In one of our fall games, a third strike was called by the home plate umpire, with no outs and a runner on third. The batter took off for first base, in case the ball hit the ground (as many girls are being trained to do now). My catcher thought she caught the ball, and so threw the ball back to the pitcher. The third base coach starts yelling, "Run, run." I called to the home plate umpire: "Well, is she out or not?" The umpire didn't say anything. Just had that dazed look.
So here's the situation my girls now found themselves in: A girl who they think is out is running to first. The umpires are giving no guidance as to whether they think a dropped-third has occurred or not. So the girls can make a probably needless throw to first, allowing the runner on third a chance to score on the throw. Or they can hold the ball, keeping the runner at third, but giving the batter first, if it is later ruled that the ball hit the ground.
In our game, I had our girls hold the ball (as I saw a clear catch). The opposing coach had her batter stay on first. The umpires still said nothing, and the next batter came out to hit. Before a pitch was thrown, I asked the home plate umpire, "Did you call a dropped third? Did you see the ball hit the ground?" He said, "No, I didn't see it hit the ground." He then asked the field umpire if he saw it differently. The field umpire said, "I saw it hit the ground." So the batter was allowed to stay on first.
So how should this situation have actually played out? It's certainly unfair to have the fielding team have to decide on where to throw the ball, if at all, without some call from the umpire. What if the batter is "thrown out at first", even though the ball is ruled later to have been caught, and the run scores on the needless throw. Thoughts?