Minimax Strategy in NFL Playcalling

I’ve been working behind the scenes on a new way to analyze NFL games using game theory and data-driven strategy. Instead of just guessing, I’m applying the minimax principle — the idea that each coach calls plays to protect against the worst-case scenario — and combining it with EPA (Expected Points Added) from thousands of real plays (2022–2024).

This approach builds “matchup matrices” that show how offenses perform against specific defensive looks, then runs 2,000 full-game simulations to see how those tendencies scale up. The DAL vs PHI example? Both teams’ minimax move was to attack deep, but PHI’s deep passing proved far more consistent, leading to a 67% win probability in the sim.

I’ll be using this exact method to publish my Week 1 NFL picks. Stay tuned — the data is in, and the first set of game previews and predictions will be out soon.

1. What is the Minimax Strategy?

In game theory, the minimax strategy is a decision-making framework built for situations where opponents are trying to outsmart each other. Imagine you’re on offense: you can Run, Short Pass, or Deep Pass. The defense has its own three counters: load the box (Stop Run), blitz and crowd the short zones (Stop Short), or drop safeties (Stop Deep).

Both sides are playing a guessing game. The minimax approach says: “Assume my opponent is smart enough to pick the best counter to whatever I choose. Which option still gives me the best payoff in the worst-case scenario?”

In football terms, minimax isn’t about being flashy or always right — it’s about avoiding your weakest option and sticking to the safest call, even if the defense guesses correctly.

NFL Example: 3rd Quarter of a Tied Game

Picture this: 3rd-and-4 at midfield with the score tied in the third quarter. The stadium is buzzing because everyone knows the outcome of this play could swing momentum. Both coaches know their call won’t just decide whether the drive stays alive, but could also set the tone for the rest of the game.

• Offense could run — safe, low turnover risk, but maybe short of 4 yards.

• Short pass — good chance of converting, but risks incompletion or interception.

• Deep pass — high reward, but higher risk of turnover or wasted down.

Meanwhile, the defense chooses whether to sell out against the run, crowd the short zones, or sit back deep. The outcome depends not only on execution but also on the “matchup” between those two choices.

2. Building a Payoff Matrix

We can chart this as a grid showing the average yards gained for each offense/defense pairing. Rows are offensive choices, columns are defensive calls. For example:

• If the offense runs against a stacked box, they might average ~2 yards.

• If they throw short against deep coverage, they might average ~8 yards.

This average yards matrix becomes a risk-adjusted scouting report. It doesn’t just show what works when everything goes right — it shows what still works when the defense makes the correct counter.

• Offenses look for rows where the numbers hold up well across all columns → their bread-and-butter.

• Defenses look for cells that drag those numbers down → their chance to disrupt.

Minimax logic: the offense should pick the row where the worst-case outcome is still better than the other rows. The defense, in turn, tries to drag that row down as much as possible.

3. How EPA Adds Depth

Instead of just yards, we can use Expected Points Added (EPA). EPA measures how much a play changes a team’s scoring outlook. For example, 1st-and-10 at your own 20 is worth ~0.7 expected points. After a 5-yard gain, 2nd-and-5 at the 25 is worth ~1.2. That play’s EPA is +0.5. Positive EPA means the offense increased its scoring chances; negative EPA means the defense won the snap.

4. How We Infer Intent

From play-by-play data (2022–2024), we categorize intent like this:

• Offense: “Run” comes directly from rushing attempts; “Short Pass” and “Deep Pass” come from the pass_length field (<15 air yards = short, 15+ = deep).

• Defense: “Stop Run” = 7+ in the box or heavy front; “Stop Short” = blitz or ≤5 DBs; “Stop Deep” = 6+ DBs (dime or more).

It’s not perfect — RPOs and Hail Marys blur the lines — but across thousands of plays, it captures the real strategic intent behind each call.

5. Real Example: DAL vs PHI

DAL offense vs PHI defense:

• Runs: 4–5 yards/play, ~0 EPA — safe but limited.

• Short passes: 5–6 yards, often negative EPA — PHI’s defense snuffs these out.

• Deep passes: 11–12 yards/play, consistently positive EPA — DAL’s only reliable weapon.
  DAL’s minimax: Deep Pass, even against PHI’s best counters.

PHI offense vs DAL defense:

• Runs: ~3 yards, negative EPA — DAL’s front dominates here.

• Short passes: positive but inconsistent.

• Deep passes: 12–13 yards/play, +0.44 to +0.60 EPA — reliable across all looks.
  PHI’s minimax: Deep Pass, too.

6. Simulation Results

To scale this up to a game, I ran 2,000 simulations using:

• Each team’s playcalling tendencies

• Each defense’s look distributions

• The EPA matrices as payoffs

The outcomes:

• PHI win probability: ~67%

• DAL win probability: ~30%

• Expected score: PHI ~38, DAL ~31

• Margin: PHI favored by ~7

By running the simulations thousands of times, the randomness of individual plays smooths out and the underlying tendencies become clear. Dallas shows flashes of explosiveness when it connects on deep passes, but those moments are offset by stalled drives whenever the short passing game falters. Philadelphia, on the other hand, sustains efficiency across more possessions — their deep passing game consistently produces positive outcomes, even against strong defensive looks. That reliability compounds over four quarters, which is why the model projects the Eagles not just as slight favorites, but as a team that controls the game more often than not.

In plain language: even if DAL hits some deep shots, PHI’s offense is more consistent and efficient over four quarters.

7. Big Picture

• Minimax strips away the guessing game and focuses on the safest high-value plays.

• Matrices highlight matchups — where one team’s bread-and-butter collides with the other’s best counters.

• Simulations scale those tendencies up into full game predictions.