Newbie here.... I believe this is a pretty easy question, for all leagues.
Batter hits the ball deep in the out field for an easy double. BR then tries to stretch an easy double to a triple, and is thrown out. How do you score this? I know it's an out, but some coaches are telling me that it's a scored as a hit double, but then an out at third?

What about this situation? Same scenario as above, but the BR is standing on second while the ball is being thrown back to the infield, while the ball is in the air, the BR takes off to third to try and run behind the ball, but is thrown out at third. Is that scored as a double then thown out going to third?

Both are the same, scored as a hit/double, caught stealing to 3rd.

You don't want to penalize the players batting average for their running mistake (or the base coaches mistake).

So, your saying that a hit that is easly a double, and the BR tries to stretch it into a tripple but get out is a hit. So if the BR stikes out the rest of the day, he still goes 1 for 4. What about a guy trying to stretch a single into a double? Same thing?

Yes. Separate batting from running. Don't confuse the outcome with the stats (scoring). The outcome is an out. But the stats separate batting from running.

"Both are the same, scored as a hit/double, caught stealing to 3rd."

No way, Jose' It's not caught stealing. Every attempt to advance is not a steal.

Give the batter credit for all bases advanced to safely, then record how out was made.

Score 2B hit for batter, then out recorded as to how the throw went, i.e: out, 9-4-5.


Bob

Clearing it up
 

Bob beat me to this one. All outs on the bases are not considered caught stealing. Also all advances are not stolen bases. I know of many high school players who get credited with several stolen bases each season for simply moving up on a wild pitch or passed ball. If the player was originally running with the pitch and the ball gets by the catcher then it is a stolen base. If the player advances BECAUSE of the ball getting by the catcher it is not a stolen base.