10 lung shot deer will react 10 different ways. Highly pressured/spooky deer may run WAO until they just fall dead 200-300yds (or more). A big, rutted up buck that was chasing a doe or fighting will be amped up & can take as much killing as a Cape Buffalo. Are there ALOT of coyotes/predators in the area that constantly hound the deer? We're they just feeding along, early season, unaware when you shot? They might not run out of sight... Only thing "predictable" about mortally wounded deer is that they are unpredictable!
But "usually" (if there is such?) if you put a good broad head cleanly through the pump house then "usually" they won't go over 100yds before they lay down & if you (or another critter) doesn't jump them to early then you should be able to find them right there.