

Nebraska

5.44

3.76

5.17

5.07

5.69

3.61

4.76

54

Illinois

5.68

4.87

5.71

5.3

5.82

4.25

4.71

55

Arizona

4.75

4.75

5.68

4.91

5.25

4.11

4.68

56

Wake Forest

4.5

5.65

5.3

4.71

5.04

5.22

4.68

57

Duke

4.35

6.38

5.45

4.64

4.96

5.9

4.67

58

Clemson

4.39

4.04

5.31

4.67

4.96

3.52

4.63

59

Georgia Tech

5.2

5.3

5.1

5.07

5.4

5.14

4.59

60

East Carolina

5.76

6.88

5.59

5.24

5.83

6.58

4.58

61

Virginia

5.02

6.02

5.2

5

5.23

5.66

4.5

62

Washington State

4.34

6.7

5.7

4.84

4.95

6.06

4.5

63

Indiana

5.25

6.87

5.48

5.18

5.46

6.59

4.48

64

Houston

6.24

5.67

5.26

5.62

6.04

5.84

4.44

65

South Florida

4.2

4.29

4.77

4.52

4.71

4.28

4.35

66

Connecticut

4.45

4.14

4.83

4.62

4.83

4.11

4.34

67

Syracuse

4.7

4.21

4.81

4.77

4.95

4.13

4.31

68

California

4.82

4.29

5.52

5.18

5.07

3.78

4.28

69

Wyoming

4.55

5.87

5.43

4.84

4.99

5.71

4.26

70

Colorado

4.67

5.73

5.45

5.03

4.99

5.34

4.23

71

SMU

5.89

5.08

5.55

5.52

5.71

4.94

4.21

72

Southern Mississippi

5.94

5.15

5.17

5.67

5.67

5.29

4.14

73

Rutgers

4.17

5.5

5.04

4.57

4.59

5.34

4.13

74

Florida International

5.43

4.96

4.83

5.15

5.34

5.34

4.13

75

Fresno State

5.37

5.69

5.69

5.4

5.34

5.24

4.12

76

Northwestern

4.98

5.84

5.31

5.42

5.07

5.68

4.06

77

Iowa State

4.21

5.07

5.56

4.82

4.64

4.59

4.04

78

UAB

5.53

5.87

5.14

5.51

5.36

6.13

3.96

79

Central Florida

5.77

4.06

5.17

5.67

5.42

4.2

3.89

80

San Jose State

4.15

6.49

6.01

4.98

4.56

5.81

3.84

81

Western Michigan

5.55

4.96

4.76

5.41

5.19

5.33

3.78

82

Utah State

4.29

6.2

5.69

5.08

4.59

5.85

3.77

83

Louisiana Tech

4.54

5.8

5.67

5.24

4.72

5.46

3.76

84

Toledo

5.23

4.63

4.97

5.23

5.01

4.82

3.75

85

Boston College

3.8

3.35

5.22

4.79

4.17

2.95

3.71

86

Troy

5.55

5.53

4.92

5.47

5.14

5.9

3.68

87

Army

5

5.15

5.21

5.32

4.83

5.09

3.65

88

UNLV

3.91

7.13

5.75

4.85

4.29

6.65

3.63

89

Texas

4.4

3.81

5.27

5.23

4.51

3.56

3.63

90

Temple

4.93

3.98

4.53

5.08

4.75

4.56

3.62

91

Idaho

4.87

5.35

5.3

5.51

4.77

5.31

3.6

92

UCLA

3.72

6.12

5.54

5.01

4.13

5.64

3.6

93

BYU

4.78

4.44

5.35

5.37

4.68

4.24

3.58

94

Arkansas State

5.41

5.67

5.28

5.56

4.98

5.67

3.57

95

Rice

5.09

6.81

5.56

5.52

4.84

6.72

3.53

96

Ohio

4.77

5.68

4.48

5.11

4.58

6.41

3.44

97

Eastern Michigan

4.36

8.28

4.95

4.97

4.34

8.59

3.43

98

North Texas

5.15

6.01

4.84

5.52

4.74

6.5

3.4

99

Western Kentucky

4.81

6.19

4.92

5.37

4.51

6.54

3.32

100

Colorado State

4.09

6.73

5.34

5.15

4.18

6.63

3.32

101

Purdue

3.77

4.92

5.64

5.19

4

4.41

3.3

102

UTEP

5.17

5.63

4.97

5.88

4.7

6.03

3.26

103

Miami (OH)

