Defending RealityPosted 7/30 by Jeff Pasquino, Exclusive to Footballguys.comNote: This article first appeared on Footballguys.com in 2005 here and once again last year here. This year's version of this analysis continues this alternative outlook on team defense valuation. 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 2006 Season are in Table 1: Table 1: Baseline Defense Rankings
Upon further review of Table 1, two of the Top 4 teams in Points Against were in the conference championship games. In fact, five out of the top seven teams in Points Against were in the 2006 playoffs, and 8 of 12 playoff teams ranked equally or better in Points Against than in Yardage Against. 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. Table 2: Sacks vs. Baseline Defense Rankings
Correlation: 0.626 Based upon the results, it would appear that we should stop right here as a correlation that high should tell you all we need to know, right? Well, looking back over the three years we have for data, the numbers are really all over the place. In 2005 the correlation was just 0.393 and in 2004 it was .509, which oddly enough is the average for all three seasons. This translates to a wide range of answers, anywhere from a weak correlation (39.3%) between Sacks and Baseline Defensive Ranking to a strong correlation (62.6%). Why would that be the case? 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? Table 3: Turnovers vs. Baseline Defense Rankings
Correlation: 0.169 Okay, things just got worse. 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 3, you can see most Team Defenses (28 of 32) have from 19 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 4): Table 4: Turnovers and Sacks vs. Baseline Defense Rankings
Correlation: 0.351 Now we're seeing some improvement. The correlation between the basic scoring system and Points Against is more than twice as strong as the turnover ranking correlation alone. The combination of both statistics helped in achieving point separation (ranging from 43 to 134 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:
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:
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 2006 season for data once again. Obtaining the two new statistics (4th down turnovers and forced punts), we get the following results: Table 5: All Turnovers and Forced Punts vs. Baseline Defense Rankings
Correlation: 0.688 Definite progress. The correlation between the new and improved scoring system and Points Against is over 60% (68.8%), a sign of a strong correlation and the best correlation so far. This also matches well with prior years (66.6% in 2005, 62.4% in 2004). The addition of all turnovers and punts forced has increased the point separation once again, ranging now from 103 to 198 (a range of 95 points instead of 59 as before in Table 4). There are additional benefits to this new equation. First, the scores are higher (average score of 9.1 / 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 6 represents the 2006 average score by position of the Top 12 players based upon the default Footballguys.com scoring system. Table 6: Average Fantasy Points / Game for Top 12 Players by Position
*Based upon the new Realistic Team Defense formula. Now the Team Defense is comparable to the value of just under a Top 12 wide receiver. That would seem to be an appropriate position of value for a strong Team Defense, below a 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 43 and 134 points for the season without defensive or special teams touchdowns added (see Table 4). Adding a single touchdown (6 points) varied the overall season score by 4-14%, a large impact. Now with the Realistic Team Defense formula, adding a touchdown reduces the impact to 3-6% (see Table 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. Data Sources |
