Monte Carlo in 30 lines: simulating NFL perfect-season odds
A perfect NFL season is a rare event, which makes it a good fit for Monte Carlo simulation: instead of solving the probability exactly, you play the season many times and count how often a team wins every game. The idea is simple. Give each game a win probability, draw a random number for each game, and check whether all of the draws land in the team's favor. Repeat that tens of thousands of…
Monte Carlo simulations are an effective way to calculate the odds of a perfect NFL season. Instead of determining the probability directly, the simulation plays out the season numerous times and tracks how often a team achieves an unblemished 17-0 record. Each game's outcome is determined by generating a random number and comparing it to the game's win probability.
By repeating this process thousands of times, the simulation arrives at an approximate probability of the event occurring. The provided JavaScript code illustrates this concept, where an array of win probabilities for 17 games is passed to the function. The function iterates through each game, checking if the random number generated falls within the game's win probability.
If all games are won, the counter for perfect seasons increases. Finally, the function returns the fraction of perfect seasons out of the total trials, providing an estimate of the true probability. To verify the accuracy of the simulation, the code also computes the exact probability using the win probability raised to the power of the number of games (0.85^17 ≈ 0.063).
The simulation should yield a value close to this exact answer, serving as a sanity check before introducing more complex factors. Real-world simulations require incorporating additional variables such as opponent strength, home field advantage, rest, ties, and injuries. These elements can be modeled by adjusting the input array of win probabilities accordingly.
However, it's important to note that the simulation's output is contingent upon the input probabilities, which reflect the assumptions made. Therefore, the simulation measures the consequences of these assumptions rather than the actual performance of a team. For those who prefer not to write code, a free online simulator called "17-0 Game" is available to run these experiments in the browser.
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