Pawismom,
You’re absolutely right. The catcher’s reputation has a big impact on the stolen bases attempted by the opposing team. While it does show up in the stats as one half of the SB/SBA I’m not sure that the SBA (stolen bases attempted) is indicative of a catcher's ability. For instance: If your pitcher were a LHP (better pick off move to 1b) and had a terrific outing where he only allowed 4 base runners and none attempted a stolen base, the catcher would not garner any recognition for shutting down the running game nor should he. Whereas, if you had a RHP that was allowing lots of base runners and the catcher threw out six of eight base runners the catcher would be recognized for his heroics. But if playing that same team (here is where the catcher’s reputation comes in) and the opposing coach remembered the arm of the catcher and didn’t attempt a stolen base, the catcher would NOT be recognized on the score book as having a major impact in that game but in reality the catcher did impact the outcome with his reputation. The key stat here is the percentage of the runners thrown out the catcher has established in previous games. This percentage creates the perception (reputation) you make reference to. I might add that the reputation of the outfielder’s arm can also have an impact on the outcome of the game by lessening the sac flies and extra bases.
I apologize for the log winded opinion that probabaly left you more confused than ever.
Fungo