[LIUmp]

The defensive team forfeits its right to appeal BOO when a legal or illegal pitch has been made to the following batter (this did not happen due to the third out of the inning) or when the pitcher and all infielders have clearly vacated their normal fielding positions and have left fair territory on their way to the dugout or bench. (No, this did not happen either).

So the defense has the right to appeal BOO in this situation in the OP.

Next issue...

If the error is discovered AFTER the incorrect batter has completed a turn at bat (check) and before a legal or illegal pitch has been made to the following batter (can't happen in my case) or before the pitcher and all infielders have clearly vacated their normal fielding positions and have left fair territory on their way to the dugout or bench area (THIS DID HAPPEN),

EFFECT(S)
a. The player who should have batted (B3 in my OP) is OUT. (But we already have 3 outs so now what?)

b. Any advance or score made by the improper batter shall be nullified (ground out...no advance, no anything, it was the third out so no problems there) Any out that is made prior to discovering this infraction remains an OUT. (so her ground out remains out NUMBER 3. Check.)

c. The next batter is the player whose name follows that of the player who was called out for failing to bat. (Player failing to bat was B3, so isn't that B4?)

d. If the batter declared out under these circumstances is the third out, the correct batter in the next inning shall be the batter who would have come to bat had the player been put out under ordinary play. (what? We already had 3 outs, so she was not declared the third out under these circumstances.)

I am NOT choosing which half of the effect I want. I was following the rule to the letter. I still don't see where B3 comes to bat.

I do see your argument, but I guess my real question here is....does it change the way the rule is interpreted when you have three outs? I think we all agree that if there was only one out and the improper batter grounded out for out number 2 and then the defense properly appealed BOO, we would declare B3 out, and it would be the third out and B4 would bat. Also, if there were no outs and the same thing happened, we would call B3 out for BOO, keep the out for the ground out of B2, and have B4 come up to bat. So why would this be different since it was the third out?