Defending Reality
By Jeff Pasquino
August 27th, 2012

Nearly every Fantasy League has different rules for how to score Team Defense. Many use the tried and true method of 1 point for a sack and 2 for a turnover. To add a little variety, many also add 6 points for the rare touchdown and yet another two for the rarest of scores - a safety. Other leagues try to tweak this scoring method by incorporating points against, yards against, or both.

Fantasy Football Scoring - A History Lesson

The basis for fantasy scoring comes from an attempt to quantify an individual player's performance numerically and assign that a value proportional to his team's performance. Touchdowns and yardage usually translate to team success, and the offensive player is rewarded for such productivity.

The second iteration of fantasy scoring came about as an attempt to normalize different positions to a similar scoring system. Quarterbacks produce more touchdowns and yardage than running backs, who produce even more than wide receivers. The result for many leagues was to reduce the points for passing touchdowns and also passing yardage so as to make running backs more valuable. Other leagues go one step further by awarding an extra point per catch to each player to increase wide receiver and tight end values closer to running backs.

What does any of this have to do with Team Defense? I am glad that you asked that question. This article is an attempt to determine how to quantify Team Defense scoring in a manner that reflects the impact a defense has on the outcome of a game, and also to provide a normalized score for a Team Defense that puts the value of a Defense at or near par for other fantasy football positions.

Baseline Defense

First, we have to determine what constitutes a good Team Defense. Is it one that gives up the fewest yards, or the fewest points? An argument can be made for either being the case, so let's take a look at the rankings from last year to see which method more accurately reflects a successful season. The results for the 2011 Season are in Table 1:

Team
YdsVs Rk
PtsVs Rk
Avg Rk
Pittsburgh Steelers
1
1
1.0
Baltimore Ravens
3
3
3.0
Houston Texans
2
4
3.0
San Francisco 49ers
4
2
3.0
Cleveland Browns
10
5
7.5
Cincinnati Bengals
7
9
8.0
Seattle Seahawks
9
7
8.0
Jacksonville Jaguars
6
11
8.5
Philadelphia Eagles
8
10
9.0
Miami Dolphins
15
6
10.5
Kansas City Chiefs
11
12
11.5
New York Jets
5
20
12.5
Tennessee Titans
18
8
13.0
Atlanta Falcons
12
18
15.0
Dallas Cowboys
14
16
15.0
Chicago Bears
17
14
15.5
Washington Redskins
13
21
17.0
Arizona Cardinals
19
17
18.0
New Orleans Saints
24
13
18.5
San Diego Charges
16
22
19.0
Denver Broncos
20
24
22.0
Detroit Lions
23
23
23.0
New England Patriots
32
15
23.5
St. Louis Rams
22
26
24.0
Green Bay Packers
31
19
25.0
Minnesota Vikings
21
31
26.0
New York Giants
27
25
26.0
Indianapolis Colts
25
28
26.5
Carolina Panthers
28
27
27.5
Buffalo Bills
26
30
28.0
Oakland Raiders
29
29
29.0
Tampa Bay Buccaneers
30
32
31.0

Table 1: Baseline Defense Rankings

Upon further review of Table 1, all of the Top 4 teams in Points Against were in the 2011 playoffs. Even both Super Bowl teams (New England, New York Giants), who each had weak defenses, looked better as far as points against instead of yardage. Just like in the past, it appears that Points Against is a better indicator of a good defensive team than just looking at the yardage. We shall adopt Points Against as the baseline for Team Defense.

Sack the Sack

The most common scoring system for Team Defense awards a point for every sack. This seems like a good idea, since it is an accomplishment by the defense to stop the offense from moving downfield, and it is an easy statistic to track. However, how realistic is this as a measure of Team Defense? Do sacks truly translate to team victories?

We obviously need some way to test this idea. Turning to statistics, we find that correlation is a measure of how two groups of statistics relate to one another. The formula used for correlation gives an answer between 0 and 1, with 1 representing a perfect match - 100% correlation. We can use this to see if sacks line up with our baseline, the Baseline Ranking (Points Against) from Table 1.

Table 2 lists the Team Defense rankings for sacks and the Baseline Ranking from Table 1. The correlation factor is given at the bottom of the table.

