outfield (n.)

in Old English a common prefix with nouns, adjectives, adverbs, and verbs, "out, outward, outer; forth, away," from out (adv.). The use was even more common in Middle English, and also with the senses "outer, outside, on the outside, from without, external, externally; apart; greatly, extremely; completely, thoroughly, to completion." Other senses of out that extended into the use as a prefix include "beyond the surface or limits; to the utmost degree; to an explicit resolution."

In composition out has either its ordinary adverbial sense, as in outcast, outcome, outlook, etc., or a prepositional force, as in outdoors, or forms transitive verbs denoting a going beyond or surpassing of the object of the verb, in doing the act expressed by the word to which it is prefixed, as in outrun, outshine, outvenom, etc. In the last use especially out may be used with almost any noun or verb. [Century Dictionary]

Old English feld "plain, pasture, open land, cultivated land" (as opposed to woodland), also "a parcel of land marked off and used for pasture or tillage," probably related to Old English folde "earth, land," from Proto-Germanic *felthan "flat land" (Cognates: Old Saxon and Old Frisian feld "field," Old Saxon folda "earth," Middle Dutch velt, Dutch veld Old High German felt, German Feld "field," but not found originally outside West Germanic; Swedish fält, Danish felt are borrowed from German; Finnish pelto "field" is believed to have been adapted from Proto-Germanic). This is from PIE *pel(e)-tu-, from root *pele- (2) "flat; to spread." The English spelling with -ie- probably is the work of Anglo-French scribes (compare brief, piece).

As "battle-ground," c. 1300. Meaning "sphere or range of any related things" is from mid-14c. Physics sense is from 1845. Collective use for "all engaged in a sport" (or, in horse-racing, all but the favorite) is 1742; play the field "avoid commitment" (1936) is from notion of gamblers betting on other horses than the favorite. Cricket and baseball sense of "ground on which the game is played" is from 1875. Sense of "tract of ground where something is obtained or extracted" is from 1859. As an adjective in Old English combinations, often with a sense of "rural, rustic" (feldcirice "country-church," feldlic "rural"). Of slaves, "assigned to work in the fields" (1817, in field-hand), opposed to house. A field-trial (1865) originally was of hunting dogs; the term was used earlier in reference to crops (1817).