Inherited runner

Inherited runners or inherited baserunners are the runners on base when a relief pitcher enters the game. Since a previous pitcher has allowed these runners to reach base (or was simply pitching when the runners reached base, such as in the case of a fielding error), any inherited runners who score when the relief pitcher is pitching are charged to the previous pitcher's runs allowed and/or earned runs allowed total, depending on how each runner reached base. Modern box scores list how many runners each relief pitcher inherits (if any), and how many of those inherited runners the relief pitcher allows to score, called inherited runs allowed.

"The success of most pitchers is based on statistics such as won-loss record, ERA or saves, but the unsung "innings eater" is judged by how many innings he pitches and the impact his work has on the rest of the staff.

"'I don't have a whole lot of goals going into the season. I don't shoot for a certain ERA or a certain strikeout number or certain number of wins', says Blanton, entering his second full season. 'I try to go out and get a quality start every time, six innings or more, and not miss any starts. I feel if I can do that, I'll get my 200 innings in a year and everything else falls into place with that' ".

This is a phrase used in baseball to describe runs scored by a team after they have secured the lead. This applies to any amount of runs and can be used during any segment of the game. The concept is that adding more runs on top of the lead provides a buffer between the two teams. How late in the game a team is able to score insurance runs contributes to how the team gaining the "insurance" are able to take advantage. Late game insurance runs are usually considered more valuable than insurance runs scored early.

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Wikipedia