Can We PLEASE Stop Referencing One Score Losses?

[*bfine32*]

I think the important thing to remember is:

A normal random variable can assume fractional values, but the final margin of victory in a game must be an integer. Therefore we estimate the probability that the home team wins by between a and b points (including a and b, where a < b) is: probability(margin is between a - 0.5 and b + 0.5).

The Excel function:

NORMDIST(x,mean,sigma,True)

gives us the probability that a normal random variable with the given mean and sigma is less than or equal to x.