Probably the two biggest stories of this past week in Major League Baseball are New York Yankee Alex Rodriquez's home-run barrage and Chicago White Sox pitcher Mark Buehrle's no-hitter Wednesday night, the first recorded in MLB this season.

Earlier tonight, Rodriguez hit two homers in a loss to the Boston Red Sox. According to this game article:

Rodriguez went 3-for-4 and joined Mike Schmidt, who hit 12 homers in the first 15 games in 1976, as the fastest to reach a dozen in baseball history.

Also, after Thursday's action, Trent McCotter sent in an e-mail to the SABR-L discussion list, pointing out that -- to McCotter's knowledge -- ARod is also closing in on the record for most consecutive games with two or more total bases offensively:

Most consec. games with 2+ total bases in each
19g: Harry Heilmann, DET, Sept 5 through Sept 30, 1928
17g: Chipper Jones, ATL, Jun 26 through Jul 19, 2006
17g: Alex Rodriguez, NYY, Sep 27 [2006] through Apr 19, 2007 (on-going)

After tonight, of course, Rodriguez is now at 18 games.

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As noted above, the other highlight of the week was Buehrle's no-hitter against the Texas Rangers.

In 2004's issue of the Baseball Research Journal (Number 33), Bob Kapla published an article entitled, "No-Hitter Probabilities: What Are the Odds?" This article shows how to take three simple quantities from a pitcher's career statistics -- games started, innings pitched (which gets converted into "outs achieved" by being multiplied by three), and hits allowed -- and determine the probability of his throwing a no-hitter, either in any given game or at least once in his career.

Using Buehrle's career statistics through the end of the 2006 season, he had retired 4284 batters and given up 1473 hits (for no-hitters, as opposed to perfect games, we ignore walks, errors, etc.). Buehrle's probability of getting any hitter out (on average) was thus .744. A no-hitter requires retiring 27 straight batters, yielding a probability of .0003 (.744 raised to the 27th power) for Buehrle's likelihood of no-hitting the opposition in any single game.

We can also say that his probability of not throwing a no-hitter in a given start is .9997. Buehrle had started 204 games through the end of 2006, so the likelihood that he would fail to throw a no-hitter in all 204 games in a row is .9997 to the 204th power, yielding .933. In other words, in Buehrle's 204 career starts from 2000-2006 inclusive, there was roughly a 93% chance he would never throw a no-hitter. Conversely, there was roughly a 7% chance (.067) that he would have thrown at least one. And in his third start of 2007 (207th career start), Buehrle got one.

[As an aside, given his career mix of outs recorded and hits allowed, as of the time of publication of Kapla's article, Roger Clemens had a 51.73% chance of throwing at least one career no-hitter, yet had never done so. Here's a list of all no-hitters.]

What lends even more of a "hot arm" aspect to Buehrle's no-hitter is how he closed out his previous outing on the mound. Pitching against Oakland, Buehrle gave up three runs in the first inning, but (including the final Athletic he faced in the first) retired 19 of the 21 batters he pitched to the rest of the way, before leaving after the seventh inning (play-by-play sheet).