Honorary .300+ non-HOF hitter mention goes to Frank Demaree. With 1241 hits in 4144 at bats, his batting average is .2994691. If taken out to the 5th decimal place, the 6 will round up the 4 to a 5, and then that 5 would cause the resulting .2995 to round up to the exalted .300 level for his career. If he only had gotten one more hit (that hit could even have been within 2 more at bats), or instead one less at bat, he would have made it.
Brian (I find that I more readily accept an extra dose of front damage on the 1938 Goudey cards with the cartoons, compared to the ones without, because there is so much going on with them visually, the damage just adds to the wonderful visual cacophony)
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