The game uses those stats directly. If a pitcher doesn't allow many steals, trying to steal will result in the saying "can't get a jump". It also uses both the pitchers and catchers stolen bases allowed, as well as the runners, when calculating if he is caught or not.

I.E. Catcher allows 60% base runners to steal, Pitcher allows 80%, then the defense stops steals at about 70%. This is then compared with the runner, say he steals at 90%, then the overall chance would be around 80%.

I don't have the exact equations, but this is close to how it works.

Ken