Team
PtsVs Rk
Sacks
Sacks Rk
Minnesota Vikings
31
50
1
Philadelphia Eagles
10
50
1
Baltimore Ravens
3
48
3
New York Giants
25
48
3
Cincinnati Bengals
9
45
5
Houston Texans
4
44
6
Arizona Cardinals
17
42
7
Dallas Cowboys
16
42
7
Detroit Lions
23
42
7
Miami Dolphins
6
42
7
Denver Broncos
24
41
11
Washington Redskins
21
41
11
New England Patriots
15
40
13
Oakland Raiders
29
40
13
San Francisco 49ers
2
40
13
St. Louis Rams
26
39
16
New York Jets
20
35
17
Pittsburgh Steelers
1
35
17
Atlanta Falcons
18
34
19
Seattle Seahawks
7
34
19
Chicago Bears
14
33
21
New Orleans Saints
13
33
21
San Diego Chargers
22
32
23
Carolina Panthers
27
31
24
Cleveland Browns
5
31
24
Jacksonville Jaguars
11
31
24
Green Bay Packers
19
29
27
Indianapolis Colts
28
29
27
Kansas City Chiefs
12
29
27
Buffalo Bills
30
28
30
Tennessee Titans
8
28
30
Tampa Bay Buccaneers
32
23
32

Table 2: Sacks vs. Baseline Defense Rankings

Correlation: 0.177

Based upon the results, it would appear that we are on the wrong track with such a low correlation, right? Well, looking back over the years we have for data, the numbers are really all over the place. Table 3 shows the results going back to 2004:

Year
Sack Rk to PtsVs Rk Correlation
2004
0.509
2005
0.393
2006
0.626
2007
0.444
2008
0.435
2009
0.380
2010
0.545
2011
0.177

Table 3: Sacks vs. Baseline Defense Rankings 2004-2011

This translates to a wide range of answers, anywhere from a weak correlation (17.7%) between Sacks and Baseline Defensive Ranking to a strong correlation (62.6%). Why would that be the case? The quick answer is that the sack numbers are tightly grouped together. The range of sacks for 25 of the 32 teams is just 28 to 42 sacks, or less than one per game. Results this close together will lead to correlations to other data that are unpredictable and all over the map.

So what is wrong with using sacks anyway? The common misconception is that a sack translates readily to the defense getting the ball back for the offense. The reality is that not all sacks are created equal. While a 15-yard sack on 3rd-and-10 would likely result in a Team Defense getting the ball for the offense, a 1-yard sack on first down is not nearly as valuable. However, in the 1 point for a sack scoring system, there is no differentiation between the two different sacks. It would appear that the sack statistic is misleading, and should be replaced by another one.

Turning Over Turnovers

Perhaps we should look harder at the other common statistic used in Team Defense scoring, the turnover. Surely one cannot dispute that turnovers relate strongly to team victories. That has to correlate well with Team Defense rankings, right?

Team
Takeaways
TA Rk
PtsVs Rk
San Francisco 49ers
38
1
2
Green Bay Packers
38
1
19
New England Patriots
34
3
15
Detroit Lions
34
3
23
Seattle Seahawks
31
5
7
Chicago Bears
31
5
14
New York Jets
31
5
20
New York Giants
31
5
25
Buffalo Bills
31
5
30
Atlanta Falcons
29
10
18
Jacksonville Jaguars
28
11
11
Houston Texans
27
12
4
Baltimore Ravens
26
13
3
Kansas City Chiefs
26
13
12
Oakland Raiders
26
13
29
Dallas Cowboys
25
16
16
Philadelphia Eagles
24
17
10
Carolina Panthers
24
17
27
Tampa Bay Buccaneers
24
17
32
Tennessee Titans
23
20
8
Minnesota Vikings
23
20
31
Cincinnati Bengals
22
22
9
Washington Redskins
21
23
21
San Diego Chargers
21
23
22
Cleveland Browns
20
25
5
Miami Dolphins
19
26
6
Arizona Cardinals
19
26
17
Denver Broncos
18
28
24
St. Louis Rams
18
28
26
Indianapolis Colts
17
30
28
New Orleans Saints
16
31
13
Pittsburgh Steelers
15
32
1

Table 4: Turnovers vs. Baseline Defense Rankings

Correlation: -0.007

OK, that is really not good at all. A correlation score of virtually zero means that we must be on the wrong track or else we are missing something. How can turnovers not significantly contribute to a good defensive ranking?

The answer really comes from the mathematics - correlation does not work well with numbers that are close together. From Table 4, you can see most Team Defenses (25 of 32) have from 18 and 31 turnovers, so such a tight grouping will compromise the calculations.

