There are presently 162 team-games/season x 30 teams =4,860 opportunities per season. Up until 1961, there were 154 x 16 opportunities per season, or 2464 opportunities, with the number creeping up as the season expanded to 162 games in 1961 and 1962, and both leagues gradually expanding. If we figure 50 years at 2464 games, and a weighted approximation of 3600 a year for the 50 years since, I roughly calculate that to be about 300,000 pitcher opportunities to throw a perfect or any other kind of game.
In PGA golf, I would guess that there are close to 40 sanctioned events per year, with all roughly 150 invitees playing two rounds, and the roughly half the field that survives the cut playing four rounds. So each week, you have roughly 75 x 4, plus 75 x 2, or 450 opportunities to post a given score. 450 times 50 years times 30-40 tournaments works out to 675, 000 900,000 opportunities.
And just to subject myself to ridicule, I'm going to post this off-the-top of-my-head, first draft, without even testing it so if I did something dumb in my calculation, you can all have a good time with it.
BTW, how many of the five 59s were attained under the "clean amnd place" rule. I remember that Al Geiberger's was. The other memorable thing about Geiberger's is that he didn;t have any rounds in the 60s. Johnny Vandermeer, he wasn't.