I’ve ranted about the concept of “productive outs” before - any stat in which the best AL and NL teams are the Devil Rays and the Expos respectively can’t be good. Indeed, any stat in which your best hitters are Miguel Cairo, Brandon Inge, and Tony Womack sounds dubious to me.
And yet you can’t deny that it’s better to see a runner advance from first from a ground ball to third than to see a fielder’s choice from a ground ball to short that leaves only a runner on first. So on this SoSH thread there’s an attempt to make sense of it all, chiefly the fact that teams which make Ks as a higher percentage of all outs score more runs than teams which don’t. (If you reduce this to: teams that K more often score more, the first graph on this Baseball Prospectus page should illustrate the principle) The usual explanation is that Ks prevent you from grounding into double plays, but I also think Ks correlate with a patient approach that wears out starters and lets you feast on a bullpen.
Personally, I feel the problem is the way the stat is framed. The whole premise of productive outs starts with the implication that, for any at-bat with runners on, the out was inevitable, when it’s not. Another way to look at it may be to say: the goal, when there are runners on base, is to advance the runner. You can advance the runner with a hit or a so-called productive out. Given the choice between those two, which would you take? Clearly the hit. The Ks come as a by-product of an approach that is trying not to make outs.
Still, it seems it’s to the Sox’s advantage to have as many teams as possible believe in productive outs. And the occasional team like Anaheim that succeeds while making many productive outs helps that cause, because other teams can look to Anaheim and say, hey, that approach might work. It’s like watching someone saying “hit me” when he has 18 in blackjack and getting dealt a 3: it can work, but the odds are better the other way around.