Being that the Rays have graciously given fans around the league three of the last six perfect games, it's tempting to think that they're special. There's no denying that yesterday's lineup was a relatively weak selection from an already offensively challenged team. There's also no denying that Felix Hernandez really is special. The combination of these two factors makes the perfect game seem almost inevitable.
I have no special insight into whether the Rays hitters approach under Shelton makes them any more susceptible to the perfect game and the no-hitter than another similarly limp-hitting team would be. What I can do, though, is very basic math.
League average OBP is .320. That means that the chances of a batter not reaching base in each at bat is .680. The chances of that happening 27 times in a row are .680^27, or 0.003%
But the Rays are not an average offense, and King Felix is not an average pitcher.To calculate in the particular, I first ran the lineup Joe Maddon put out there last night through my splits regression tool. Against a right handed pitcher, they should be expected to average a .321 wOBA, with Evan Longoria leading the way with a .372 wOBA and Sean Rodriguez bringing up the rear with a .291 wOBA. Hernandez has something to say about these expectations, though. Throughout his career, he's allowed a .307 wOBA to lefties and a .274 wOBA to righties (he's been even better of late, but when in doubt, I'm going with career numbers). According to The Book, hitters and pitchers affect the expected wOBA of their matchups equally, so I went ahead and averaged each player's regressed split with Hernandez's career split against their handedness. This brings the overall lineup average down to a .307 wOBA, with Matt Joyce now the Rays best hope for runs, at a .334 wOBA, and Longo brought all the way down to .323.
Caveat: This is a very crude way of explaining the batter-pitcher dynamic. For instance, Jose Lobaton, batting left handed, is expected to hit a .295 wOBA against right handed pitchers, so Hernandez's .307 career mark actually brings his expectation up. This is obviously incorrect. Bad hitters should be expected to hit worse against good pitchers, not better. This is just a frivolous, celebratory calculation though, so I'm not spending the time to normalize things the way I should.
To turn these wOBA projections into OBP projections, I used my wOBA breakout tool. This takes a wOBA and a player's expected hit distribution (against all pitchers) and supplies the right number of PAs to make them jive. The result? a .309 expected OBP for this Rays lineup against Felix Hernandez. After accounting for two pinch hit appearances, I have a final result: King Felix has a
0.0043% 0.0042% chance of throwing a perfect game against Maddon's lineup.
Four thousandths of a percent is better odds than three thousandths of a percent, but it's still far from a certainty. Yes, the Rays are not very good at hitting a baseball; yes, Felix Hernandez is extremely good at throwing a baseball; and yes, you should still be amazed by what happened yesterday afternoon.