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Mickey Mantle was very good at baseball. Obviously. But the thing about baseball is that when you get the sample sizes small enough, you can find weird things. You can find pitchers that you've never heard of that Mantle weirdly couldn't hit.
In the final five years of Mantle's career, the Tigers had a pitcher named Joe Sparma. Sparma made his debut in 1964 and had an okay season. He followed that up with another good year in 1965. Every year after that, his stats are below average. Sparma made a career for himself in baseball, but he wasn't particularly good. Mantle's career slash line against Sparma was .162/.225/.216 in 40 plate appearances. He recorded just six hits against a pitcher who allowed five home runs to Carl Yastremski in a fairly similar sample size.
Mantle's at bats against Sparma did come towards the end of Mantle's career. While he was still a good hitter in his twilight, those results are a little more explainable. Mantle's at bats against Saul Rogovin came at the very beginning of his career. Rogovin was a solid pitcher in his time, once leading the league in ERA. He is not someone you would expect to get the better of Mickey Mantle on a consistent basis, but he did.
In 48 plate appearances against Rogovin, Mantle hit .150/.292/.150. Of the six hits Mantle got against Rogovin, three came in the first five times he faced him. In the final 18 times Mantle faced him, he got just one hit.
The player Mickey Mantle faced the most without ever reaching base at all was Bob Heffner. Mantle faced Heffner nine times in 1964 and 1965. He struck out three times, grounded out twice, and flew out four times. The same Bob Heffner allowed Chuck Hinton to get seven hits off him in ten at bats.
By far the weirdest stat line that Mantle had against a pitcher was what he did against Wally Burnette. This one arguably shouldn't be grouped in here. You can't really say that Burnette did especially well against Mantle, but it's going in this post anyway because it's interesting. In fourteen career plate appearances against Burnette, Mantle got just one hit. Mantle did manage to walk eight times against him though. And the one hit he had against him was a home run. For his career, Mantle had a triple slash line against Burnette of .167/.643/.667. So, yes, he didn't get that many hits against Burnette, and for that, I'm counting it.
Again, these are very small sample sizes. You can find excellent pitchers that Mantle owned. (He hit Hall-of-Famer Hal Newhouser to the tune of a 1.524 OPS.) You can also find crappy pitchers that Mantle destroyed in a handful of plate appearances and then never faced again. Baseball is a weird sport. Even legendary players can have bad results against not-great opponents. You just have to look hard enough.
Sources
http://www.baseball-reference.com/players/m/mantlmi01.shtml
http://www.baseball-reference.com/players/r/rogovsa01.shtml
http://www.baseball-reference.com/players/s/sparmjo01.shtml
All data courtesy of the Baseball-Reference Play Index