I'm hoping someone might know the correct mathematical way to approach this. The best way I can frame it is in terms of sports betting. Let's say I project the New York Yankees to score 5 runs today, while Vegas projects them to score 4 runs. I know the mean and the standard deviation for my projected runs and Vegas's projected runs for the entire population of teams.
How often would I expect the Yankees to score above Vegas's 4 run estimate, and how often would I expect the team to score below 4 runs?
I'm fairly certain there's an easy formula to figure this out, and it's one of those things that feels like it's on the tip of my tongue but I can't remember. Any help would be greatly appreciated. Thanks!