It's generally accepted that in terms of preventing other teams from stealing bases Yadier Molina is one of the best, if not the best, catchers in MLB. Al Hrabosky is fond of saying that Yadi is so good that teams just don't steal on him anymore (and Al's not the only one). Which always made me wonder... Given that base-stealers must be successful at least 75% of the time to benefit their team, is it really a good thing if Yadi's excellence at throwing out stealers prevents teams from running? After all, if teams ran on him more, he'd generate more outs. Perhaps it would be better for the team is Yadi was worse, thus generating more attempts, thus generating more outs.
I had a few hours to kill tonight, so I thought I'd plot some data, all of which comes from Baseball Reference. The first graph shows the percentage of would-be stealers that Yadi has caught in his career, as well as the National League average.
As expected, Yadi has been very good over the course of his career, well better than the league average, although so far this year has been his worst. But has his success had an effect on other teams? In other words, do teams run on Yadi much less than other catchers? This next graph shows the stolen attempts for Yadi (per 162 games) compared to the NL average. (Formulas: (SB+CS)*(162/GP) for Yadi; ((SB/G)+(CS/G))*162 for NL.)
Okay, so teams really don't run on Yadi: he routinely has 50-60 fewer attempts against than the NL average catcher -- or would have, if he played all 162 games. So Yadi has fewer attempts against but more outs per attempt than the average catcher. We might think that the team would benefit if we could maximize the number of outs made (so long as the percentage of caught stealing remains above 25%). How does this translate into outs over the course of a season? (Formulas: CS*(162/GP) for Yadi; (CS/G)*162 for NL. Again this is normalized as if Yadi played in every game.)
The answer is... there's not a huge effect, but Yadi's prodigious ability to catch potential base stealers probably doesn't help the team, and might even hurt it a bit. In four years (2004, 2008, 2009, 2011), Yadi generated fewer outs on the bases than the NL average. In two years (2007, 2010), he generated more. In two years (2005, 2006), he generated almost exactly the same. In no year is the difference all that large. For the stats-minded: I doubt the effect is statistically significant, but in this case a failure to reject the null hypothesis is very interesting, since it contradicts the Hrabosky-esque conventional wisdom. Obviously this is a crude analysis, but often simple stats are the most illustrative.
The broader point that I'm interested in making is that baseball, like all games, is strategic. If a player is really, really good (or bad) at one thing, then other teams will respond by changing their approach to the game in order to neutralize that advantage. Think of NBA teams fouling Shaq intentionally to make him shoot free throws. Or MLB teams walking Barry Bonds 232 times (!) in 2004. In some cases, it might benefit the team if the individual player were a little bit worse, so that their opponents didn't focus so much attention on them.
In other words, Yadi probably hasn't hurt the team with his cannon arm, at least not much. But he hasn't helped the team much either. It would probably be better for the team if he was slightly above average (say, 30-35% caught-stealing rate rather than 40-50%) but not enough for teams to drastically alter their base-running patterns.