Putting the E in Explosives: A Note on Accounting for Game State in Big Play Rate

What estimating explosive rate with a two-stage model can tell us about how college football teams attack.

In college football, big plays are often how a game gets decided. Longtime followers will be familiar with years of the “Did We Really Get Beat That Bad?” graph showing teams with even (or negative) success rates but winning by big margins, in large part due to explosives. Now, success rate is more stable than explosives, but explosives can explain why the final margin of a game looked like it did.

I’m taking a week off the FOOTBALLNOMICS series to crank out a quick note about a way to account for the situational aspect of explosive plays.

In this note, I’ll ask and answer the following questions:

• Where do explosives come from?

• Is there a better way to account for when a team creates explosive plays rather than a simple rate?

• What practical game-planning applications can coaches and analysts take from this approach?

For the duration of this piece, we’ll consider an explosive play a designed run of at least 10 yards or a dropback (including scrambles) of at least 15 yards. Additionally, I’ve filtered out all goal to go situations, all kneels, scrambles, broken plays, and quarterback sneaks. This provides us a better sample of plays to understand how an offense intends to function, which gives us a leg up for game-planning and opponent scouting.

As an additional note, this framework extends nicely to a lot of applications - if you want to define explosives a different way, you can change those parameters and use this simple approach. If you want to look at run/pass tendencies, you could use this approach as well. The specific example will pertain to explosive plays, but the general framework of “adjusting for context in football stats with a two-stage model” extends far beyond this unique case.

Inception: Models within Models

The two-stage approach to modelling is quite common in economics. From instrumental variables for identifying causal effects to the Heckman selection correction, the idea of using a model on one variable, then using the output of that model to model another variable is a convenient process to account for linkages and dependencies among your data.

In this case, the algorithm is straight-forward. We will answer two questions: (1) what situations lend themselves to explosives in college football more often? and (2) which teams are better at explosives accounting for situation?

One driving motivator of my inquery today comes from an immutable reality of college football data analysis: We can’t separate intent from execution in play-by-play data. We don’t have a base rate of how successful a play designed to be an explosive is because, well, we can’t know which plays were designed to be explosives. When we talk about “explosive play rate”, what we’re actually talking about is “percent of all plays that were explosives”, not “explosive play success rate”. That’s a subtle, but meaningful, distinction.

I’m sure if you talked to coaches, they would have a plethora of heuristics for when and what explosives look like (I tend to be partial to 1st and 5, 2nd and 1, and, well, just generally taking more shots). Aside from those obvious situations, or plays where a defense commits offsides and the quarterback recognizes it and the receiver recognizes it and you get a free play, it’s difficult to know when a team is trying for an explosive play rather than a chunk gain or just a conversion. Additionally, we’d need to get deeper into the weeds to separate out a “schemed open” explosive play from a “the defender fell down or our running back just trucked a dude who should’ve tackled him” (explosive play). All of the above are useful avenues to pursue, but at the onset, what we can do is try to empirically derive the situations in college football games where explosives happen most often. From there, we can examine which teams find themselves in the most “explosive-friendly” situations and help better refine our perception of team offensive attacks.

Finding Explosive-Friendly Situations

The method for the first stage of the model here is simple. Using play-by-play data since 2019 from Sports Info Solutions, I create a binary “explosive play” variable, filter out the aforementioned goal-to-go, kneel down, QB sneak, and broken play situations, and select the relevant variables.

I’m using a random forest here, mostly for interpretability and flexibility. Sophisticated analysts could quibble, preferring a gradient boost approach, a logistic regression, or whathaveyou. To my economist brain, that’s beside the point, I just want a reliable model that works, so we’re going to go with the Random Forest.

The model predicts the probability of an explosive play based on the following factors: down, yards to go, yards to opponent end zone, score differential, and quarter (could easily sub in time remaining to get more granular here). We’re keeping it simple.

From the Random Forest model, we can extract variable importances, which give us some indicators about the factors that most affect when explosives happen. In order, the importances are:

• Yards to End Zone (makes sense, more space on the field to defend means more probability for a long tail play)

• ScoreGap (when a team outmatches their opponent, things tend to spiral in their favor; when a team is outmatched, they get weird and desperate)

• Yards to Go

• Quarter/Time Left

• Down

This in and of itself is informative! The factors that most impact explosives are where you are on the field and game state. That helps coaches immediately begin to drill into whether an offense is explosive in “neutral” time, or whether they’re explosive when they are backed up, or any number of specific situations that are going to require specific preparation.

The three down-and-distance combinations that are most conducive to explosives (have the highest probability according to this model) are 3rd and long (7+ yards), 2nd and long (7+ yards), and 3rd and medium (4-6 yards).

There we have it: our first stage model provides some useful insights (and, frankly, more than I’ve scratched the surface of) about what situations explosives happen in, and also bears out that we can learn more about the timing of explosives from a simple model, as opposed to just a raw explosive play rate. Now, we’re on to accounting for team ability to create explosives, given the situation.

(A techincal disclaimer about all of the above - we can glean a lot from this simple implementation of a model. The accuracy is decent, but also explosives are rare events. To extend this to production for the use of a team, you’d probably want to account for the rarity of explosive plays and choose a better distributional assumption in your Random Forest model. It’s Sunday afternoon in Februrary, so we’re just building basics out for now).

