Here is a visual representation of the distribution of 1B fielding, as per the UZR/150s of qualified 1Bs in the UZR era (which is 2002 and thereafter). The mean is 0.8 runs, which is slightly above average because unqualified 1Bs tend to be worse. The standard deviation is 7.5 runs. The bin labels represent the right endpoint of the bin, so UZRs between 0.1 and 4, inclusive, are counted as part of the “4” bin, and so forth. Note that the left side of the distribution is essentially bounded at -16, with little exception, as teams are just utterly unwilling to play someone worse than that, defensively, for long enough that he might qualify for the batting title.
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