The events underlying certain proposition bets of the form "How many … ?"
follow what is known as the Poisson distribution. If an event is Poisson
then it has the property that if you know the average number of times it's expected
to occur over a given time interval, then you can estimate the probability of the
event occurring any number of times. (For example if you expect a basketball
player will make 12 three-point attempts in a given game then the Poisson distribution
tells us that the player makes exactly 10 3-point attempts during the game
will be roughly 10.4837% , and the probability that he'll make more than 12
attempts is roughly 42.4035%). For an event to be Poisson, these conditions need
to be met:
Examples of (approximately) Poisson events include:
It's also possible to compare two Poisson events of the form "How many … versus How
many … ?". For example, a book might offer the proposition that a defensive
line might have more sacks in one game plus three than a kicker might have field
goal attempts in another game. To be able to use the Poisson distribution to compare
these two events the events need to be independent meaning that knowing the
outcome of one event tells you nothing about the likelihood of the outcome of the
other. The Poisson calculator calculates the probability and associated fair odds
of both one-variable and two-variable Poisson events.
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