When Roy Halladay died tragically last November, one of the recurring themes while he was being remembered was that he and Don Larsen remain the only pitchers to ever throw a no-hitter in a postseason game (for good measure, Larsen threw a perfect game). Every no-hitter is a wonderful feat in its own right - even A.J. Burnett's version - but throwing one in the playoffs is the stuff of legends. The stage is bigger. By default, one could argue that the competition is guaranteed to be strong. And the very act moves one's team that much closer to the ultimate prize (assuming the no-hitter means said team wins the game, which is almost a guarantee but not quite).
Per above, Bob Gibson did not throw a no-hitter in the playoffs but he probably did something even better when he famously struck out a still-postseason record 17 batters in Game 1 of the 1968 World Series. He also scattered five innocuous hits (four of which were singles), and walked just one batter. It makes perfect sense that this happened in 1968 because Gibson was nearly untouchable in 1968. That season, Gibson was one of four pitchers ever to throw 300+ innings and have an ERA under 1.25. And his 1.12 ERA was the best of those four. Oh, and he was also the first (and last) person to pull off that feat since 1915.
But back to Game 1 of the 1968 World Series, let's start with the 17 strikeouts.
Turning to Baseball Reference's Play Index, for 9-inning games dating back to 1913, there have only been 40 instances in the regular season in which a pitcher racked up 17 or more strikeouts in a single game. By contrast, there have been 227 no-hitters in MLB during this span (including the multiple-pitchers variety). So on any given day, you're almost six times more likely to see a no-hitter than witness a single pitcher fan at least 17 batters, though the former still likely brings more fanfare (even Burnett got the customary celebratory pile when he threw his no-no despite nine walks).
Cherry-picking a bit more because that's what the Play Index is for, if you do a search for pitchers since 1913 in the regular season who have struck out 17 batters or more, allowed one or zero walks, and gave up no more than five hits - similar to Gibson's line - you're left with just 14 games. Here they are (sorted by strikeouts):
A few notes: One, Kerry Wood's 20-strikeout game might be the greatest game ever pitched. I'm not sure what would be better.
Second, Roger Clemens is the only pitcher to accomplish this feat twice. Third, there are brothers on this list - Ramon and Pedro Martinez. The odds of that happening seem quite small. And finally, Max Scherzer's no-hitter to close out the 2015 season is the most recent example, beating out Corey Kluber, who dominated our own birds on a cold, dreary day in Cleveland (if you so remember) by a couple of months.
More notably though, again, only 14 times in regular season history has a pitcher equaled or exceeded Bob Gibson's strikeout, walk, hit-line from Game 1 of the 1968 World Series. Fourteen times. To put that in perspective, there have been 23 total perfect games on record in the regular season (there would be 24 if instant replay had been a thing in 2010), and that's an insanely small number for a sport with as rich of archives as baseball. If you're lucky enough to find yourself in attendance at a perfect game, thank the baseball gods. Maybe even buy a lotto ticket on your way home.
But then realize this: What Gibson pulled off that day in 1968 was even more special. More rare. If there's a killjoy to this story it's that the Cardinals ended up losing that series in seven games, but not for a lack of Herculean effort from Gibson to put the finishing touches on a truly historic season.