Run support per nine innings measures how many runs an offense scores for a certain pitcher while that pitcher is in the game. That number is then set over a nine-inning timeframe. So the stat essentially answers the question, "How many runs of support does a pitcher receive per nine innings?"
RS/9 is an important tool for evaluating pitchers in the context of their records. Often times, pitchers who haven't pitched well have good records simply because they've received solid RS/9. A similar concept holds true for pitchers who have pitched well but have low RS/9; they sometimes have less impressive records despite their effectiveness.
In no way is RS/9 something a pitcher can control. (On the mound, at least. In National League parks, a pitcher can help his cause as a hitter.) Instead, RS/9 is a nice way of adding context to a pitcher's win-loss record. Does a given pitcher's winning percentage seem a bit too high or a bit too low given his other stats? RS/9 is often the culprit.
It's important to note that for this metric, run support constitutes only the runs that are scored for a pitcher while he is in the game. A few other run-support metrics will take into account how many runs a team scores for its starting pitcher over the course of an entire game. In that vein, RS/9 also works for relief pitchers (although those numbers should be taken with a grain of salt, because relievers have such small sample sizes in terms of innings pitched).
Because pitchers who get better run support tend to win more games, RS/9 can be a useful tool for choosing between two pitchers with similar numbers. A pitcher with a high RS/9 is likely to earn a higher number of wins -- although RS/9 can often be volatile, especially in small samples.
In A Call
"average run support," "support per nine," "runs of support per nine"