Baseball statistics are approximations.

Something happens every year or two to remind me of this, and the latest reminder comes courtesy of intrepid baseball researcher Herm Krabbenhoft.

For more than four decades, we all "knew" how many walks Ted Williams drew in his career: 2,019, including 145 in his magical 1941 season.

Except that, as Krabbenhoft recently discovered, Williams did not draw 145 walks in 1941; he drew 147 walks, and thus he drew 2,021 walks in his career (or at least that's now our best guess).

Where did those two extra walks come from? They came from the first game of a doubleheader between the Red Sox and Washington Nationals on September 24. On the official sheets, Williams is shown having gone zero for three with no walks, no HBP, no sacrifice hits. This is obviously incorrect, though, because the players preceding and succeeding Williams in the lineup both came to the plate five times, which leaves two of Williams' plate appearance unaccounted for.

Checking further, Krabbenhoft found accounts in four different newspapers -- The New York Times, The Washington Post, The Boston Herald, and The Boston Post -- confirming that Williams had, indeed, walked twice in that first game.

To make sure that Williams hadn't been credited with two extra walks at some other point during the season, Krabbenhoft checked the box score for every Red Sox game that season against the official day-by-day sheets. They all matched up, except for that game on September 24.

A couple of years ago, there was a major revision in Babe Ruth's walk totals. Now, Ted Williams (and who knows what would happen if somebody checked every season of Williams' career?). And again, the lesson is that if the stats are wrong for players like Ruth and Williams, whose careers have been studied as much as anybody's, how many stats are wrong for everybody else?

The answer, of course, is "A lot of them." When I say that baseball statistics are approximations, that's what I'm talking about. They're close approximations, but they're only approximations.