I have the June 26 - August 2, 1883 Providence booklet of Wrights.
I think I may have an answer regarding as to whether Harry Wright actually scored the games directly into these scorecards/scorebooks during the game. My answer is that sometimes he did and sometimes he didn't.
In some of these scored games Harry has multiple small tic marks for tracking assists, errors, etc. These were the games he scored during the game.
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In other games, he did not use these multiple tic marks and I believe he scored them on other scorecards and then entered them into the booklet later.
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For further proof I'll digress for a moment. On the back of each booklet, or at least the one I have, Wright has cut down a single scorecard and glued it to the back of the booklet to add a little color.
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I figured that scorecard may hold a clue so I pulled it back as best I could. Sure enough, it has a scored game on it and it's one of the games from my booklet. That game in my booklet did not have the multiple tic marks on it. So, I believe Harry scored that particular game on the individual scorecard and then added it to the scorebook later.
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One more thought, I believe the scorebook Harry is holding in the dugout is actually one of these booklets.
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He had these trimmed down and gilded before they were put into the the full year's scorebook. You can see where part of his writing is cut off from the top of the scored pages.
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Rob M