Defending Reality
By Jeff Pasquino
August 8th, 2010

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 2009 Season are in Table 1:

Team
Yds vs Rk
Pts vs Rk
Avg Rk
New York Jets 
1
1
1
Baltimore Ravens 
3
3
3
Green Bay Packers 
2
7
4.5
Cincinnati Bengals 
4
6
5
Dallas Cowboys 
9
2
5.5
New England Patriots 
11
5
8
Minnesota Vikings 
6
10
8
Carolina Panthers 
8
9
8.5
Pittsburgh Steelers 
5
13
9
San Francisco 49ers 
15
4
9.5
Denver Broncos 
7
12
9.5
Indianapolis Colts 
18
8
13
San Diego Chargers 
16
11
13.5
Washington Redskins 
10
18
14
Houston Texans 
13.5
17
15.3
Philadelphia Eagles 
12
19
15.5
Arizona Cardinals 
20
14.5
17.3
Buffalo Bills 
19
16
17.5
Atlanta Falcons 
21
14.5
17.8
Chicago Bears 
17
21.5
19.3
New York Giants 
13.5
30
21.8
New Orleans Saints 
25
20
22.5
Jacksonville Jaguars 
23
24
23.5
Miami Dolphins 
22
25.5
23.8
Oakland Raiders 
26
23
24.5
Seattle Seahawks 
24
25.5
24.8
Cleveland Browns 
31
21.5
26.3
Tampa Bay Buccaneers 
27
27
27
Tennessee Titans 
28
28
28
Kansas City Chiefs 
30
29
29.5
St. Louis Rams 
29
31
30
Detroit Lions 
32
32
32

Table 1: Baseline Defense Rankings

Upon further review of Table 1, all but one of the Top 8 teams in Points Against were in the 2009 playoffs, and Arizona, San Diego, Minnesota and the Colts all made the postseason due to their scoring defense more than holding teams from racking up 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
Pts vs Rk
Sacks
Sacks Rk
New York Jets 
1
32
20
Dallas Cowboys 
2
42
7
Baltimore Ravens 
3
32
20
San Francisco 49ers 
4
44
4
New England Patriots 
5
31
23.5
Cincinnati Bengals 
6
34
16.5
Green Bay Packers 
7
37
11.5
Indianapolis Colts 
8
34
16.5
Carolina Panthers 
9
31
23.5
Minnesota Vikings 
10
48
1
San Diego Chargers 
11
35
14
Denver Broncos 
12
39
10
Pittsburgh Steelers 
13
47
2
Arizona Cardinals 
14.5
43
6
Atlanta Falcons 
14.5
28
27
Buffalo Bills 
16
32
20
Houston Texans 
17
30
25
Washington Redskins 
18
40
8.5
Philadelphia Eagles 
19
44
4
New Orleans Saints 
20
35
14
Cleveland Browns 
21.5
40
8.5
Chicago Bears 
21.5
35
14
Oakland Raiders 
23
37
11.5
Jacksonville Jaguars 
24
14
32
Miami Dolphins 
25.5
44
4
Seattle Seahawks 
25.5
28
27
Tampa Bay Buccaneers 
27
28
27
Tennessee Titans 
28
32
20
Kansas City Chiefs 
29
22
31
New York Giants 
30
32
20
St. Louis Rams 
31
25
30
Detroit Lions 
32
26
29

Table 2: Sacks vs. Baseline Defense Rankings

Correlation: 0.380

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 three 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 Pts vs Rk Correlation
2004
0.509
2005
0.393
2006
0.626
2007
0.444
2008
0.435
2009
0.380

Table 3: Sacks vs. Baseline Defense Rankings 2004-2009

This translates to a wide range of answers, anywhere from a weak correlation (38.0%) 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 26 of the 32 teams is just 28 to 44 sacks, or just 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
Pts vs Rk
Green Bay Packers 
40
1
7
New Orleans Saints 
39
2
20
Philadelphia Eagles 
38
3
19
Carolina Panthers 
37
4
9
Buffalo Bills 
33
5.5
16
San Francisco 49ers 
33
5.5
4
Baltimore Ravens 
32
7
3
New York Jets 
31
8
1
Denver Broncos 
30
9
12
Arizona Cardinals 
29
10.5
14.5
Tampa Bay Buccaneers 
29
10.5
27
Atlanta Falcons 
28
14
14.5
Chicago Bears 
28
14
21.5
Kansas City Chiefs 
28
14
29
New England Patriots 
28
14
5
Houston Texans 
27
16.5
17
Tennessee Titans 
27
16.5
28
Cincinnati Bengals 
25
19
6
Indianapolis Colts 
25
19
8
Jacksonville Jaguars 
25
19
24
Minnesota Vikings 
24
22
10
New York Giants 
24
22
30
San Diego Chargers 
24
22
11
Seattle Seahawks 
23
24
25.5
Detroit Lions 
22
25.5
32
Pittsburgh Steelers 
22
25.5
13
Dallas Cowboys 
21
27.5
2
Miami Dolphins 
21
27.5
25.5
Oakland Raiders 
20
29
23
Cleveland Browns 
19
30.5
21.5
St. Louis Rams 
19
30.5
31
Washington Redskins 
17
32
18

