# Baseball Expected Runs

From Robin Zimmermann, a clever rule-of-thumb for how many runs to expect will score in a given situation, depending on how many outs there are in the inning and where the runners are:

• When there are no outs and no runners, start with 0.5 (half a run)
• If there are runners on base, consider the lead runner: add 0.4, 0.3, and 0.2 in turn to advance the runner to first, then second, then third base
• Correct for the number of outs: to go from no outs to one out, divide by 2 (unless the lead runner is on second or third: a lead runner on second is worth 0.7 runs, on third is worth 1.0 runs.) To go from no outs to two outs, divide by 4
• If there is a runner on first base behind the lead runner, add 0.4, 0.2, or 0.1 runs with 0, 1, or 2 outs, respectively
• If there is a runner on second behind the lead runner, add 0.6, 0.4, or 0.2 runs with 0, 1, or 2 outs, respectively

Summarizing in a chart, and rounding:

 Outs none 1st 2nd 3rd 1&2 1&3 2&3 loaded 0 0.5 0.9 1.2 1.4 1.6 1.8 2.0 2.4 1 0.2 0.4 0.7 1.0 0.9 1.2 1.4 1.6 2 0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7

This results in a prediction that roughly concurs, according to Robin, with a Baseball Prospectus article tabulation of average runs scored depending on where the runners are and the number of outs. That data changes over time, and of course varies wildly among teams and with specific baserunning and hitting and pitching and fielding abilities of the players on any given day. But for a "ballpark estimate" (<groan!>) it's not bad. Many thanks, Robin!

(cf. SquareRootOfBaseball (2005-05-13), InTheBigInning (2006-01-31), BaseballOdds (2007-04-21), ...) - ^z - 2015-04-16