'centrally-evaluated' is a compound of 'centrally' and 'evaluated'. 'centrally' derives from 'central', which comes via Old French and Latin from Latin 'centralis' and ultimately Greek 'kentron' meaning 'center'. 'evaluated' comes from French 'évaluer', from Late Latin related to Latin 'valere' meaning 'to be worth'.

'central' passed into English from Old French/Latin (Latin 'centralis' ← Greek 'kentron'), and 'evaluate' entered English via French 'évaluer' (from Late Latin/vernacular Latin roots related to 'valere'). The compound form 'centrally evaluated' is a modern English coinage combining the adverb and past participle to describe centralized assessment.

Individually, 'evaluate' originally meant 'to determine value' or 'to assess worth'; over time its meaning broadened to 'assess, judge, estimate'. In the compound 'centrally-evaluated' the focus shifted to indicate that the assessment was performed by a central authority or centralized procedure rather than locally.