Under what conditions can a run be scored on a play that results in a 3rd out for the team? I was under the impression that if a 3rd out happens, all runs that might have scored before time during that at-bat are invalid, but apparently there is more to it than that.
If the 3rd out is the result of a force-out (example: bases loaded, batter hits to the third baseman, third baseman steps on third base before runner reaches), then the run from third base will not count.
If the 3rd out is the result of gunning for extra bases (example: bases loaded, batter hits past third baseman, batter reaches first and goes for second, left fielder throws to second baseman who tags out the batter before he reaches 2nd base), then any run scored (given the runner has reached home before the batter was tagged out) will count as the batter reached first base.
If the 3rd out is the result of tagging up (example: runner on 1st and 3rd, batter hits sacrifice fly, outfielder catches the ball for the out, runner on 3rd reaches home, runner on 1st goes for 2nd but gets tagged out), then the run from 3rd base will count because the out at 2nd was not a force-out.
As for myself, I would like to know the intricacies as well, and will update as I do more research.
Rule 4.09 of MLB's Official Baseball Rules of 2012 states:
Basically the run is recorded only if all the runners were "safe" initially. That is, a batter made it to first base (safe) while the runner on third came home, then the batter was tagged out trying for second base.
Or a fly ball was recorded for the second out. All baserunners (not counting the hitter) were safe initially. The third base runner tagged up and came home. A first base runner tagged up and was tagged out at second.
The last out must have been through a voluntary play of the runner, not a forced out.