He pitched for the 1923/24 Santa Clara Leopards team that is considered the most dominant in the history of Cuban baseball; other members of that team included Oscar Charleston, Alejandro Oms, Dobie Moore, Bill Holland, and Eustaquio Pedroso.
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In the fall of 1908, in the middle of the Second Occupation of Cuba, Méndez pitched the games that established him as a legend.
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The average major league winning percentage of the opposing pitchers he faced was .595; he faced star pitchers including Eddie Plank, whom he beat twice, and Chief Bender, whom he beat once.
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