On the topic of baserunning and how good or bad the Sox have been, there are stats for that.
For overall baserunning skills, BsR, the Sox rank 7th in MLB at 5.4 runs above average.
The Sox do very well in stealing bases, as mentioned in other posts. They are ranked first with 4.9 runs above average. They also do well in staying out of double plays, ranking 4th with 2.2 runs above average.
However, in terms of UBR, Ultimate Base Running, the Sox are below average, ranking 23rd with -1.7 runs above average. This stat measures things like advancing to 3rd from 2nd on a ball hit to the shortstop, going 1st to 3rd on a single, and scoring on a sac fly, among other things.
So overall, their aggressiveness on the basepaths has helped them. However, take away the stolen bases and they haven't done as well with their aggressiveness as some think.
These stats are available for individual players also, if you want to see how well a particular player is running the bases. Sometimes it is obvious. Other times, not so much. Fangraphs is a wonderful site, as MVP78 will attest to.