Bequeathed runners represents the number of runners left on base by a pitcher when that pitcher leaves the game. It's often used as a statistic when assessing a starting pitcher's luck regarding his ERA, because any bequeathed runners who score an earned run after a pitcher has left the game will negatively affect his ERA.
Bequeathed runners, however, is a stat over which a pitcher has a great deal of control. He, after all, is the one who let those runners reach base in the first place -- and he's also the one who couldn't make it through the inning.
Along with being a pitching metric, bequeathed runners can be an assessment of a manager's philosophy. Some managers try to avoid bringing their relief pitchers into a game with men on base. As a result, those teams usually have lower bequeathed runners totals.
Watch: Dan Straily exits a game with two men on, bequeathing runners.
In A Call
"inherited runners" (for the pitcher who is entering the game)