Guess it's all based on what the definition of 'hitter' is in this context. I would take the number of runs produced in a player's career and divide it by the number of games they played in their career to arrive at an average runs produced per game stat. An imperfect formulation, but runs win games, so it makes sense. Of course, there'd still be a helluva lot of screaming about what exactly constitutes a 'run produced' (does knocking in a run and scoring a run both count?), along with everyone who will once again only base their opinions on the theoretical stat of WAR.
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