A sanity check is in order - we need to use the common scoring method in its entirety (1 point per sack + 2 points for a turnover) and correlate that result against Average Points (See Table 5):

Team
TAs x 2 + Sks
TAs x 2 + Sks Rk
PtsVs Rk
San Francisco 49ers
116
1
2
Detroit Lions
110
2
23
New York Giants
110
2
25
New England Patriots
108
4
15
Green Bay Packers
105
5
19
Baltimore Ravens
100
6
3
Houston Texans
98
7
4
Philadelphia Eagles
98
7
10
New York Jets
97
9
20
Minnesota Vikings
96
10
31
Seattle Seahawks
96
10
7
Chicago Bears
95
12
14
Atlanta Falcons
92
13
18
Dallas Cowboys
92
13
16
Oakland Raiders
92
13
29
Buffalo Bills
90
16
30
Cincinnati Bengals
89
17
9
Jacksonville Jaguars
87
18
11
Washington Redskins
83
19
21
Kansas City Chiefs
81
20
12
Arizona Cardinals
80
21
17
Miami Dolphins
80
21
6
Carolina Panthers
79
23
27
Denver Broncos
77
24
24
St. Louis Rams
75
25
26
San Diego Chargers
74
26
22
Tennessee Titans
74
26
8
Cleveland Browns
71
28
5
Tampa Bay Buccaneers
71
28
32
New Orleans Saints
65
30
13
Pittsburgh Steelers
65
30
1
Indianapolis Colts
63
32
28

Table 5: Turnovers and Sacks vs. Baseline Defense Rankings

Correlation: 0.111

Now we're seeing some improvement. The correlation between the basic scoring system and Points Against is certainly better than the turnover ranking correlation alone and clearly dominates the first score with sacks. The combination of both statistics helped in achieving point separation (ranging from 63 to 116 points) and agreement with the baseline, but there is definitely room for improvement.

The basic argument against using the sack as a standard measure remains - there is little direct correlation between the sack and elite defenses. Another measure of defense should be considered in place of sacks. However, if sacks are going to be eliminated from the Team Defense scoring system, what will be inserted in its place?

Give Me The $#@!! Ball

Let us reconsider the basic premise of Team Defense. Defenses have two main objectives - keeping the opposition from scoring, and getting the ball back for their offense. We have already seen that the first objective is the baseline measure of Team Defense, so we need to quantify the second criteria to the best of our ability to see if this should be the new fantasy football measure of the performance of a Team Defense.

There are two defensive categories of getting the ball back for the offense that are overlooked in the "turnover" category. Defenses succeed in stopping the opponent by forcing the traditional turnover (fumbles and interceptions) and also by forcing punts and stopping the opponent on fourth down. Our new formula for Team Defense needs to have basis in reality to weigh the value of forced punts and turnovers on downs.

Punts happen numerous times during the game, but they rarely result in the defense giving the offense a short field (under 50 yards from a touchdown). As such, forcing a punt has to be viewed as less opportunistic and less valuable than a fumble or interception, which results in a short field about half of the time. Therefore, our formula begins to look like this:

New Team Defense Score = Turnovers (INTs and Fumbles) x 2 + Forced Punts

Now for the second portion of the new formula - incorporation of turnovers on downs. While this can happen anywhere on the field, it is more likely to occur at both a crucial point in the game and also in a position where the opposing team is in scoring territory. While the resulting field position may not be as good as with a traditional turnover, the impact of both getting the ball for the offense and the likelihood that the 4th down turnover kept the opposition off the scoreboard gives this type of turnover approximately equal value to a fumble or interception. Therefore, we modify the formula to be:

New Team Defense Score = Turnovers (INTs + Fumbles + 4th Down Stops) x 2 + Forced Punts

We label this new equation the "Realistic Team Defense" scoring system. Now all that is left is to test our new formula.

