• Deciding between man and zone coverage is a crucial strategic decision.
• Offenses try to decode these decisions by using pre-snap motion.

➡ Set up a model that forecasts the defensive schema based on pre-snap motion.

Roadmap

1. Supervised Learning

   1. Predict man/zone coverage based on features before motion with ML models.
   2. Predict man/zone coverage based on naive post-motion features with ML models.
      

Data

• NFL Big Data Bowl 2025 provided tracking data of the first 9 weeks of the 2023 season

• After data cleaning (e.g., omitting plays with bunch formations), we focus on pass-plays with pre-snap motion

  • in our data, defenses play \(\approx 74\%\) in zone coverage, \(\approx 26\%\) in man; per PFF

Hidden Markov Model

1. Each \(X_t\) is generated by one of \(N\) state-dependent distributions \(f_1,\ldots,f_N\).

2. The state process \(S_t\) selects which of the \(N\) distributions is active at any time, with the state at time \(t\) only depending on the state at time \(t-1\).

5-State HMM formulation

Guarding assignments cannot be observed but inferred from the defenders’ responses to the offensive players’ movements (Franks et al., 2015) with

Lagged observations within the HMM

We expect defenders to trail offensive players, i.e., alter the state-dependent means as \[ \color{darkblue}{\mu_j = y}_{\color{darkblue}{\text{off}}_{\color{darkblue}{j,} \color{red}{t-l}}} \]

thus, allowing that the state process at time \(t\) depends on observations at \(\color{red}{t-l}\).

Including random effects in transition probabilities

To account for heterogeneity across positions and teams, we include random effects into the transition probabilities \(\color{brown}{\gamma_{ij}}\) as

\[ \text{logit}(\color{brown}{\gamma_{ij}^{(p,t)}}) = \beta_{ij} + u_{ij}^{(\text{position}[p])} + v_{ij}^{(\text{team}[t])} \]

where

• \(\beta_{ij}\) is a global fixed effect,

• \(u_{ij}^{(\text{position}[p])} \sim \mathcal{N}(0, \sigma^2_{\text{position}})\) captures differences between defensive positions,

• \(v_{ij}^{(\text{team}[t])} \sim \mathcal{N}(0, \sigma^2_{\text{team}})\) captures team-specific tendencies in defensive schemes.

Model fitting and state decoding

• to retain probabilistic information, we perform local decoding (Zucchini et al., 2016)

• we construct the conditional distributions \(P(S_t = j \mid X_1, \ldots, X_T)\) for each \(t\).

• this assigns for every defender and time point a guarding probability of offensive player \(j = 1, \ldots, 5\).

HMM random effects results

Example decoded state sequence

   playId       player p_off1 p_off2 p_off3 p_off4 p_off5
31    291 Marco Wilson      0 0.0001      0      0 0.9998
32    291 Marco Wilson      0 0.0001      0      0 0.9998
33    291 Marco Wilson      0 0.0002      0      0 0.9998
34    291 Marco Wilson      0 0.0002      0      0 0.9998
35    291 Marco Wilson      0 0.0002      0      0 0.9998
36    291 Marco Wilson      0 0.0002      0      0 0.9998
37    291 Marco Wilson      0 0.0001      0      0 0.9999
38    291 Marco Wilson      0 0.0001      0      0 0.9999
39    291 Marco Wilson      0 0.0001      0      0 0.9999
40    291 Marco Wilson      0 0.0001      0      0 0.9999

Deriving features from decoded states

A caveat of the decoded state probabilities is the multi-dimensional time series structure, complicating their direct inclusion in the ML models. Thus, we

1. compute for each defender and time \(t\) the most likely guarded offensive player and
   • the sum of state switches per play
     
   • the number of defenders that switch offensive players during a play,

Supervised Learning - Accuracy

Supervised Learning - AUC

Supervised Learning - negative logloss

Significance test I

Significance test II

Team analysis

Discussion

Summary

• Modeling pre-snap motion via HMMs significantly improved the coverage prediction.
• Random effects give insight into assignments of different positions and teams.

If you…

tell me now or send me a message to rouven.michels@tu-dortmund.de!

Thank you for your attention!