Although the word “umpire” has been in the language since the late fourteenth or early fifteenth century, it is a variant of a still older word, noumpere, which entered the language in the mid-fourteenth century but lasted less than a hundred years.
For a noumpere became altered to an oumpere, which then underwent many changes of spelling until the one we know was adopted in the seventeenth century.
The original English form was adopted from the Old French non per, nom per, “not equal,” from non, “not,” plus per, “peer.”
It has reference to the third man who was called in to settle a dispute when the two arbitrators first appointed could not agree, that man thus making the total number of referees unequal so that there would necessarily be a majority opinion.