"-field" joining rule for compound words?

Looking through the OneLook Dictionary Search results for *field, no obvious pattern jumps out at me.

I thought it might be related to syllables, but there are polysyllabic compounds that are usually written closed (e.g. battlefield) as well as examples of monosyllables that are usually separated from field by a space (left field, right field, as well as your example of maize field).

Overall, the spelling of field compounds seems to be as unpredictable as the spelling of compound words in general. Following what I think is a usual pattern for compounds, -ing words are usually written with a space after them: e.g. playing field, flying field, killing field.