Air carrier pilot reported the ramp crews are not compliant with new push back procedures at many different airports.

Narrative

There is almost zero knowledge below the wing of our new pushback procedures; after X days of having it in effect. Thus far I have flown two trips since the new pushback procedures have taken effect; for a total of ten flights. Out of those ten flights; just two pushback crews were even aware of the new procedures; and even those two didn't know the procedure - they just knew that there was something new. Even better; out of those ten flights; only two of the ground crews got the prior procedure even close to correct; one was perfect (ZZZ) and another was about 60% there. Given that we are supposed to release the parking brake allowing 150;000 lb. or more of airplane to freely roll as part of this procedure *and the only way to know what the ground crew is expecting is to ask them outside of the standard phraseology over headsets that frequently barely work; it seems like a certainty that someone will get hurt or equipment damaged; or both. Given my prior interaction with the [Chief Pilot] ('it's an opportunity to mentor;' it might take a couple of weeks for everyone to get on the same page;'not all work groups hold themselves to our standard') I'm not at all confident that anything will get done in a timely manner.