What I really meant was--if one went through and calculated it, I think that the general odds of getting a second single in a game, given that a first one has already been hit, is basically the same as getting the first one, once correcting for the number of plate appearances remaining in the game. This is what I mean. Take an average .280 hitter. Let's say that guy get a single in his first plate appearance. I don't think the odds that he gets a hit in his next few appearances goes up dramatically just because he got a hit in the first plate appearance. His odds are still about .280 in each of his subsequent plate appearances, obviously ignoring issues such as specific pitcher matchups, runners on base, etc.

It's true that it's much more likely for Curtis Granderson to hit 2 triples in a game than, say, David Ortiz, but what I measured here is just the ratio of 1-triple games to 2-triple games. I don't think the results are any different than if I measure it for games where ANY players hit 1 triple or 2 triples. I will check that.

2009 stats for four names chosen (somewhat) at random:
Mark Reynolds: 44 HR, 3 games with multiple HRs
Curtis Granderson: 30 HR, 3 games with multiple HRs
Albert Pujols: 47 HR, 10 games with multiple HRs
Alphonso Soriano: 20 HR, 1 game with multiples HRs

So at a quick glance, it's looking like I'm wrong

For 2009, the rates were:
1B: 1 per 6.50 PA
2B: 1 per 21.4 PA
3B: 1 per 197 PA
HR: 1 per 37.1 PA

This leads me to believe that BSK is right. These ratios (from 2009) are roughly half of the ones from Andy's set (from 2000-2009). Though I'd like to see the ratios from the full decade for an apples-to-apples comparison, it seems pretty conclusive that a player who's gotten a hit is actually more likely than average (perhaps significantly so) to get another.

A bit of a quibble with how "independent" the events are. The frequency of a given outcome is league wide or, really, historic. But that does not mean it provides the odds for a given player. The likelihood we'll see one of these events happen at any given time follows the ratios given. But, for a given player, they can vary wildly.

Albert Pujols hitting 2 HRs in a game is not the same as Rey Ordonez. Yes, each at bat is 'independent' of the previous one. But for Pujols, it's like flipping a coin where one outcome is HR and the other one is everything else and for Ordonez it's more like rolling a die where one outcome is HR and the other five are everything else (obviously, this is grossly oversimplified and not scaled properly). Now, this party is pretty obvious.

But taking it a step further, the guy more likely to hit 2 HRs in a game is also the guy more likely to hit 1 HR in a game. So, if we know a guy already hit 1 HR in a game, we can make a certain (albeit very minor) assumption about his ability to hit HRs. And can assume that he is more likely to hit 2 HRs in the game than the guy who has zero, and not ONLY because he has a head start.

This is like the, "Are you more likely to score multiple runs in an inning with a lead-off HR or a lead-off walk?" Despite what Joe Morgan thinks, you have a far better chance with the former and not only because you are already guaranteed of one run... but also because it can be reasonably assumed you are more likely to score runs off a pitcher giving up HRs than one giving up runs. The difference may be marginal and even negligible, but it's certainly not zero.