Defending Reality
By Jeff Pasquino
August 27th, 2011

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 2010 Season are in Table 1:

Team
YdsVs Rk
PtsVs Rk
Avg Rk
Pittsburgh Steelers
1
2
1.5
Green Bay Packers
2
5
3.5
New York Jets
6
3
4.5
New Orleans Saints
7
4
5.5
San Diego Chargers
10
1
5.5
Baltimore Ravens
3
10
6.5
Chicago Bears
4
9
6.5
Miami Dolphins
13
6
9.5
Atlanta Falcons
5
16
10.5
New York Giants
17
7
12.0
Kansas City Chiefs
11
14
12.5
Minnesota Vikings
18
8
13.0
Tampa Bay Buccaneers
9
17
13.0
San Francisco 49ers
16
13
14.5
Oakland Raiders
20
11
15.5
St. Louis Rams
12
19
15.5
New England Patriots
8
25
16.5
Philadelphia Eagles
21
12
16.5
Cleveland Browns
14
22
18.0
Cincinnati Bengals
24
15
19.5
Detroit Lions
19
21
20.0
Tennessee Titans
15
26
20.5
Indianapolis Colts
23
20
21.5
Carolina Panthers
26
18
22.0
Buffalo Bills
28
24
26.0
Seattle Seahawks
25
27
26.0
Washington Redskins
22
31
26.5
Dallas Cowboys
31
23
27.0
Jacksonville Jaguars
27
28
27.5
Arizona Cardinals
30
29
29.5
Houston Texans
29
30
29.5
Denver Broncos
32
32
32.0

Table 1: Baseline Defense Rankings

Upon further review of Table 1, all but one of the Top 5 teams in Points Against were in the 2010 playoffs, with both Super Bowl teams on that short list. Three playoff teams that were Top 12 in yards against in the regular season (New England, Kansas City and Atlanta) were one and done in the postseason, while still another (Baltimore) won just once - against New England. 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
Pittsburgh Steelers 
2
48
1
Green Bay Packers 
5
47
2
Oakland Raiders 
11
47
2
San Diego Chargers 
1
47
2
New York Giants 
7
46
5
Detroit Lions 
21
44
6
St. Louis Rams 
19
43
7
Tennessee Titans 
26
40
8
New York Jets 
3
40
8
Kansas City Chiefs 
14
39
10
Miami Dolphins 
6
39
10
Philadelphia Eagles 
12
39
10
Seattle Seahawks 
27
37
13
New England Patriots 
25
36
14
San Francisco 49ers 
13
36
14
Dallas Cowboys 
23
35
16
Chicago Bears 
9
34
17
Arizona Cardinals 
29
33
18
New Orleans Saints 
4
33
18
Carolina Panthers 
18
31
20
Atlanta Falcons 
16
31
20
Minnesota Vikings 
8
31
20
Houston Texans 
30
30
23
Indianapolis Colts 
20
30
23
Cleveland Browns 
22
29
25
Washington Redskins 
31
29
25
Baltimore Ravens 
10
27
27
Buffalo Bills 
24
27
27
Cincinnati Bengals 
15
27
27
Jacksonville Jaguars 
28
26
30
Tampa Bay Buccaneers 
17
26
30
Denver Broncos 
32
23
32

Table 2: Sacks vs. Baseline Defense Rankings

Correlation: 0.545

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 PtsVs Rk Correlation
2004
0.509
2005
0.393
2006
0.626
2007
0.444
2008
0.435
2009
0.380
2010
0.545

Table 3: Sacks vs. Baseline Defense Rankings 2004-2010

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 23 of the 32 teams is just 27 to 43 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
PtsVs Rk
Arizona Cardinals
30
9.0
29
Atlanta Falcons
31
7.0
16
Baltimore Ravens
27
15.5
10
Buffalo Bills
22
26.0
24
Carolina Panthers
29
11.5
18
Chicago Bears
35
3.0
9
Cincinnati Bengals
26
18.0
15
Cleveland Browns
28
13.5
22
Dallas Cowboys
30
9.0
23
Denver Broncos
18
31.0
32
Detroit Lions
29
11.5
21
Green Bay Packers
32
6.0
5
Houston Texans
18
31.0
30
Indianapolis Colts
21
28.0
20
Jacksonville Jaguars
18
31.0
28
Kansas City Chiefs
23
23.5
14
Miami Dolphins
19
29.0
6
Minnesota Vikings
26
18.0
8
New England Patriots
38
2.0
25
New Orleans Saints
25
20.5
4
New York Giants
39
1.0
7
New York Jets
30
9.0
3
Oakland Raiders
24
22.0
11
Philadelphia Eagles
34
4.5
12
Pittsburgh Steelers
34
4.5
2
San Diego Chargers
23
23.5
1
San Francisco 49ers
22
26.0
13
Seattle Seahawks
22
26.0
27
St. Louis Rams
26
18.0
19
Tampa Bay Buccaneers
28
13.5
17
Tennessee Titans
25
20.5
26
Washington Redskins
27
15.5
31

