Sure he made 3 more outs in less opportunities...
Um...that's kind of a big deal. In the same amount of opportunites as Pedroia, you'd be looking at 7 more outs (actually a little over 6.5 if you don't round off). Or you could look at it this way: If given the same number of opportunites, Andrus would be thrown out over twice as often (2.3 times as often, to be exact). There are good reasons why the system treats the cost of an out as 3 times more than the advantage of taking an extra base. For one thing, a significant number of times taking an extra base turns out to be irrelevant, either because the runner would have scored anyway on a subsequent hit or because the runner just dies on 3rd instead of on 2nd when the inning ends. So sometimes the extra base helps, sometimes it doesn't--but an out always hurts.

Andrus takes the extra base at a higher rate than Pedroia

Is that the case? There is something about the BIS system I don't understand because when I add up the numbers in the three "Adv." columns, I don't get the total in the "Bases Taken" column. So the following may be based on a false assumption. (If so, I sure hope someone is willing to correct me!) Let's adjust both Andrus' "Bases Taken" and "Outs" results as if he had the same 75 opportunities as Pedroia's:

Andrus: Bases Taken = 20, Outs = 12 (actually 11.54)
Pedroia: Bases Taken = 25, Outs = 5

Seems like an easy choice to me. If a runner was costing me 11 or 12 outs to get me 20 extra bases, I'd tell him to cut it out and stay put. Plus Pedroia's rate of taking extra bases actually seems to be higher than Andrus' rate.

But I don't know if that is right because when I add up the "Adv." numbers I actually get 24 and 30 for the two players, not 14 and 25. So maybe it is the "Adv." numbers that matter most, not the "Bases Taken" numbers. Comparing the "Adv." numbers with the "Opp." numbers, I get a 46% rate for Andrus and a 40% rate for Pedroia. An advantage for Andrus, but definitely nowhere near enough to justify being more than twice as likely to be thrown out.