“He’s not Hamlet. He gets to pile up a lot of stats off of a lot of pitchers who started the year in A, or AA ball .… Check out his stats against the top pitchers in the league this year or the past few years.”

That was one reader’s response to yesterday’s column on the latest Alex Rodriguez controversy, in which I painted Rodriguez as too refined for baseball and the teammates and managers who think that brutal public criticism is the way to get him back on his game as either malicious or unthinking. It’s a point people have made to me quite a lot this year, and to be honest it’s one I’ve always brushed off as the product of selective memory. You don’t put up numbers like Rodriguez has while only hitting the scrubs.

Still, it’s never bad to examine a prejudice. Maybe Alex Rodriguez really can only hit the bottom feeders. It’s not the kind of thing that’s difficult to check, so I did so, checking out the numbers for Jason Giambi and Derek Jeter as well. Both are renowned clutch hitters whose careers are contemporaneous with Rodriguez’s, so the comparison is fair.

For my sample of the top pitchers in the league, I picked Johan Santana, Roy Halladay, Bartolo Colon, Roger Clemens, Barry Zito, Pedro Martinez, and Tim Hudson. You could pick different pitchers, but that list encompasses every American League Cy Young winner dating back 10 years plus Tim Hudson, the most consistently elite pitcher in the league not to win the award in that time. This isn’t anything remotely approaching a comprehensive study — to do that you’d want to judge how the three hitters did against pitchers of a certain caliber over a defined period of time, and strip out park effects and so forth in so doing— but it’s something against which to measure the common impression that Rodriguez can’t hit the good pitchers, while Jeter and Giambi can.

Here are the three players’ career lines against those seven pitchers:

You can probably guess the punch line here: Player A is of course Rodriguez, Player B is Jeter, and Player C is Giambi. I suppose that if you combed over the play-by-play records you might find that every one of Rodriguez’s hits against all these pitchers was in a meaningless situation, while every one of Jeter’s came in the clutch, but the more mundane explanation seems more likely: Rodriguez is not only the best hitter of the three, he’s better against the best pitchers the league has to offer.

The one caveat to note here is that Rodriguez has completely owned Colon, by far the least of these pitchers, hitting .444 with 8 home runs in 44 atbats against the portly Angel. On the other hand, Jeter (.353, 2 HR in 34 AB) and Giambi (.286, 2 HR in 28 AB) have also hit well against him. They just haven’t hit as well as Rodriguez has.

Going down the ledger of other pitchers Rodriguez is better than Jeter, usually far better, against every one of them save Zito. He’s hit .377 against Clemens and slugged .625 in 39 at-bats against Santana; Jeter’s numbers are .188 and .429, respectively. These are small and really quite meaningless numbers of at-bats, but if they support any conclusion it’s that Jeter can’t hang against the tougher competition.

Giambi does better than Jeter in the comparison—while Rodriguez owns Hudson (.359/.405/.641), Giambi treats him like Charles Oakley treats debtors (.421/.500/.947), and he’s also been better against Halladay and Zito. On the other hand, Rodriguez has faced Giambi’s longtime Athletic teammates more than five times as often, and his overall numbers are vastly better.

There is a lot of subjectivity in watching baseball and judging baseball players, and you can chop statistics a lot of ways to make different points, but I think the numbers here speak pretty plainly for themselves. And the fact that most everyone thinks the exact opposite of what the numbers reflect also speaks pretty plainly about the kind of impression these three players leave on people. Think about Giambi and you’ll think about him posing at home plate while watching a ball disappear into the upper deck; think about Jeter and you’ll think of him pumping his fist, think about Rodriguez and you’ll probably think of Brandon Arroyo’s glove.

Luckily for the Yankees, baseball games aren’t won and lost based on the impression players leave with spectators, but on what players do on the field, and especially what the best players on a team do against the toughest competition. Judged by that standard, you still might not think Rodriguez is the man you want up against Santana come playoff time. What he and his teammates have actually done, though, makes you think he’s probably the man who should be up.