Wolfish: Its more than theory; its practice. Even a Ben Sorer — who is UNDER 13, is said (according to one) to have happened. THAT was rare. A 13 year old receiving the maximum penalty of Beis Din, there is no basis to say it was any rarer than a 50 year old. If a 13 or 50 year old was Mechallel Shabbos (with the requisite attachments — i.e. warning, witnesses, etc.) both of them were just as culpable to the death penalty — and Beis Din would NOT provide any consideration to the 13 year olds age more than the 50 year olds age.
I encourage you to learn the seventh perek of Gemara Sanhedrin — Arba Misos. You will see that very often almost any possible loophole was taken to avoid giving a death penalty — to the extent that a Beis Din that executed a person every seventy years was known as a bloodthirsty court. Some Tana’im publicly took the position that if they sat on a court, there would NEVER be a death penalty.
All that being said, I have to believe that, if at all possible, a court would have bent over backwards to excuse a 13 year old due to immaturity.
So, in practice, the death penalty was rarely carried out, even when technically deserved.
The Wolf