What to Expect When You’re Explosive

If you’ll pardon the punny title, we’ll move on to the second stage of the model. Now that we have probabilities of an explosive play for our entire dataset, we’ll feed that back into a second model that focuses on the team-specific proclivity to create explosive plays.

We could - as I have in the past with RROE - simply take the sum of predicted explosivenes, the sum of the actual explosives, subtract the two and divide by plays for each team to get an “Explosive Rate Over Expected”. I’ve come to believe that actually ignores meaningful information about how a team behaves over the course of a season, and so my first pass at amending that is to use a random effects model.

For the non-technical audience, all we’ll do is create a regression where we have explosive plays as a function of the situation (predicted explosive plays) and a team-season effect. There are fun possibilities to model coaches and coordinators as “dynasties” over multiple years here [any time I’ve done gameplanning work for college football teams, they always want to look at what a team has done in years past], but for today we’re treating each team-season as an independent group. [On theme with the message in the introduction, the extensions to this general framework are abundant, and who knows, I’ll probably get to a lot of them this offseason.]

What this output gets us then is a team’s explosive play talent relative to the situations they faced in their games.

We’ll look at two outputs from this model. The most explosive teams since 2019 and the entire landscape of explosive plays for the 2024 season.

The Most Explosive Offenses Since 2019

Before I show you this table, I want to clarify- these estimates are not opponent-adjusted, they’re situation-adjusted. That means that an offense having a higher explosive ability than another does not mean they were “better”, but simply as a matter of style they created more explosives relative to the situations they faced. Treat this stat as you would a rush rate, not as you would EPA/play.

1. 2023 LSU +.700

2. 2021 Virginia +.651

3. 2024 Miami +.649

4. 2020 Florida +0.583

5. 2024 San Jose State +0.562

6. 2019 LSU +0.560

7. 2023 Washington +0.535

8. 2022 Arizona +0.527

9. 2024 Syracuse +0.508

10. 2020 BYU .495

I’m only showing the top ten, but there are a lot of great offenses just knocking on the door (2020 Alabama, 2021 Pittsburgh, 2023 Georgia, etc). The disclaimer about “style” vs “efficiency” makes a lot of sense here, because even though this is correlated with efficiency, there are some fun appearances on this top ten list (Kyle Trask’s Florida! Jayden de Laura’s Arizona!).

What these numbers start to do here is tell you which offenses rely on explosives most often. There’s some level of optimization in the explosiveness-efficiency tradeoff for most teams, and a lot of “elite” teams are in the middle on explosive power, mostly because they’re so efficient, they are trying for explosives less often.

The Explosive Play Landscape in 2024

Comparing the raw explosive play rate to the estimated effect, we see of course they’re correlated! Good offense are good offenses, duh! What gets fun here is the additional information that the estimated effect gives us. Consider the cases of Florida and Colorado. Florida is a standard deviation above the mean in terms of estimated explosive effect, but firmly in the middle in explosive play rate, suggesting that the Florida offense had a lot of explosive potential, but suffered from a lack of “explosive-friendly” situations that we estimated in our first step. That’s information opposing coaches can use - Florida’s offense is dangerous, and not-highly situation dependent. Colorado, on the other hand, is near the top of raw explosive rate, but well within a standard deviation of the mean of estimated effect. Also information opposing coaches can use - when Colorado gets in an “explosive-friendly” situation, they’re going to make you pay.

Game planning becomes really nice here, because not only are you accounting for how potent your opponent’s offense is, you’re getting an idea of how often they capitalize on (or find themselves in) explosive-friendly situations. We’re starting to chain together sequences of plays that lead up to explosives, not just looking at base rates. For coaches and coordinators on Sunday afternoon trying to prioritize where to spend their practice time for the week, this is an invaluable resources that helps you identify the particular contexts that will be the highest-leverage for your upcoming matchup.

Conclusion, Limitations, and Extensions

So, what I’ve done here on a Sunday afternoon is demonstrated how a two-stage modelling approach can add value to an analyst’s toolkit, particularly in this example of understanding the context in which a stat occurs. We saw that field position and game state were the driving forces behind “explosive-friendly” situations, and from examining the outputs of the second stage, that not all explosive offenses happen in the same way. With targeted analysis like this, teams can begin to understand their opponents at a deeper level than just raw rate stats and create valuable strategies for prioritizing their game preparation.

Now, as for limitations, I’ve made a few technical comments throughout. The most glaring, is of course, the rare-event nature of explosive plays. I’ll probably tweak the first stage to account for that in building this out. Beyond that, definitions about explosiveness, whether to include different sorts of plays, and the like are all in the hands of the analyst.

In terms of extensions, this gets most interesting when you begin to link this across coaches and years. Understanding a team’s style when it comes to explosive plays provides invaluable context for game-planning, and could be particularly useful for coaches who switch teams. Additionally, you could add another layer to this model: opponent adjustments. We shouldn’t count all explosive plays against all opponents the same. You could easily grab the schedule matrix, put the team effects against each other, even adding offense and defense, and optimize to get a true “quality” estimated explosive effect as well.

If you’ve made it this far, I appreciate you reading. I hope that this simple general framework is interesting and useful to you. If you’d like to chat more about this approach, extending it, or applying it to a team, feel free to reach out via twitter, substack, or email.