'round-based' is a compound of 'round' + 'based'. 'round' originates from Old English 'rund' meaning 'circle' or 'a course, a turn', while 'base' (as in 'based') derives from Latin 'basis' via Old French 'bas(e)' and Middle English 'base', with 'based' being the past participle meaning 'having a foundation in'.

'round' developed from Old English 'rund' into Modern English 'round'; 'base' came from Latin 'basis' through Old French 'bas(e)' and Middle English 'base', and the past-participle-derived form 'based' combined with 'round' in modern English compounding to form 'round-based'.

Individually, 'round' originally referred to something circular or a turn in sequence, and 'base' referred to a foundation; combined as 'round-based' the compound came to mean 'having rounds as the basis or organizing principle'.