West Coast Offense vs Southeastern Defense?

© Copyright 2005, Paul Kislanko

One of the interesting observations about the 2005 season is that games involving "western" teams (usually defined as the Mountain West, Pac 10, and WAC teams) tend to have high scores compared to games involving SEC (or other non-western) teams. Conference fans, being more partisan than political party members, each want to put a different spin on the results.

Pac 10 fans snort indignantly "we do too play defense, it's just that our offenses are so good they spoil the defensive stats. The only reason your defenses look good is that they don't play any decent offenses." To which SEC fans reply "oh, yeah? Our offenses wouldn't look so bad if they played the same defenses yours do!" and before you know it we're into another "my Daddy is smarter than your Mother is better looking" argument.

Of course, both arguments are correct to one degree or another, and facts should never get in the way of a good football argument, but there are ways to analyze the data using an objective measurement. The basic idea is to make an adjustment to the statistics based upon strength of schedule. The tricky part is figuring out which "SOS" is most appropriate.

A plethora of choices

"Strength of Schedule" can be (correctly) defined in an infinite number of ways, and if all one is concerned about is ranking SOS values, any choice is valid. For instance, the most basic example of an SOS is opponents' winning percentage. A more sophisticated approach might take into account opponents' opponents' winning percentage, game location adjustments, or more.

But to use "SOS" to normalize a statistic, you need a value, not an ordinal ranking, and it must be related to the statistic that is being normalized. While it is certainly true that the ability to score points and prevent points from being scored contributes to winning percentage, you can't derive scoring or scoring defense directly from winning percentage.

The Iterated Strength of Victory algorithm combines winning percentage with the "strength" of the wins and "closeness" of the losses to relate all teams through all possible paths of common opponents. Since it explicitly depends upon points-scored and points-allowed, we can use it to find an SOS that relates to Scoring Offense and Scoring Defense.

The ISOV can be thought of as F(PS,PA) over all games for all teams, where PS and PA are integrals of a rational function involving game scores. Then ∂F/∂PS is the SOS function for points scored, and ∂F/∂PA that for points allowed. We can't find those explicitly, but internally the ISOV approximates F′(team) for all teams, and from this we can approximate ∂PS/∂(PS+PA) and ∂PA/∂(PS+PA) for every team.

Note that the "SOS" that is required is not just the average of opponents' ISOV values. That is a measure of which teams were on the schedule, and what we need is a measure of how representative those are of the field as a whole. This is the "internal" SOS that is used to derive the ISOV values, and while it will be approximated by the average opponents' ISOV, it is different enough to matter.

While the bars and sports talk-radio are consumed with "they don't play defense out west" and "those guys out east don't have any offenses that would test a defense" we can use the ISOV SOS values to find to which degree both arguments are correct. (Note: in the tables below, "WM" is what I call a "weighted median", which is a measure of how top or bottom-heavy a conference is. Like all ordinal ranks, lower numbers are better.)

Normalized Scoring Offense - Ordinal Ranking by Conference
6 Dec 2005 11:41:07 (US Central)

WM #Teams Best Median Worst Conf
-19.3 11 3 15 91 B10 3 5 6 13 13 15 18 22 26 71 91
-5.7 10 1 24.5 71 P10 1 9 12 15 22 27 42 60 64 71  
20.7 12 2 39.5 82 B12 2 8 21 28 30 39 40 41 51 78 80 82
  1 4 4 4 ND 4                    
33.3 12 7 45 100 ACC 7 17 33 34 37 44 46 54 61 76 83 100
46.9 12 10 53 109 SEC 10 25 29 31 38 51 55 59 75 88 101 109
55.4 9 24 58 101 MW 24 35 48 48 58 61 65 77 101    
63.8 8 11 65 103 BigE 11 20 45 63 67 84 93 103      
86.6 12 36 76 97 CUSA 36 47 48 55 73 74 78 85 90 92 96 97
104.7 9 18 86 113 WAC 18 32 69 70 86 105 107 108 113    
111.5 12 43 89.5 119 MAC 43 55 65 67 81 86 93 95 97 111 114 119
114.3 3 51 89 116 Ind 51 89 116                
158.8 8 99 110.5 118 SBC 99 103 105 109 112 115 117 118      

Normalized Scoring Defense - Ordinal Ranking by Conference
6 Dec 2005 11:41:37 (US Central)

WM #Teams Best Median Worst Conf
-5.9 12 1 26.5 99 ACC 1 3 9 16 18 24 29 32 37 41 52 99
-3.9 12 2 25.5 91 SEC 2 6 8 10 17 21 30 38 54 72 72 91
9.3 12 5 35 85 B12 5 14 19 22 26 31 39 49 50 55 64 85
13.4 11 4 36 95 B10 4 7 12 14 34 36 40 45 56 68 95
29.4 8 13 42 94 BigE 13 22 33 41 43 58 83 94      
38.8 10 11 53 87 P10 11 27 28 47 48 58 63 68 71 87  
  1 25 25 25 ND 25                    
85.7 12 44 76 107 CUSA 44 46 50 61 68 72 80 81 85 90 100 107
86.6 9 20 75 106 MW 20 52 60 75 75 79 88 89 106    
102.0 3 61 78 113 Ind 61 78 113                
123.1 12 56 95.5 119 MAC 56 64 67 75 84 93 98 101 103 105 116 119
129.9 9 35 97 118 WAC 35 64 92 96 97 108 109 117 118    
156.1 8 82 110.5 114 SBC 82 102 104 110 111 112 114 114      

The team details are listed under the Scoring Stats link on the main page.