There have been plenty of thoughtful posts about Braden's perfect game by more eloquent writers than me, such as Joe Posnanski, or the more numerically inclined, such as Jack Moore at Fangraphs, who pegs the likelihood at 15.2 in a million. But the thing that I noticed is that the Rays have been victims of the last two perfect games. Since there have only nineteen perfect games in MLB history, it shouldn't be all that surprising.
What surprises me is that both in 2009 and 2010 the Rays are a very good offensive club. They're second in the AL in runs this year (174), only behind the Yankees, and 5th in OBP. In 2009, the Rays were 5th in runs scored and OBP in the AL too. There are two things that do jump out at me though - first, both games were day games after night games, and were "get away days", games before the team travels. The other thing I noticed is that Dallas Braden and Mark Buehrle have similar styles. Both rely on good control to minimize walks and a good defense behind them, as neither strike out many batters. Statistics from Buster Olney (Insider required) show that Braden and Buehrle had the lowest number of swinging strikes in all no hitters since 2007. Their pitching repertoires are also quite similar, with both having fastballs that top out in the mid to high 80's, but include a mix of 4 seamers, two seamers, and cut fastballs to go with a changeup and a slider.* If you guys can think of more pitchers in the AL with similar repertoires, I think it would be really interesting to compare how the have Rays hit against those pitchers over the last few years versus how they hit against other starters.
*According to Fangraphs' Pitch FX data, Buehrle hasn't thrown any sliders this year, but has thrown them regularly (12-22% of his pitches) over the past years. I assume that this may have something to do with a change in the classification system, rather than a change in approach.