There were somewhere around 22,000 innings played in the Major Leagues this year.
There were zero three pitch innings. It is kind of rare.
Based on this report (not mine) it happened at least twice in 2015.
Given the data gaps evident in that report prior to 1988, I'm assuming the necessary PBP data is scarce for dates prior, so it's pretty sketchy before that, but it looks like it happens 3-4 times a year on average these days, so I'd guess the 175 number might be based on verifiable ones, and doesn't account for all the ones that happened prior to comprehensive PBP data.
Edited to add, it looks like that report might have been limited to 1-inning relief outings (possibly due to limitations in the search functionality at BBREF), since there are a bunch of 2-pitch innings in there. But that would probably mean there are a bunch more by SP that aren't getting caught.
Jac, if you add IR=0 (Inherited Runners), that might be more accurate. Thanks for posting that. I didn't know you could query BR like that.
Also, regarding the gaps in the Baseball Almanac list, that page does note the list is "far from being comprehensive", and was compiled from press accounts, not from game stats.
