Anytime a manager sends a pitcher into a game, no matter if he's a starter or reliever, there's luck involved. Sometimes good and sometimes bad. The more inconsistent the pitcher has been during the season and he is successful, the more luck is involved. No manager knows in advance what a certain pitcher is going to have during a certain game.
That a reliever now, in most instances, has to face at least 3 batters, that increases the luck factor.