With no runners on, they have allowed a .318 OBP and a .390 SLG but with runners on, those numbers are .295 and .329. This differential is much better than any team over the years 2101-14. We can measure this by using OBP and SLG to estimate wOBA or weighted on-base average, a stat from Tangotiger. See this definition at Fangraphs. All data from Baseball Reference.
The idea is that each event has a run value and once that is found it is divided by something like plate appearances. The following estimator is a good approximation:
wOBA = (1.7*OBP + SLG)/3
So that gives the Cards a .310 wOBA with no runners on (NONE) and .277 with runners on (ROB). So, they are .033 better with ROB. The team with the best differential from 2010-2014 was the 2011 Phillies, who allowed a .296 wOBA with NONE and a .276 with ROB. So they were only .020 better, not even close to the Cards this year. The 2013 Red Sox were next being .018 better.
I ran a regression to estimate runs per game allowed using this wOBA estimator for all teams (in all situations) from 2010-2014. Here is the equation:
R/G = 30.136*wOBA - 5.20
The standard error was 23.94 per 162 games. The Cards have about a .296 wOBA allowed in all situations this year. The equation predicts they would allow about 3.72 runs per game while it is actually 3.21. So they are allowing about half a run per game less than expected. Their performance with ROB helps out here.
I also ran the regression with wOBA in both NONE and ROB situations. Here is the equation:
R/G = 11.72*NONE + 18.52*ROB - 5.32
The standard error was 21.1 per 162 games. It predicts the Cards would allow 3.44 runs per game (only .23 above the actual). So over half the difference between their actual runs allowed per game and that predicted by wOBA is eliminated if we break things down into wOBA allowed in NONE and ROB situations.
Some of the remaining differential is probably explained with their wOBA with runners in scoring position (RISP). That is just .269.