2020 Fantasy Defense Rankings with Least Squares Defense Rankings
In fantasy football, the strategy for one position is unlike any other. For fantasy defenses, the expected points scored depends heavily on the specific offense they are matched up against. Because of this, many players resort to streaming fantasy defenses which requires them to determine their fantasy defense rankings every week.
The most basic approach is to find those defenses which are available that have the best possible matchups in the current week. One does this by determining which offenses are the worst and hoping that even a middle-of-the-pack defense can do well against the worst offenses in the league.
In this article we turn this ad hoc idea into a quantitative thing. We develop a technique that assigns a rating to each team’s offense and each team’s defense that helps predict defensive fantasy points based on matchup.
This question has been tackled by many other outlets before but our fantasy defense rankings provide a bit more:
- Our technique is not nearly as sensitive to high variance events such as punt return touchdowns, kick return touchdowns, and pick sixes as others methods.
- We provide a specific matchup-driven D/ST rankings that is entirely objective. That is, we only use this season’s data and no opinions are used in our rankings.
- In addition to single week rankings, we highlight the best defenses over the next two weeks, the next three weeks, and for the rest of season (ROS).
To skip ahead, use these links to go directly to our least squares defense rankings team ratings and to go to the week 4 fantasy defense rankings
Offensive and Defensive Rating Systems
We call our model the least squares defense rankings because the way we generate our predictions is by solving a least-squares optimization problem. We assign each team in the NFL an offensive rating and a defensive rating. These ratings are optimized so that if we take a team’s defensive rating and subtract their opponents’ offensive rating, the result predicts the points scored by the defense in fantasy. The ratings are determined so that, if you were to do this process over all previously played games, the error between the predicted and observed fantasy points scored by a defense is as small as possible.
Let me give a more concrete example. If I compute a defensive rating of 9 for the Colts and an offensive rating of 3 for the Saints, then I would take the difference (9-3=6) as my prediction for the fantasy points for the Colts defense in this matchup.
It should be important to note that the numbers generated should be interpreted as ‘relative quality of the unit from a fantasy perspective’. For example, the Bengals’ have a fairly bad offensive rating because they allow so many sacks. Because they allow so many sacks, opposing defenses often score many fantasy points (valued at 1 point per sack) even if the Bengals’ offense is quite productive.
In the next section we discuss how least squares defense rankings reduces the impact of high variance events to deliver higher quality fantasy defense rankings
Reducing Variance in Fantasy Defense Rankings
Whenever a defense has a huge week in fantasy, it is often because of a punt return TD, kickoff TD, fumble recovery TD, or an INT return TD. When a typical defense scores, say, 6-10 points per week, one of these rare touchdowns worth 6 points by itself can double a team’s output.
The trouble is that these events are extremely hard to predict and are more ‘chance’ events than they are indicative of a defense’s actual performance. Sure, your defense has to be good in order to get the interception to score the touchdown. But, these unpredictable events are probably not as indicative of a defense’s future production as some other statistics.
So, instead of actually using fantasy defensive points to generate our rankings, least squares defense rankings uses a modified version that only takes into account yards allowed, points allowed, sacks, fumbles, interceptions, and safeties. If a defense has benefited greatly (looking at you, Indianapolis) from defensive touchdowns, using fantasy points to predict success gives them more credit than they are due. Using our modified rating, we are giving defenses credit only for things more in their control. Because of this, it should be more likely to accurately predict future performance.
Possible Extensions
There are a few possible extensions and changes one could make to least squares defense rankings in order to potentially increase performance. However, at this point we are only using the simplistic version where we solve the least squares problem for the modified defensive scoring.
Adjusted Points for Interceptions Relative to Fumbles
Instead of just ignoring the effect of interceptions and fumbles returned for a touchdown, we could adjust the value of interceptions and fumbles to account for the chance that it will be returned. Roughly 1/6 interceptions are returned for touchdowns while the probability for fumbles is significantly lower. Therefore, instead of assigning two points for interceptions, we could assign 3 points. These three points account for two points for the interception plus a 1/6 chance at scoring the extra 6 points. This would reward teams that record many interceptions and punish offenses that throw lots of interceptions.
