I've done some analysis of the D/ST scoring scheme, to investigate whether it could possibly be improved. I know that this post won't appeal to everyone, but if you're curious then read on.

TL;DR - D/ST scoring can be made a bit more predictable (correlation increasing from 0.15 to 0.20) while focusing on strictly defensive traits alone. Projection models could give correlations of 0.42 instead of 0.37. If you want less variance and more predictability from your league's D/ST position, then: (1) reduce the reward for TDs to 2 points, (2) crank up the effect of yards-allowed while shrinking the effect for points-allowed, (3) eliminate sacks, (4) shrink-- but don't eliminate-- the reward for turnovers.

Motivation

Since I have worked so closely with forecasting D/ST scores with statistics, I have long wondered if we could improve fantasy predictability by changing the points structure. For example, some people have suggested reducing randomness by making TDs count less. Contrary to popular belief, I recently showed that the predictability of the D/ST position is actually decent, when compared to other fantasy positions (during the last 3 years). But still-- can we improve the score weightings, to improve consistency and reduce variability?

Framing the problem

I defined my target as creating the most "meaningful defensive predictor", based on 4 criteria:

1. The new scoring should use the same, familiar variables (sacks, ints, fr, score, yards, tds).

2. The variables should be weighted in simple linear combination (no arbitrary "tiers").

3. The best solution should best reflect that "past fantasy scores are useful for predicting future fantasy scores."

4. As a final but soft target, it is necessary to define a range of outcome scores. I wanted my scheme to produce a narrower range than usual, more similar to kickers-- approximately 0 to 20 fantasy points. Avoiding negative scores is important, in order to avoid the strategy of "maybe I just won't roster a D/ST at all".

In other words, a D/ST scoring scheme will be considered "best" if it optimally "predicts itself", and is based on purely defensive traits (not tuned to the predictability of opposing offenses).

Remark on chasing predictability alone

I often see a comment that fantasy is already so random that we should use any opportunity to remove as much randomness as possible. It turns out that, if you only care about predictability, then you will end up strongly weighting outcomes that are controlled by the opposing offense-- but the point should be to reward skills under the defense's control. Furthermore, chasing predictability alone would make the D/ST position almost equivalent to betting on Vegas lines. So I disregarded this line of optimization, believing it gets away from the spirit of things.

Predictability of individual variables

For reference, let's first understand how predictable ("self-predictable") each component variable is. I.e. "How well does a defense's season average of TDs (or sacks/ints/etc.) predict future occurrence of the same thing?" So here is a chart of the correlation coefficients between running averages and weekly outcomes, using fantasy data covering every week of the last 3 years 2017-2019:

For most defensive factors, there is a very low correlation between the running season average and weekly outcome, indicating that these events are not very predictable.

Note that the first bar ("D/ST score allowed") actually describes an offensive trait; its high correlation reflects the fact that such offensive traits are more consistent than the less-predictable defensive results. You can read for more insight in my recent post about points-allowed for all positions. The second bar represents the a typical D/ST scoring system (ESPN default), and it is shown for comparison against the predictability level of its components.

It is also evident from the chart that "yards-allowed" is the most consistent defensive variable = best at predicting its own future outcome, with correlation 0.175. This is already better than the value of 0.145 you see for default D/ST scoring. We will next see that this fact makes Yds-allowed the dominant factor in an optimized D/ST scoring formula.

Designing a more optimal D/ST scoring scheme

Now we put the factors together, mixing the variables in linear combination, with the goal of optimizing the "self-predictability" of the new aggregate indicator. With some math magic... it turns out we can improve on the 0.175 of yards-allowed... but only slightly: up to almost 0.20.

Here is the final scheme:

The range of scores was somewhat arbitrary-- You could just double all the values, for example, to double the variability. (Obviously correlation is unchanged.) But, to give you an idea of what scores this would produce, here is the distribution of scores (2017-2019) created by my draft scheme:

In the scheme presented, D/ST fantasy points would usually fall between 0-17 points. Predictability/correlation is independent of scale, so you could multiply the scores by any factor, if you wanted to widen the distribution.

And to get a feel for how strongly each variable matters, the following chart shows variable's contribution to score average and the (individual) standard deviation of scores:

The new scoring scheme is essentially dominated by Yards-allowed, with lesser influence from Score-allowed and TDs. FR/Int/Sacks become practically irrelevant when optimizing for predictability.

I found the following to be surprising:

1. Sacks essentially just add randomness, once you have already accounted for yards etc. Besides this covariance, another reason sacks disappear is that they depend more on the opposing team. I investigated more and found that defensive sacks have an especially strong tendency to "regress to the mean"-- meaning that defensive sacks trends tend to correct themselves (e.g. if there have been recent fluctuations up or down). This is another way to explain why sacks are worse indicators.

2. Points-allowed comes out weaker (but mostly because it is so covariant with yards allowed, which is more consistent).

3. TDs don't go away as much as Ints and FRs. This does not mean TDs are predictable of future TDs (they are not), but it implies that TDs are indicative of an ability to limit yards-- and that the ability to limit yards may be predictive of future TDs. Somehow TDs are complementary to yards-allowed, but not so covariant as to disappear.

Is it more predictable though?

Yes, a full projection model can perform better on the new D/ST scheme than it is able to perform on the default scoring. Without too much work, I was able to show this. The bars to the right show the increase in predictability. I've included the other variables again, for the sake of comparison.

It might be important to note: this modified D/ST scoring scheme would make the position become the most predictable position in fantasy football-- even more than QB.

The right-most bars on this chart represent the projection accuracy for default D/ST scoring and the possible accuracy to predict modified scoring, respectively.

Summary

D/ST scoring can be made more predictable, but it's up to you to decide how significant that is. I've shown that D/ST score self-correlation can be boosted from today's 0.145 up to 0.20. This is desirable and would make D/ST become more self-consistent than RB/TE/WR. Furthermore, the potential accuracy of a full D/ST projection model could get boosted from correlation 0.37 to above 0.42-- higher than QB and every other fantasy position. Nevertheless, I'm sure it's not a big enough jump to convince everyone to change their settings.

But if you do feel like playing around with modified scoring, then I suggest: (1) reduce TDs to 2-3 points, (2) crank up the effect of yards-allowed while shrinking the effect for points-allowed, (3) eliminate or reduce the reward for sacks, (4) shrink but don't eliminate the rewards for turnovers. The result will be that it becomes easier for you to choose a D/ST based on its own historical results; while at the same time your opponent's D/ST is a bit less likely to explode unpredictably.