。
He loves baseball so much that he rarely misses a big game.
Literal
Baseball [subj-が] loved-[and-で] big-game [topic-は] mostly miss-seeing thing [subj-が] not-exist.
Two clauses joined by the te-form of 大好きだ (大好きで, 'being very fond of (and thus)...'). まず here is the adverb 'hardly, scarcely' (a slightly unusual use) + the ~たことがない experiential negative: 'there is hardly any case of having missed.' 見逃す ('overlook, miss seeing') is a compound verb: 見る+逃す ('let escape').