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How many extra pitches are required for ten defensive runs allowed?

For example, if Travis Snider was 10 runs better than Eric Thames defensively this year what would the effect on the bullpen be? Would the number of extra pitches be negligible or would it be a valid concern if you are choosing one player over the other?

My guess would be that to allow an extra 10 runs a team would have to throw at least 100 extra pitches or perhaps an equivalent of around 7 extra innings. That is just a guess though and I’m curious is someone out there can quantify the number more precisely.

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