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Today it's twelve to thirteen. Back in the 60s and 70s it was ten to eleven, with nine not unheard of (especially in the 60s).
I BELIEVE that it was the standardization of the five man rotation combined with the new roles of setup man and closer that made the difference. Probably each added one pitcher to the roster. Previously the fifth starter was a spot starter and long relief man. When he became a fulltime starter an extra reliever needed to be added.
The same occurred when setup/closer came into vogue. My recollection is that 'back in the day' if your team was up by two or three runs at the time the other team came to bat it would never enter your mind to bring in a reliever.
Two other factors probably enter into it, but they evolved more gradually. Pinch hitting for position players has decreased over time, so there's less need for bench strength. Righty/lefty pitching matchups have been in use since immediately after WWII (as far as I know Casey Stengal was the first manager to do that as a regular thing, and also the first to institutionalize the platooning of position players), but didn't take off in a really big way until maybe twenty years ago.
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