A round stick or cudgel, or a hockey stick; a variant term used in some dialects.
From 'ball' (round object) + likely '-ogan' (diminutive or tool suffix). Regional dialect term with unclear exact origin, possibly Irish or Scottish.
Obscure dialect words like 'ballogan' remind us that English has thousands of local terms that never made it into standard dictionaries—entire vocabularies that nearly died out.
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