What is an earned run, and how are runs charged when the pitcher changes mid-inning?

Earned run (rule 9.16): a run the pitcher is held responsible for. Reconstruct the inning without errors (except catcher's interference) and passed balls, always giving the pitcher the benefit of the doubt on which bases would have been reached. An earned run is charged when a runner reaches home by the aid of a safe hit, sacrifice bunt, sacrifice fly, stolen base, put out, fielder's choice, base on balls, hit batter, balk or wild pitch before fielding chances (outs or decisive errors) have been offered to put out the offensive team. Mark it by colouring the run circle green.

Unearned run: no run is earned when scored by a runner whose time at bat was prolonged by a muffed foul fly, who reached first through interference, obstruction or any error, or whose life on base was prolonged by an error when errorless play would have put him out. Mark it red.

Change of pitcher (9.16(g) and (i)): a relief pitcher is not charged with any run scored by a runner who was on base when he entered, or by a runner who reaches on a fielder's choice that puts out a runner left by the previous pitcher. A new pitcher inherits the outs but not the errors. Runs charged as earned against a reliever can sometimes be unearned against the team, shown by a half-red, half-green circle.