By now, you have observed that compounds of two words can be closed, like paperback, hyphenated, like light-year, or open, like “ice cream.” This inconsistency (sometimes persisting, sometimes differing as the prevailing style changes) is one of the maddening vagaries of the English language, but the puzzlement intensifies when the style differs even among compounds beginning with the same word. Take compounds that start with half, for instance.
The variability exists regardless of which part of speech the compound represents. Consider these sample nouns: In field sports such as football and soccer, one of the positions is halfback. But a brother or sister related to one by only one parent is a half brother or a half sister, and when the moon is half full, it is called a half-moon.
Further inconsistency prevails, for example, in classes of similar terms: A fifty-cent piece is a half-dollar, but several other numismatic terms beginning with half — “half crown,” “half dime,” and “half eagle” — are open. (These are all discontinued values of currency, but the discrepancy persists.)
Adjectives incorporating the word half also vary in style: Something that is lacking in effort is halfhearted — the adverbial and noun forms, halfheartedly and halfheartedness, are also closed — while something incomplete or lacking in some quality is half-baked. (I know of no adjectives beginning with half that are open compounds.)
The compound verbs beginning with half that I found listed in one dictionary are consistently hyphenated, but there are only three: half-mast, half-sole, and half-volley. Adverbs are rare, too, but they follow the style of the adjectival forms.
The form for a given compound may differ depending on part of speech or on meaning: For example, a book cover consisting of two distinct materials is half-bound, but the style is called half binding, and “half hour” is open, but half-hourly, as an adjective or adverb, is hyphenated. Meanwhile, the term for the intermission of a competition, whether used as a noun or an adjective, is halftime (“I walked around the stadium to stretch my legs during halftime”; “The halftime show seemed interminable”), but in the adjectival or adverbial sense of working half of the normal workweek, it is styled half-time.
I could use another hyphenated compound beginning with half to describe my feelings about this imperfect system, but I’ll just say that the inconsistent nature of terms that belong in this broad category requires that I often do what I recommend you do whenever you plan to use one: Look it up.