4.74

4.5

4.56

5.28

4.38

5.02

3.22

104

Kansas

3.74

6.48

5.43

5.16

3.89

6.14

3.16

105

Vanderbilt

3.44

5.6

5.29

5.15

3.68

5.15

3.14

106

Tulane

4.39

5.97

5.44

5.46

4.22

5.95

3.13

107

Central Michigan

4.57

5.45

5.22

5.32

4.18

5.43

3.05

108

Kent State

4.02

4.06

4.51

5.01

3.93

4.65

3.04

109

Marshall

4.1

4.88

5.18

5.28

4

5.07

3.02

110

Memphis

3.73

7.25

5.53

5.25

3.74

7.15

2.89

111

Louisiana Monroe

3.89

5.45

5.32

5.26

3.77

5.35

2.87

112

Louisiana Lafayette

4.31

5.85

5.21

5.44

3.93

5.94

2.84

113

Ball State

3.86

5.4

4.78

5.23

3.62

5.83

2.72

114

Florida Atlantic

3.79

5.37

4.93

5.27

3.59

5.76

2.68

115

New  Mexico State

3.43

7.46

5.39

5.42

3.39

7.46

2.59

116

Middle Tennessee

4.33

5.04

4.76

5.73

3.7

5.56

2.55

117

Bowling Green

3.36

5.86

4.97

5.01

3.26

6.13

2.5

118

Akron

3.39

6.49

4.96

4.97

3.21

6.7

2.46

119

New Mexico

2.66

6.82

5.44

5.26

2.69

6.65

2.1

120

Buffalo

2.92

4.43

4.88

5.38

2.38

4.67

1.68

Note: There are several confounding variables that may be skewing my data. 

First, these numbers include garbage time (plays run when the game was already decided and back-ups are potentially in the game.)  I would love to only include non-garbage time in my caculations, but I think that would literally multiply the data gathering workload by about 1000.  As of now, using cfbstats.com, it is about a 15 second calculation for gross O-uAYA and D-uAYA for each team.  Until there is an easy way to filter for competitive plays only, we're stuck using all plays.
 
Second, these are complete season numbers, which includes yards gained against FCS opponents.  Further worsening the reliability of the data, my Strength of Schedule calculations could only include FBS opponents.  This means that the O-uAYA represented above includes yards gained against FCS opponents, but that each teams Opp. D-uAYA (i.e. the average uAYA allowed by their opponents) does not include the D-uAYA of FCS opponents.  Hopefully, the fact that most teams played 1 FCS opponent will make the potential difference negligible.  
 

 

FSU single game uAYA - 2010

Chart_1_medium

I apologize for the formatting of this graph.  For some reason all of the team names won't appear on the x-axis. As a reminder, so you can correlate which dot represents which teams, our schedule order was as follows: Samford, OU, BYU, Wake, Virginia, Miami, BC, NCSt, UNC, Clemson, Maryland, UF, VT, and USCe.

Single game uAYA accurately predicted 12 of 14 games (BC and NCSt incorrectly predicted).

 

Our best O-uAYA performance, outside of Samford, was against Miami.  Our worst performance came against BC the following week.  Not surprisingly, our worst O-uAYA performances, in order, were against BC, OU, USCe, and Clemson.

 

Would it be possible to use this data to better predict the upcoming season?  Can we give a more meaningful prediction of what we expect from our offense?  Can we predict using a 'yard per play' measure, rather than simply a ranking?  If nothing else, I think it could be a valuable stat for explaining the absolute difference between teams, rather than just a ranking. 

I think it could also be a useful measure in comparing performances between years. For example, when we look at D-uAYA rankings, we'll see that FSU's unadjusted D-uAYA improved significantly from 2009 to 2010.  We know that per Football Outsider's rankings we moved from 107th to 41st, but how much of an improvement is that on the field?  Ideally, uAYA may give us an idea of what that improvement actually was as we see that FSU's unadjusted D-uAYA in 2009 was 6.58 yards per play and FSU's unadjusted D-uAYA in 2010 was 4.24 yards per play.

It will also allow interesting comparison between different teams from different seasons.  For example, in 2010 Boise St. was ranked by Football Outsiders as the #1 defense in the country and allowed an unadjusted D-uAYA of 2.8 yards per play against a set of offenses that ranked 90th in the nation.  In 2009, two teams (unanimously considered elite defenses) matched that performance: Alabama allowed an unadjusted D-uAYA of 2.8 and Nebraska allowed an unadjusted D-uAYA of 2.63 yards per play against a set of offenses that were surely much better than what Boise faced in 2010 (SOS data not available for 2009 at Football Outisders).  

What are your ideas for how this data can be used?

 

Just for fun, I'll give an offensive prediction for 2011.  I expect our offense to have an unadjusted O-uAYA around 6-6.5.  Because our strength of schedule won't likely be near the toughest in the nation in 2011, we won't get a boost in the adjusted rankings like above, so I think our adjusted O-uAYA will stay around 6-7 (top 15). 

Next week, look for Part II of this series - 'Defensive uAYA'. 

What I've shown above is just a snippet of all the data I've collected.  After next week's article I hope to add my 2010 data to MonarchNole's ongoing data collection page, so we can have a place where users can go for all of Tomahawk Nation's statistical data.  I also plan on compiling this data thoughout the 2011 season to track how we're doing.

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