Separate Ratings for Special Teams
You can note that I am entirely ignoring the effect of special teams on my ‘D/ST ratings’. The reason for this is that special teams contribute points so infrequently that it is extremely difficult to predict. However, one could argue that certain teams are more likely than others to return touchdowns and punts for TDs and more likely than others to block punts.
It is possible that punt and kickoff return TDs are not entirely random and that some teams are more likely to record one. Part of the effect of ‘more likely to return punts for TDs’ could be attributable to much better field position. This, in turn, is a by-product of a good defense.
On the other hand, kickoff returns TDs are highly impacted by opportunities. You have more opportunities the worse your defense is.
It is possible that one could improve the performance of this technique if we gave each NFL team a ‘Special Teams’ rating too, but I expect the effect to actually be quite negligible.
Using Past Season Data at the Beginning of the Current Season
Here is one important thing to note. In the current form of this technique, I cannot predict a team’s performance in week 1. This is because I rely on scoring data from the current year in order to make my predictions. Even in weeks 2 and 3 I don’t have that much data to work with and so my predictions are probably a bit too sensitive to noise.
Unfortunately, it is precisely in these early weeks that it is most important to be able to distill which teams have the best defenses. If somebody is flying under the radar or has an easy schedule (Pittsburgh), they can be extremely valuable to grab at the beginning of the season and hold on to for the long run.
There is one very easy way to fix this without imparting too much bias. Things change rapidly in the NFL, but because of the size of rosters and the distribution of responsibility for offensive and defensive performance, a team’s skills in general will not change too much year-to-year. That is, the Buccaneers defense in 2019 should be a relatively good barometer for how good the Buccaneers defense is in 2020.
So, in order to attain week 1 rankings, we could simply perform all the analysis here but use the 2019 data as our training data. Then, as the season progresses, we could perhaps use a mixture of, say, the last half of 2019 and the first game or two of 2020. This would allow us to use least squares defense rankings to deliver accurate fantasy defense rankings even at the beginning of a season.
What if Teams Get Better or Worse Throughout the Year?
Oftentimes when we have a young offense – in particular if they have a young quarterback – their offense will change rapidly in quality over the course of the year. Similarly, defenses can change quality throughout the year by virtue of adjusting to a system, making trades, or whatever other mechanism.
If a team gets much better or much worse throughout the course of the year we would like for our system to be able to detect this. We have done a similar thing before when studying hot streaks. The technique is this: we add extra weight to more recent games. Doubling the weight of the most recent game makes it so that our model basically thinks the most recent game happened twice.
Increasing the weight of recent games and decreasing the weight of games a long time ago makes it so that the assigned ratings fit the recent data better. This means that a team’s offensive and defensive ratings are more indicative of their recent performance. This means that if a team improves or gets worse on either offense or defense, our model will react more quickly and reflect this fact much sooner.
What about Injuries?
If injuries occur (which they do quite often in professional football), we might like our ratings to reflect this fact. If a non-quarterback player gets injured, perhaps the best way for us to update our rankings is the same way we do in the previous section. Simply weight more recent games more heavily so that the games without a key player have a bigger impact on that team’s offensive or defensive rating. Individual players’ contributions (outside of QB) to an entire offense or an entire defense are often quite small so letting our model determine this value over a few weeks is the best we can do
However, if a quarterback gets injured, the effect can be dramatic. Offenses can go from elite to bottom tier very quickly if they lose an elite quarterback. A similar thing may happen if a team benches a bad quarterback (recently think Trubisky, Tyrod Taylor) and starts someone different (Foles, Herbert). In this case, we would need to be able to determine the amount of value that the quarterback contributed to that offense and update the ratings based on this amount of value.
This is in general quite difficult to do. fivethirtyeight has attempted something similar by adding in a quarterback adjustment to their ELO. That is roughly the equivalent of what we want to do.
