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MLB didn't officially start recording CS until 1951. Before then, I think it was occasionally reported, but not on a consistent basis. The pre-1951 CS stats that you see in BBRef are probably the result of work done by researchers going through old boxscores. That's an ongoing process, so it's possible that OOTP's stats haven't been keeping pace with the research.
As with other stats that weren't recorded, I think OOTP estimates them for purposes of creating ratings. As such, the incomplete CS stats might not be as big of a problem as it might appear.
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