One of the mysteries of the English language finally explained.
Definition of right half in English:
right half
noun
1The side or region that lies immediately to the right of a person or other object of reference; (also) the right-hand side of (part of the) body or other object. Compare a right (also left) half, right side, 3.
2Football and Hockey. A player whose position is on the right side of the central area of the pitch and who has both attacking and defensive responsibilities.
Origin
Middle English; earliest use found in Ormulum. From right + half.