Fantasy Defense Rankings With Least Squares Defense Rankings
Using these techniques, we have assigned each team the following values using least squares defense rankings. These rankings take into account only offensive and defensive performance through each team’s first three weeks. The table below contains the fantasy offense rankings and the fantasy defense rankings used to make weekly predictions
| Team | Defense Rating | Offense Rating | |
|---|---|---|---|
| NE | 10.2 | 2.1 | |
| NO | 9.4 | 2.8 | |
| TB | 8.2 | 0.6 | |
| IND | 7.1 | 2.6 | |
| CAR | 4.6 | -0.0 | |
| BAL | 4.3 | -3.0 | |
| MIA | 3.2 | -0.9 | |
| MIN | 3.1 | -8.6 | |
| NYJ | 3.0 | -9.5 | |
| DEN | 2.9 | -10.1 | |
| NYG | 2.8 | -11.3 | |
| JAX | 2.8 | -4.6 | |
| LAC | 2.7 | -3.3 | |
| SEA | 2.3 | 5.1 | |
| DET | 1.9 | -2.7 | |
| PIT | 1.7 | 0.5 | |
| DAL | 1.5 | -0.3 | |
| CHI | 1.3 | -3.5 | |
| GB | 1.1 | 11.1 | |
| LV | 1.0 | 5.4 | |
| KC | 0.4 | 4.9 | |
| ARI | 0.3 | -3.9 | |
| WSH | 0.3 | -11.6 | |
| BUF | 0.2 | 1.1 | |
| LAR | -0.1 | 0.2 | |
| HOU | -0.2 | -6.5 | |
| ATL | -0.2 | 1.0 | |
| SF | -0.9 | 1.4 | |
| CLE | -1.2 | -3.4 | |
| CIN | -3.9 | -7.9 | |
| PHI | -4.1 | -11.9 | |
| TEN | -5.1 | 3.6 |
We also plotted the output of least squares defense rankings in a graphic. Below, the blue line represents the labeled team’s defensive rating. The orange line represents the team’s opponent’s offensive rating. The distance from the blue line to the orange line is the projected fantasy points by the defense. The further above the orange line the blue line is, the better the matchup for the defense. The teams are ordered by expected fantasy points in week 4.
Fantasy Defense Rankings Week 4, 5, and 6
So far we have provided a way to rate fantasy defenses, rate the quality of the offenses they face, and haveshown how to combine these numbers to achieve weekly fantasy defense rankings. Sometimes, though, when one wants to stream defenses, one would like to know things other than ‘who has the best matchups this week’. Other questions you could ask include:
- Who has the best matchup two weeks from now? Sometimes there is high competition for the current week’s most favorable defense, so looking two weeks out makes it easier to acquire quality streaming options.
- Who has the best matchups over the next two weeks? Over the next three weeks? Instead of switching to the best defense every week, sometimes it is preferable to find a team that has favorable matchups over the next two or three weeks and stick with them for a while.
- Which defenses are expected to score the most over the course of the rest of their season based on their schedule? Maybe you find yourself in the situation that you started with a defense that you thought was good but turned out not to be (like for me, the Titans).
In the following (sortable) table we show the answers to these questions. We compute the expected adjusted fantasy points for each team two games from now, over the next two games, over the next three games, and for the rest of the season based on their past performance and based on their opponents. Using least squares defense rankings, you should be able to accurately predict the best defenses over the next few weeks.