Table 4: Turnovers vs. Baseline Defense Rankings

Correlation: 0.307

OK, things did get a little better, but it is still not a very high correlation. 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 (22 of 32) have from 22 and 32 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 Diego Chargers
93
12
1
Pittsburgh Steelers
116
2
2
New York Jets
100
8
3
New Orleans Saints
83
19
4
Green Bay Packers
111
4
5
Miami Dolphins
77
27
6
New York Giants
124
1
7
Minnesota Vikings
83
19
8
Chicago Bears
104
6
9
Baltimore Ravens
81
23
10
Oakland Raiders
95
9
11
Philadelphia Eagles
107
5
12
San Francisco 49ers
80
25
13
Kansas City Chiefs
85
17
14
Cincinnati Bengals
79
26
15
Atlanta Falcons
93
12
16
Tampa Bay Buccaneers
82
22
17
Carolina Panthers
89
16
18
St. Louis Rams
95
9
19
Indianapolis Colts
72
28
20
Detroit Lions
102
7
21
Cleveland Browns
85
17
22
Dallas Cowboys
95
9
23
Buffalo Bills
71
29
24
New England Patriots
112
3
25
Tennessee Titans
90
15
26
Seattle Seahawks
81
23
27
Jacksonville Jaguars
62
31
28
Arizona Cardinals
93
12
29
Houston Texans
66
30
30
Washington Redskins
83
19
31
Denver Broncos
59
32
32

Table 5: Turnovers and Sacks vs. Baseline Defense Rankings

Correlation: 0.419

Now we're seeing some improvement. The correlation between the basic scoring system and Points Against is nearly 50% 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 59 to 124 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 2010 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
New York Giants
226
1
7
Green Bay Packers
217
2
5
Pittsburgh Steelers
209
3
2
Chicago Bears
206
4
9
San Diego Chargers
206
4
1
Oakland Raiders
205
6
11
Philadelphia Eagles
203
7
12
New York Jets
201
8
3
Kansas City Chiefs
200
9
14
Detroit Lions
199
10
21
St. Louis Rams
189
11
19
New England Patriots
186
12
25
San Francisco 49ers
184
13
13
Seattle Seahawks
184
13
27
Atlanta Falcons
182
15
16
Baltimore Ravens
182
15
10
Miami Dolphins
182
15
6
Minnesota Vikings
178
18
8
Tennessee Titans
177
19
26
Dallas Cowboys
175
20
23
Washington Redskins
175
20
31
Arizona Cardinals
173
22
29
Carolina Panthers
173
22
18
Tampa Bay Buccaneers
170
24
17
New Orleans Saints
166
25
4
Cincinnati Bengals
165
26
15
Indianapolis Colts
159
27
20
Cleveland Browns
157
28
22
Buffalo Bills
148
29
24
Jacksonville Jaguars
146
30
28
Denver Broncos
144
31
32
Houston Texans
137
32
30

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

Correlation: 0.651

Definite progress. The correlation between the new and improved scoring system and Points Against is over 60% (65.1%), 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 PtsVs Rk Correlation
2004
0.624
2005
0.666
2006
0.688
2007
0.669
2008
0.617
2009
0.649
2010
0.651

Table 7: Reality Defense vs. Baseline Defense Rankings 2004-2010

The addition of all turnovers and punts forced has increased the point separation once again, ranging now from 137 to 226 (a range of 89 points instead of 65 as before in Table 5).

There are additional benefits to this new equation. First, the scores are higher (average score of 12.7 / game) than under the original system (5.6 / 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 2010 average score by position of the Top 12 players based upon the default Footballguys.com scoring system.

Pos
Non-PPR Pts
PPR Pts
QB
20.2
20.2
RB
14.6
17.6
WR
11.4
16.5
TE
7.1
11.0
PK
7.7
7.7
Def*
12.7
12.7

*Based upon the new Realistic Team Defense formula.

Table 8: Average 2010 Fantasy Points / Game for Top 12 Players by Position

Now the Team Defense is comparable to the value of close to a Top 12 wide receiver but below a 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 59 and 124 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 (137 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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