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.