Is the Fantasy a Reality

Let us revisit the 2011 season for data once again. Obtaining the two new statistics (4th down turnovers and forced punts), we get the following results:

Team
TOs x 2 + Punts
Reality Def Rk
PtsVs Rk
San Francisco 49ers
183
1
2
New York Jets
172
2
20
Detroit Lions
168
3
23
Chicago Bears
167
4
14
Baltimore Ravens
160
5
3
Green Bay Packers
158
6
19
New England Patriots
157
7
15
Cincinnati Bengals
156
8
9
Jacksonville Jaguars
155
9
11
Kansas City Chiefs
153
10
12
New York Giants
153
10
25
Philadelphia Eagles
153
10
10
Tennessee Titans
153
10
8
Houston Texans
151
14
4
Seattle Seahawks
151
14
7
Miami Dolphins
147
16
6
Atlanta Falcons
143
17
18
Denver Broncos
140
18
24
Oakland Raiders
140
18
29
Arizona Cardinals
138
20
17
Buffalo Bills
138
20
30
Dallas Cowboys
136
22
16
New Orleans Saints
135
23
13
Cleveland Browns
132
24
5
Pittsburgh Steelers
127
25
1
Washington Redskins
124
26
21
St. Louis Rams
123
27
26
Minnesota Vikings
121
28
31
San Diego Chargers
118
29
22
Carolina Panthers
116
30
27
Indianapolis Colts
114
31
28
Tampa Bay Buccaneers
114
31
32

Table 6: All Turnovers and Forced Punts vs. Baseline Defense Rankings

Correlation: 0.454

Definite progress. The correlation between the new and improved scoring system and Points Against is over 45% (45.4%), a sign of a strong correlation and the best correlation so far. This also begins to align well with prior years as shown in Table 7:

Year
Reality Defense Rk to PtsVs Rk Correlation
2004
0.624
2005
0.666
2006
0.688
2007
0.669
2008
0.617
2009
0.649
2010
0.651
2011
0.454

Table 7: Reality Defense vs. Baseline Defense Rankings 2004-2011

The addition of all turnovers and punts forced has increased the point separation once again, ranging now from 114 to 183 points (a range of 69 points instead of 53 as before in Table 5). The smaller correlation in 2011 than in previous years is a reflection of a smaller range from the top to the bottom teams in 2011. In 2010, the range in Reality Defense was 137 to 226 points, a difference of 89 points. It appears that there were fewer turnovers in general last season, which compresses the range yet Reality Defense correlation is the best of all the measures of defense.

There are additional benefits to this new equation. First, the scores are higher (average score of 9.0 / game) than under the original system (5.5 / game), which goes more towards a better normalization of the Team Defense position on the fantasy roster. By increasing the average score, the net effect is that a Team Defense is now representative of another normalized position player. Table 8 represents the 2011 average score by position of the Top 12 players based upon the default Footballguys.com scoring system.

Pos
Non-PPR Pts
PPR Pts
QB
23.0
23.0
RB
13.8
16.5
WR
12.0
17.2
TE
8.4
13.0
PK
8.5
8.5
Def*
9.0
9.0

*Based upon the new Realistic Team Defense formula.

Table 8: Average 2011 Fantasy Points / Game for Top 12 Players by Position

Now the Team Defense is comparable to the value of close to a tight end or kicker and just below a Top 12 wide receiver, Top 12 RB or QB. With PPR, the Team Defense declines to a good RB2 or WR2 or an average TE1 in value. That would seem to be an appropriate position of value for a strong Team Defense, below a top skill position (QB, RB, WR) but above the lesser valued tight end or kicker position.

One last additional benefit (and variance to the Realistic Team Defense formula) is that the addition of scoring points for a Team Defense scoring play (Touchdown or Safety) allows for the added point value, and also reduces the impact of that event to a lower percentage of the total Team Defense score. Previously, under the original scoring method, teams scored between 63 and 116 points for the season without defensive or special teams touchdowns added (see Table 5). Adding a single touchdown (6 points) varied the overall season score by 5-10%, a large impact. Now with the Realistic Team Defense formula, the range is much larger (114 to 183, see Table 6) so adding a touchdown reduces the impact to 3-5%. This smaller valuation relative to the seasonal performance does seem to be more appropriate.

Conclusion

Adoption of the Realistic Team Defense formula for defensive scoring for fantasy leagues going forward would result in a more accurate representation of the value of a Team Defense and better reflect how the actual defensive unit for each team performs in that particular season. The formula incorporates the significant statistics to quantify how well an actual defense performs, and results in a normalized score relative to the skill position players. The variation of adding back in the relatively rare event of a defensive score reduces the impact of the additional points to less of an overall change to the season Team Defense total, and increases the relative value of a Team Defense closer to that of an upper echelon wide receiver.

As always, questions, suggestions and comments are always welcome to pasquino@footballguys.com..

Data Sources

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