Calculating probabilities for events which occur in different increments

[rfr3sh]

I was looking for some guidance in how to tackle the calculation of probabilities / EV for events that occur in different increments such as Passing Yards or Total Points .

For events which are incrementing in the same interval (Assists, Rebounds, Strikeouts) I will typically use Poission, but it cannot be applied in the scenario I'm looking to solve.

[Waterstpub87]

Its difficult for things like that. On top of a standard deviation for pass yards, there would be a standard deviation for completions as well. Football also has the wrinkle that a team that is up passes less. This leads to interesting times when the QB covers the pass yards from all the junk yards at the end of the game.

I would normally use monte carlo method, assume something like passes completed 14 +- 3, yards per pass 15 +- 5.

There must be a way that people solve it closed form, but to me it seems to be too complex to do so.