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man on 1st and 3rd. coach calls a bluff play where catcher will throw to shortsop off the bag to try and catch the runner on 3rd when he breaks to home. catcher overthrows the shortsop and the 2nd base backing him up misses the ball as well. runner on 3rd scores and runner from 1st goes all the way to 3rd. when i score it seems like most appropriate is 'on the throw' as reason for advancing runner but im quite sure an error should be tagged to somebody. please hlep. thx.

Assuming the runner on 1st is breaking to second on the pitch, then I would score the play as a stolen base for the runner on 1st going to 2nd. I would score the runner on 3rd going home and the runner originally on 1st going from 2nd to 3rd as advancing on an error on the catcher (E2).

The runner going home wouldn't get a steal though correct? That would be charged to the error as well assuming the runner didn't go till the overthrow.

Yes, R3 would advance as part of the same error on the catcher.