A player is awarded a run if he crosses the plate to score his team a run. When tallying runs scored, the way in which a player reached base is not considered. If a player reaches base by an error or a fielder's choice, as long as he comes around to score, he is still credited with a run. If a player enters the game as a pinch-runner and scores, he is also credited with a run.
The league leaders in runs scored are generally adept at reaching safely and running the bases. But they also tend to score frequently because of favorable positions toward the top their teams' lineups -- a factor that has little to do with the run-scorer's own abilities.
With almost no exception, a pitcher is charged with having allowed a run if a runner he allows to reach base comes around to score. This is different from earned runs, which are not applied if the pitcher allows runs due to defensive errors by his team.
On rare occasions, a pitcher can be charged with a run even when he did not directly allow the scoring player to reach base. If a pitcher allows a baserunner before exiting, and the following pitcher gets a fielder's choice out, the original pitcher is still responsible for the batter who just reached base. This is because the batter who has reached on a fielder's choice is merely replacing the runner put on by the previous pitcher.
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