If you define "compiling Python" as basically "taking what the interpreter would do but hard-coding the resulting CPU instructions executed instead of interpreting them", the answer is, you don't get very much performance improvement. Python's slowness is not in the interpreter loop. It's in all the things it is doing per Python opcode, most of which are already compiled C code.

If you define it as trying to compile Python in such a way that you would get the ability to do optimizations and get performance boosts and such, you end up at PyPy. However that comes with its own set of tradeoffs to get that performance. It can be a good set of tradeoffs for a lot of projects but it isn't "free" speedup.