Table 4: Turnovers vs. Baseline Defense Rankings

Correlation: 0.370

OK, things barely got any better. 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 (24 of 32) have from 21 and 33 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
Pts vs Rk
New York Jets 
94
11
1
Dallas Cowboys 
84
18
2
Baltimore Ravens 
96
9
3
San Francisco 49ers 
110
4
4
New England Patriots 
87
14
5
Cincinnati Bengals 
84
18
6
Green Bay Packers 
117
2
7
Indianapolis Colts 
84
18
8
Carolina Panthers 
105
5
9
Minnesota Vikings 
96
9
10
San Diego Chargers 
83
23
11
Denver Broncos 
99
7
12
Pittsburgh Steelers 
91
12
13
Arizona Cardinals 
101
6
14.5
Atlanta Falcons 
84
18
14.5
Buffalo Bills 
98
8
16
Houston Texans 
84
18
17
Washington Redskins 
74
28
18
Philadelphia Eagles 
120
1
19
New Orleans Saints 
113
3
20
Chicago Bears 
91
12
21.5
Cleveland Browns 
78
25
21.5
Oakland Raiders 
77
27
23
Jacksonville Jaguars 
64
31
24
Miami Dolphins 
86
15
25.5
Seattle Seahawks 
74
28
25.5
Tampa Bay Buccaneers 
86
15
27
Tennessee Titans 
86
15
28
Kansas City Chiefs 
78
25
29
New York Giants 
80
24
30
St. Louis Rams 
63
32
31
Detroit Lions 
70
30
32

Table 5: Turnovers and Sacks vs. Baseline Defense Rankings

Correlation: 0.546

Now we're seeing some improvement. The correlation between the basic scoring system and Points Against is about 50% better than the turnover ranking correlation alone and also our first score with sacks. The combination of both statistics helped in achieving point separation (ranging from 63 to 120 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 2009 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
Points vs Rk
Philadelphia Eagles 
226
1
19
San Francisco 49ers 
223
2
4
Green Bay Packers 
221
3
7
New York Jets 
216
4
1
New Orleans Saints 
210
5
20
Arizona Cardinals 
209
6
14.5
Buffalo Bills 
200
7
16
Minnesota Vikings 
199
8
10
Baltimore Ravens 
195
9.5
3
Carolina Panthers 
195
9.5
9
Denver Broncos 
191
11
12
Dallas Cowboys 
188
12.5
2
New England Patriots 
188
12.5
5
Houston Texans 
184
14
17
Cincinnati Bengals 
183
15.5
6
Pittsburgh Steelers 
183
15.5
13
Chicago Bears 
176
17
21.5
Indianapolis Colts 
175
19
8
Cleveland Browns 
175
19
21.5
Seattle Seahawks 
175
19
25.5
Tennessee Titans 
172
21
28
Washington Redskins 
170
22
18
Tampa Bay Buccaneers 
168
23
27
Miami Dolphins 
167
24
25.5
Kansas City Chiefs 
166
25.5
29
New York Giants 
166
25.5
30
San Diego Chargers 
165
27
11
Oakland Raiders 
164
28
23
Atlanta Falcons 
163
29
14.5
St. Louis Rams 
150
30
31
Detroit Lions 
146
31
32
Jacksonville Jaguars 
136
32
24

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

Correlation: 0.649

Definite progress. The correlation between the new and improved scoring system and Points Against is over 60% (64.9%), a sign of a strong correlation and the best correlation so far. This also matches well with prior years as shown in Table 7:

Year
Reality Defense Rk to Pts vs Rk Correlation
2004
0.624
2005
0.666
2006
0.688
2007
0.669
2008
0.617
2009
0.649

Table 7: Reality Defense vs. Baseline Defense Rankings 2004-2009

The addition of all turnovers and punts forced has increased the point separation once again, ranging now from 136 to 226 (a range of 90 points instead of 57 as before in Table 5).

There are additional benefits to this new equation. First, the scores are higher (average score of 11.4 / 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 2009 average score by position of the Top 12 players based upon the default Footballguys.com scoring system.

Pos
Non-PPR Pts
PPR Pts
QB
27.6
27.6
RB
19.6
23.2
WR
15.4
22.9
TE
10.8
17.0
PK
10.4
10.4
Def*
12.9
12.9

*Based upon the new Realistic Team Defense formula.

Table 8: Average 2009 Fantasy Points / Game for Top 12 Players by Position

Now the Team Defense is comparable to the value of close to a Top 12 tight end but below a Top 12 RB or WR. With PPR, the Team Defense declines to a good RB2 or WR2 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 120 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 (136 to 226, see Table 6) so adding a touchdown reduces the impact to 3-4%. 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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