Calculating Probability of Score Comparison between Two Distributions

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SUMMARY

The discussion focuses on calculating the probability that a value from one distribution (A) exceeds a value from another distribution (B) using known means and standard deviations. Specifically, it presents an example with baseball teams where Team A has a mean score (μA) of 5 runs and a standard deviation (σA) of 1 run, while Team B has a mean score (μB) of 4 runs and a standard deviation (σB) of 2 runs. The method suggested involves defining a new variable C = A - B and using standard statistical methods to determine the distribution of C, ultimately calculating P(C > 0) to find the desired probability.

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This discussion is beneficial for statisticians, data analysts, and anyone involved in sports analytics or probability theory who seeks to understand comparative analysis between two distributions.

cstoos
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Forgive me if this is a silly question, but here goes:

Say you have two unrelated distributions (A and B) with known means and standard deviations. How would you determine the probability of any single value of A being greater than any single value of B?

The easiest example I can come up with for clarification would be something like this:

Over 1000 games baseball team A scores: μA=5 runs, σA=1 runs per game.
Over 1000 games baseball team B scores: μB=4 runs, σB=2 runs per game.

What is the probability on any given day that Team A outscored Team B? Sorry if this example seems elementary, but I am far from a statistician. Thanks for the help.
 
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Direct method: Let C = A-B (there are standard methods to get the distribution function for C, given the distribution functions for A and B). Then compute P(C > 0).
 

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