When Does the Run Count?


I saw a variation of this play today:
 
Bases loaded, two out and a full count, so all runners are running on the pitch. The batter hits a ground ball to the shortstop, whose throw to first is poor.  In the following 3 situations, when does the run score from 3rd base?
 
A. The first baseman catches the wild throw from the shortstop and swipe tags the batter just before the batter arrives at first, but well after the runner from third has crossed the plate. Does the run count?

Call
No runs score. 8-2-6k: With 2 outs, if the base missed was the first to which the batter or runner was force to advance, then no runs score.

B. The shortstop's throw pulls the first baseman well off the bag and the base umpire properly calls the batter safe. However, the batter misses first base. The first baseman chases down the batter (who is in foul territory in short right field) and tags him and appeals to the base umpire that the batter missed first. Meanwhile the runner from third has scored and is already in the dugout. The base umpires agrees with the first baseman that the batter missed first and calls the batter out. Does the run count?

Call
No, NF 8-2-6k and MLB 4.09 (no run shall score during a play in which the 3rd out is made by the batter runner before he touches first base.).


C. The shortstop's throw pulls the first baseman off first base and the batter is declared safe at first, but the batter turns and takes several steps toward second, then dives back to first and is tagged out. The runner from third scored well before the batter was tagged out while diving back to first. Does the run count?

Call
Yes, this a a timing play because the defense did not appeal the missed base, but instead tagged the runner after he had made an attempted to advance to second. On this timing play, one run scores.