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Visualize this: Enhanced Toxic Differential and the Chicago Bears

Is there a better way to look at “toxic differential?”

Cincinnati Bengals v Chicago Bears Photo by Jonathan Daniel/Getty Images

One of my favorite football stats is called “toxic differential.” Brian Billick put this idea out into the NFL stat-osphere and I instantly took a liking to it. The idea was to account for team health by balancing the big plays you create on offense and defense with the bad plays you allow. In the article linked above, Billick describes explosive plays as over 20 yards. Teams have different thresholds for what they consider explosive and there is no consistent reportable mark on a lot of publicly available stat sites.

My memory of that article attributed an explosive run as any over 15 yards, but that comes from Sharp Football Stats, which I have adopted as my standard as well. Sharp uses 15 yard runs and 20 yard pass plays as explosive marks and tracks that data for all teams. The Football Database serves as a good source for turnovers.

Using information from those sites allows us to calculate the traditional toxic differential number by plugging numbers into the following:

(Number of takeaways + Number of explosive runs + number of explosive passes) - (Number of turnovers + number of explosive runs allowed + number of explosive passes allowed) = Toxic Differential.

As much as I love toxic differential, I believe it can be improved. For one thing, sacks can be easily added into the equation. They’re big plays that we know have a high likelihood of killing drives. Yes, there is a potential for some double counting if a sack results in a fumble recovered by the defense, but I think I can live with that. Second, I think turnovers need to be worth more than what a sack or explosive play is worth.

As a result, I applied simple tweaks to toxic differential to create what I’m calling “Enhanced Toxic Differential.” I’m applying a crude doubling of the value of turnovers and adding sacks to the equation as such:

((Number of takeaways x 2) + Number of explosive runs + number of explosive passes + number of sacks) - ((Number of turnovers x 2) + number of explosive runs allowed + number of explosive passes allowed + number of sacks allowed) = Enhanced Toxic Differential.

Here’s what this looks like for the Chicago Bears so far this year. My visual approach aims to look like a series of sliders, where more blue is good, orange is bad. The Enhanced Toxic Differential is the top line and each individual components has its own slider as well.

Enhanced Toxic Differential for Bears 2021

Obviously, it’s early and zero explosive passes thus far for the Bears makes this look particularly bad, so it might be worth revisiting this down the road. I went back in time with available data to see what previous years look like. Important note: I narrowed the edges to amplify the visual to let the color quickly show the differences, making the min/max 25% and 75% of the total. It’s a fair criticism to want to keep the axis to show 0-100 but trimming off equal portions to allow the eye to quickly identify color differences seemed worth it in this instance. Here’s what the previous four years look like:

Chicago Bears Enhanced Toxic Differential 2017-2020

We can go back with the data to 2016, but Sharp’s explosive play information ends there. Some reflection on trying to improve on Toxic Differential: I don’t know if doubling the value of turnovers and takeaways is the right number but it’s at least directionally correct. I do believe that missed field goals and turnovers on downs should be added to turnovers/takeaways but it’s not readily available information. If we were going to try and standardize this approach, I would find a way to pull that data into the mix easily.

Here’s each slider from 2021 going back in time to 2016 in gif form, just for fun:

Enhanced Toxic Differential 2016-2021 starting in 2021 and moving back in time

What do you think of this information? Is Toxic Differential an interesting stat and we should leave it alone or can it be improved? Did this way of visualizing the information work or can we improve it? Let me know in the comments below or find me on Twitter @gridironborn.