## Simulating the Game: Eagles vs. Cardinals

Mark J. Rebilas-USA TODAY Sports

Bleeding Green Nation simulated the game between the Philadelphia Eagles and Arizona Cardinals. Eagles eat Cardinals.

Thanksgiving may have come and gone but the bird feasting continues. Next up, served with some leftover sides, are Carson Palmer and the Arizona Cardinals.

Due to the holiday, I have to keep this post a little shorter than normal. Nick Foles and the Philadelphia Eagles enter this game against the Cardinals needing to keep pace with the Cowboys, who won yesterday. The Eagles do own a slight advantage, but both offenses have been equally efficient, so the margin for error is low. Good thing it's the month of Folesember... Happy Nicksgiving!

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Note: 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.

*Simulation Details

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. Offensive performances throughout the season were entered into a logistic regression formula born from the HFA research, and randomized according to standard error values and turnover differential.

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 Opponent) + C, where A, B, and C are constants.

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