One of the things former Red Sox manager Terry Francona did that occasionally upset me (and many others) was pinch-run for one of his big hitters late in a close game. The idea behind this was to help the team score a run fast, as someone like David Ortiz or Adrian Gonzalez might not score from second on a single, and all the team needed (to either win or tie) was that one run. The downside, of course, is that when they didn't score, and the game ended up in extra innings, the lineup was now short a Gonzalez or Ortiz, and someone like Darnell McDonald or Jose Iglesias would then be in the middle of the lineup, where their bat did not belong.
Baseball stats have come a long way, so now we can see just how poor of a baserunner someone that Francona was replacing is. Both Baseball Prospectus and Fangraphs have a baserunning runs statistic, and while the very best runners add around a win (and the worst take one away), in general, baserunning is an area where very few runs are gained or lost. This is simply because, to be in the majors, you have to be of a certain quality on the basics, like running the bases on a base hit, so the separation between even a fast runner and a slower one isn't always as big as you think.
Think of it like pitcher BABIP. Yes, some pitchers have higher BABIP allowed, and others lower, but most tend to slide towards that .290-.300 area. The rule only applies at those numbers in the majors, though, as pitchers incapable of coming anywhere close to that figure have likely been weeded out. Baserunning is the same. There are better baserunners, and worse ones, but baserunning is absolutely a bell curve with a big, fat middle.
Adrian Gonzalez is on the slow end of that curve. In 2011, he was the second-worst baserunner in baseball, behind Ryan Howard, costing himself about eight runs of value. Now, baserunning is accounted for in Prospectus's wins above replacement, and Gonzalez's bat and glove still netted him nearly six wins even with the chunk of baserunning awful. Don't take this as a criticism of Gonzalez, who will be the first one to tell you that, in order to gain his super powers with the glove and at the plate, he had the ability to move his legs in a timely fashion removed.
Gonzalez isn't always that bad of a baserunner. In 2010, for instance, Gonzalez cost himself just five runs via Prospectus, and about a run via Fangraphs (the difference between the two is odd, given they both have him for almost the same exact 2011 score). But it's safe to say he isn't going to be confused for Jacoby Ellsbury on the bases anytime soon, too.
Boston as a club is not a good baserunning team. This is one of the reasons Carl Crawford was signed that doesn't always show up easily in a batting line, as Crawford is one of the league's best. I'm not talking steals, either: first to third, second to home, and any situation like that is something Crawford (and many other Rays) excelled at, while Boston has failed to have a quality baserunning team often. Even with Crawford and Ellsbury, the Sox ranked 19th in baserunning runs, at -3.2 as a club. Ellsbury led the team, but Crawford, who had a .300-ish OBP and missed a month of games, was essentially tied with him. It's a good thing Ellsbury started hitting for more power, because for someone with his wheels, he isn't a great baserunner.
What did pinch-running for Gonzalez do for Boston, for a team that doesn't run all that well to begin with? It (obviously) put a better baserunner out there, since even David Ortiz would have been an upgrade most days. But was the effect enough to justify removing him from the game? This is incredibly rough-sketch, but with 182 opportunities for advancement on the bases last year, and -8.4 runs on the year, Gonzalez's opportunities were worth -0.05 runs each.
Is that enough to merit a pinch-runner? Especially when you consider that the Red Sox didn't employ any kind of super pinch-runner, instead relying on the very average Darnell McDonald and players like him for that role. Whichever one of Marco Scutaro or Jed Lowrie was on the bench that night was the actual best bet to improve the odds in those situations, but even they were worth just .02 and .03 per opportunity.
Then again, if all the Red Sox needed was the one run to go ahead, or to keep the game alive, it's possibly worth it. It depends on the chances of Gonzalez's spot in the lineup coming back up, as whatever was gained by plugging in even a good base runner for Gonzalez would likely be lost (and possibly eclipsed) by not having him in the lineup again later.
Mike Fast from Baseball Prospectus drummed up some general numbers to help envision this scenario:
If the gain is +.07 runs from pinch running, on average, and -.09 runs if Scutaro/Lowrie bats later in the game, then you need his [Gonzalez's] lineup spot to come up less than 40-50% of the games where you do this in order to come out ahead overall. So there's probably some point in the game after which that is true (e.g., pulling a number out of the air, once there's one out in the 8th inning and the game is not tied).
This is one of those situations where context is important -- you can't generalize a right or wrong here. Pinch-running for Gonzalez is a risk, as if the Red Sox fail to score, they are now sans Gonzalez in a game they haven't won yet. But there is also the chance that, given how slow he is, leaving him in to run could result in seeing him gunned down at the plate, too. It all comes down to how much the Red Sox need that one run, at that moment, and how likely it is Gonzalez will be coming back to the plate. We'll have to see how the next manager handles these situations, but maybe Terry Francona knew what he was doing with pinch-running after all.