Who gets the run?

Question
How do you determine which pitcher gets the run when a pitcher comes in in the middle of an inning?  The run was scored off a hit from the "relief" pitcher but the scoring runner was on put on base by the previous pitcher(BB).

Answer
The pitcher that is responsible for a specific runner on base is the charged pitcher....

Example:  Two men on base, pitching change.  Next batter hits a home run.  The first two runs are charged to the previous pitcher, teh HR to the latter.

Thanks, for the question.....Andy