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World Series no-no not as rare as you think?

How improbable was The Houston Astros no-hitter against the Phillies in game 4 of this year’s World Series?  Statistically speaking, there are on average about 2 no-hitters per season in the major leagues so let’s do the math.  There are 30 teams playing 162 games and since you need two teams to play a game, the total number of games in an MLB season is 15x162 or 2430. So that means you can expect a no-no every 1215 games – since there are on average about two per season.

So, what should we expect in the WS? In the modern era (defined as starting in 1903) there have been 685 WS games.  As the Houston no-no was the second WS no-hitter (how can we forget Don Larsen in 1956), that means we’re way ahead of quota on WS no-nos as we’ve now had one every 342.5 games.  One could argue that the odds of a no-hitter in the WS would be higher than the regular season because in theory you have better than average pitchers from the two best teams, but you could also say it’s less likely because you also have hitters from the two best teams.  I won’t even attempt to offer a conclusion about that, but I have a better question for you.  As I watched a well struck line drive to right caught just below the knees in the Astro-Phillies game, it got me wondering…is a no-hitter really a masterful pitching performance or just a statistical anomaly that every ball put in play is, against the odds, imminently playable by the defense?

How do we make sense of a baseball universe where bloops fall in and screaming line drives are caught for outs? They say these should even out over time so if this randomness is true, then something like a no-hitter is just the luck of the draw that happens periodically and is something that we can mathematically demonstrate with computer models, right?  I say “we” of course, but I don’t really mean you and I - we’re not that smart. The geniuses over at the Society for American Baseball Research (SABR) are however and indeed, completed such an investigation about 10 years ago.

The idea was to simulate games with a computer program based on statistical knowledge from 133 seasons (1879-2009) and see how many no-hitters occurred. In reality, there were 250 no-hitters in that span, but when SABR ran their first simulation the model only produced 123 no-hitters. In other words, if no-hitters were completely random events, they would happen only about half the time they actually do. The SABR guys don’t give up that easy so rather than use average probabilities based on the 133-year dataset, they tweaked the program to use hitting statistics for each year of the 133 years they rolled through. This time the model produced 214 no-hitters, better, but still far short of the 250 actual number. Realizing they were on to something, they tweaked the program on the other side of the ball and used year-by-year pitching stats as well. This third simulation produced 243 no-hitters, just a 4% differential from the real-world result of 250. To summarize, if SABR simply used a flat-rate of probabilities based on the history of baseball, no-hitters would happen far less often than they do, but when the simulation took into account year-to-year pitching and hitting statistics, the model simulated a true number of no-nos.

So, what does this all mean?  The conclusion from the study said, “using year-by-year data indicates that those who have pitched no-hitters and perfect games had, in general, far superior pitching ability than the average pitcher in baseball history.”  

Duh, duh and double duh!