| Team | Def | Off | Wk4 | Wk5 | Wk6 | Wk4-5 | Wk4-6 | ROS |
|---|---|---|---|---|---|---|---|---|
| NE | 10.2 | 2.1 | 5.2 | 20.2 | 0.0 | 25.5 | 25.5 | 170.6 |
| NO | 9.4 | 2.8 | 12.1 | 12.7 | 0.0 | 24.8 | 24.8 | 153.1 |
| TB | 8.2 | 0.6 | 11.5 | 11.7 | -2.9 | 23.3 | 20.4 | 110.0 |
| IND | 7.1 | 2.6 | 10.6 | 10.5 | 14.9 | 21.1 | 36.1 | 106.0 |
| CAR | 4.6 | -0.0 | 8.5 | 3.5 | 8.1 | 12.0 | 20.1 | 75.5 |
| BAL | 4.3 | -3.0 | 16.0 | 12.2 | 16.2 | 28.2 | 44.4 | 105.8 |
| MIA | 3.2 | -0.9 | -1.9 | 1.8 | 13.2 | -0.1 | 13.1 | 65.5 |
| MIN | 3.1 | -8.6 | 9.6 | -2.0 | 2.1 | 7.6 | 9.7 | 44.0 |
| NYJ | 3.0 | -9.5 | 13.1 | 6.9 | 6.3 | 20.0 | 26.4 | 40.9 |
| DEN | 2.9 | -10.1 | 12.4 | 0.8 | 3.8 | 13.2 | 17.0 | 27.3 |
| NYG | 2.8 | -11.3 | 2.6 | 3.1 | 14.4 | 5.7 | 20.2 | 96.3 |
| JAX | 2.8 | -4.6 | 10.6 | 9.3 | 5.5 | 19.9 | 25.4 | 63.6 |
| LAC | 2.7 | -3.3 | 2.1 | -0.1 | 12.2 | 2.0 | 14.2 | 46.7 |
| SEA | 2.3 | 5.1 | 3.2 | 10.9 | 0.0 | 14.1 | 14.1 | 87.1 |
| DET | 1.9 | -2.7 | -0.9 | 0.0 | 6.5 | -0.9 | 5.6 | 46.5 |
| PIT | 1.7 | 0.5 | -1.9 | 13.6 | 5.1 | 11.7 | 16.9 | 72.0 |
| DAL | 1.5 | -0.3 | 4.9 | 12.7 | 5.4 | 17.6 | 23.0 | 113.4 |
| CHI | 1.3 | -3.5 | -1.3 | 0.7 | 1.4 | -0.6 | 0.8 | 16.4 |
| GB | 1.1 | 11.1 | 0.1 | 0.0 | 0.5 | 0.1 | 0.6 | 47.0 |
| LV | 1.0 | 5.4 | -0.1 | -4.0 | 0.0 | -4.1 | -4.1 | 37.8 |
| KC | 0.4 | 4.9 | -1.7 | -5.0 | -0.7 | -6.7 | -7.4 | 20.7 |
| ARI | 0.3 | -3.9 | 0.4 | 9.9 | 0.7 | 10.3 | 10.9 | 23.2 |
| WSH | 0.3 | -11.6 | 3.2 | 0.1 | 11.5 | 3.3 | 14.8 | 44.8 |
| BUF | 0.2 | 1.1 | -5.1 | -3.4 | -4.7 | -8.5 | -13.2 | 5.7 |
| LAR | -0.1 | 0.2 | 11.2 | 11.6 | -1.4 | 22.8 | 21.4 | 28.1 |
| HOU | -0.2 | -6.5 | 8.4 | 4.4 | -3.8 | 12.9 | 9.1 | 7.3 |
| ATL | -0.2 | 1.0 | -11.4 | -0.2 | 8.4 | -11.6 | -3.2 | -6.6 |
| SF | -0.9 | 1.4 | 11.0 | 0.0 | -1.1 | 11.0 | 9.9 | -10.9 |
| CLE | -1.2 | -3.4 | -0.8 | -3.8 | -1.7 | -4.6 | -6.3 | 27.3 |
| CIN | -3.9 | -7.9 | 0.7 | -0.9 | -6.5 | -0.2 | -6.7 | -13.0 |
| PHI | -4.1 | -11.9 | -5.5 | -4.6 | -1.1 | -10.1 | -11.2 | -29.0 |
| TEN | -5.1 | 3.6 | -5.6 | -6.1 | 1.4 | -11.7 | -10.3 | -46.0 |
Conclusions
In this article we have introduced a system for generating matchup-based fantasy defense rankings using least squares defense rankings. Our system allows us to generate weekly rankings for fantasy defenses based on their quality and the quality of their opponent. We intend to update our data every week and provide weekly fantasy defense rankings.
