random baseball idea i had bc this is all i think about

If pitcher is hitting with a runner on 2nd and 1 out, what is the optimal play?

.095 is the median batting average for an NL pitcher with at least 10 PAs

0.65 is the odds of a runner on 2nd scoring on a single

1.00 are the presumed odds of a runner on 3rd scoring on a single

0.70 is the assumed Sac Bunt success rate (in reality the MLB average is slightly lower)

0.273 is the median batting average for a leadoff hitter, min 100 PAs at the 1 hole

.062 for pitcher to get the RBI, simply 0.95*0.65

.273 for #1 hole to knock in player from 3rd

~0.19 for successful sac bunt + hit from leadoff hitter (0.7*0.273)

1-0.938 (odds of no pitcher RBI) *0.823 (odds of no leadoff RBI) = 0.772

~0.228 for pitcher or leadoff hitter to get RBI

Given this (albeit largely rudimentary and dumbed down math that ignores small factors like the possibility of wild pitches or passed balls, not to mention the clear difference between Cedric Mullins and Trent Grisham, for example), letting your pitcher hit with a runner on 2nd and 1 out gives a greater chance of scoring that runner than sac bunting.