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Paul"issued in the first year the player is eligible to appear on a trading card".
What does that mean? It is utterly meaningless when applied to vintage cards. Babe Ruth was "eligible" to appear on a trading card as soon as he left his mother's womb.
For modern cards, I think this is a reference to the fact that MLB, Topps, and Upper Deck have an agreement not to issue a card of a player until he meets certain elibility conditions. (I forget what those conditions are -- but it probably has to do with major league games played, or designation on a team's roster, or something similar).