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With the Super Bowl around the corner, I've been attempting to price various prop bets. My question is, can I use the Poisson distribution to calculate the odds of the total number of field goals being over/under a certain amount? So far, my approach has been to generate a table of the odds of each possible combination of field goals such as 3-0, and then sum up the probabilities of each of the events that would result in being over/under for the bet. Does this work? I feel like I might be overlooking some correlation between the number of field goals one team kicks and the number of field goals the other team kicks. I just used the average number of field goals kicked for the last 16 games or so to do all my calculations.

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Interesting question! It would be nice to find out how good the Poisson model is, say for regular season games in the last decade. – André Nicolas Jan 21 '13 at 21:58
up vote 1 down vote accepted

In one article, outline a solution to a simple betting situation using Poisson distribution

Knowing that team A scores 1.5 goals per game on average, and team B scores 1.2 goals per game on average, what are the chances that in a game between A and B: 1) A will score more than B 2) B will score more than A 3) Game finishes as a tie.

Using an Excel spreadsheet they show that

  • A wins = 44.14%
  • B wins = 30.37%
  • Tie = 25.48%

Modeling sports data is a hot topic now. Read Who's #1?: The Science of Rating and Ranking.

The Poisson distribution has to do with the law of rare events:

If $n \to \infty,\; p \to 0 \text{ and }np \to \lambda$ then $$\mathbb{P}[k\text{ successes}] = \binom{n}{k} p^k (1-p)^{n-k} \to e^{-\lambda} \frac{\lambda^k}{k!}$$ The Poisson distribution is a ``rare" limit of the Binomial distribution.

You should check that your favorite statistic, field goals, touchdowns, yards pass ... actually has a Poisson distribution. It should be close and all you have to do is estimate the rate. This rate should depend on all sorts of extraneous factors like weather, venue, turf, injuries, etc.

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