PEP: Evaluating tackles in American football.

Deriving the expected points prevented by a tackle via conditional density estimation of the yards gained by the ball carrier.

Resources on the Project

Table 1

Resource	Date	Link
Paper published in Journal of Quantitative Analysis in Sports	2025	DOI
Preprint on arXiv	2024	arXiv preprint
Talk presented at the Sports Analytics Workshop (SAW) 2024 at AUEB	2024-05-24	Presentation (SAW 24)
Submission to the NFL Big Data Bowl 2024	2024-01-08	BDB submission on Kaggle

NFL BDB Update

Sadly, we narrowly missed a top-ten ranking, but we received an honorable mention.

PEP Values to play with

In the interactive table below you can analyze the tackling ability of players for the BDB data. Further information on the methodology can be found in the resources Table 1 above as well as in the sections below (e.g. Section 2).

Position

CB DE DT FS ILB NT OLB SS

TEAM

Number of tackles

Overview

In this project, we developed the metric PEP for quantifying the value of tackles. It allows practitioners to assess players, particularly in terms of their tackling abilities. Our approach allows for within-play conditional density estimation of the end-of-play yard line which serves as a basis for the evaluation of tackle performance measured by prevented expected points by artificially removing the tackler from the data. Importantly, our method incorporates distributional information, i.e., heteroscedasticity and multimodality, which would be lost when solely relying on point predictions. Therefore, the uncertainty can propagate to the level of expected points, leading to an accurate quantification of expected points prevented by the tackle. The main results as well as an animation of our idea can be found below.

Visualisation and Results

The below animation illustrates the conditional density estimation for a sample play. There are a few observations: First, at the beginning of the play the density is concentrated because the model expects a tackle from the closest defender. As soon as T.J. Hockenson (the ball carrier in our example) is able to evade the first tackle, the density changes. The distribution’s variance increases and we even observe bimodality with a lot of mass at the endzone. Finally, at the time of tackle the distribution narrows again, as we expect the runner to make only a few more yards. The main takeaway here is that there is a lot of uncertainty in the predicted yards to be gained, and thus mean estimation has to be interpreted with care. This is especially relevant in our case, where we are interested in measuring the value of a tackle on the scale of expected points (EP), which is a common and interpretable scale in football.

In order to calculate the value of a tackle, we compare two scenarios. First, we consider the inclusion of the closest defender who executed the tackle (left panel of the below figure), and in a next step, we exclude this player (right panel of the below figure). We obtain one predictive density, based on the original features, and one based on a replacement procedure. For the replacement procedure, we systematically remove the closest defender at the moment of the tackle and replace the features with those of the second closest defender. Further on, we replace the second closest with the third closest, and so on. In this way, we come up with a prediction for a hypothetical “what if the tackle would be missed” scenario which then can be compared to the real existing tackle.

We propagate the yards-to-be-gained distribution of each of the two scenarios onto the scale of expected points, which results in our prevented expected point (PEP) metric for each tackle. Details of this procedure are omitted in this summary but can be found in our BDB submission (see link above). Below, a table with the evaluation of tackles from weeks 1-9 of the 2022 NFL season is provided. We calculate for each player his cumulative \(\text{PEP}\) and display these together with the average \(\text{PEP}\) per tackle. To get a reliable average for these, we set the minimum number of tackles to ten. In the above results section you can play with the results for the BDB data.

When comparing players in the above table across different positions, it quickly becomes apparent that, for example, defensive linemen do not have similar PEP values to defensive backs. This is mainly due to the fact that defensive ends, nose tackles, or defensive tackles are protected by linebackers, safeties and cornerbacks. It is necessary to take into account such stylized facts when comparing defensive players among positions.

Update: Due to the above-mentioned drawbacks of the cumulative and average PEP values, we updated the evaluation of players and use mixed effects models to value a player’s contribution to the PEP values¹.

Further Information

A much more detailed description of the project can be found in the link to our BDB submission (see also resources table above). Furthermore, the code to reproduce our analysis can be found on github. Feel free to contact me via e-mail if something is not working out.

Update: We now have a preprint on arXiv that you can check out as well (see resources table above).

Footnotes

1. Some more details about this can be found in the presentation I did for SAW 2024.