Simulating the Game: Eagles vs. Broncos

NFL simulations are far from an exact science. They attempt to mathematically project the future based on history and past performance, but they can’t account for everything. A stiff breeze, a tipped ball, a freak injury, a rolling fog bank, an ol’ coach’s return, or simply a change in player attitude can alter results in a large way. Instead, simulations give us a blurry view of a series of possibilities among an infinite number of potential realities. But they’re fun. If you believe in parallel or multiple universes, then one of these simulated results could possibly occur.

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Last week I simulated the matchup between the Philadelphia Eagles and Kansas City Chiefs. Even though the Eagles won 71% of the simulation runs, the model’s worst case scenario was eerily similar to what actually happened. When the Eagles reached the model’s limit of giveaways (three), they lost to the Chiefs by an average score of 26-17 (actual score, 26-16, and I have since increased the simulation’s turnover limit to five).

The simulation is based on my home field advantage (HFA) research, which shows how there have been small but distinct and different offensive efficiency behaviors between home teams and away teams in the NFL. And not surprisingly, turnovers play a large role in equalizing the playing field. The Philadelphia Eagles’ and Denver Broncos’ offensive performances over the past three weeks were entered into a logistic regression formula born from the HFA research*, and randomized according to standard error values and turnover differential.

This week, the Broncos win 67% of the simulated games by an average of 6 points. If the turnover differential is 0, the Broncos win 91.7% of the time by an average of 9 points. But according to this model, there is hope (Brandon Gowton, see? Hope!). The Eagles win under the following circumstances:

• If the Philadelphia Eagles’ offense operates with at least 75% efficiency, the Denver Broncos’ offense operates with no greater than 75% efficiency, and turnover differential is 0, the Eagles win 65% of the time by an average score of 23-21 (the problem is, the Broncos offense has operated at near 80% efficiency for the season, while the Eagles have operated at 67% efficiency).
• If the Philadelphia Eagles get two more takeaways than giveaways, the Eagles win 56% of the time by an average score of 22-21.

Of course, if the Eagles turn the ball over more than they take it away, all hope is lost. But never say never!

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*Simulation Details (because someone will ask)

Step 1: Calculate Offensive Efficiency (OE). I used Chip Kelly’s definition for this:

(Rushes + Completions) / (Total Off Plays + Offensive Penalties)

If you check out the HFA research, there’s a really strong correlation between offensive efficiency and team success.

Step 2: Calculate Win Probabilities using the logistic regression formula that correlated OE to team success. Here’s the formula:

Win Probability = 1 / (1 + e^-((A*OE+error value) + (B*Turnover Diff + error value) + C)), where A, B, and C are constants.

Step 3: Convert the results from Step 2 into points using a linear formula:

Points = A*(Win Probability for Eagles) + B*(Win probability for Chiefs) + C, where A, B, and C are constants.