Why Gunblade is actually damn good on Jax
T8 CaliTrlolz just built Gunblade as a second item on Jax in his LCS game against Coast, and in his post game interview, he didn't really explain why Gunblade is so good on Jax (neither did Jatt & Phreak on the analyst desk). The real reason why Gunblade is great on Jax isn't just that the raw AD + AP synergize really well with his ability ratios; it's that Spell Vamp is a GODLY stat on Jax, who gets the full spell vamp value on his Q, W, and Ult AA procs. Combined with the lifesteal from HTGB, Jax functionally becomes a drain tank hyperbruiser. Every Q, W, and Ult proc give Jax huge bust heals, on top of Jax already crazy high damage.
BotRK is more commonly built on Jax, and overall it DOES give him more sustained damage than HTGB, but Gunblade gives Jax the burst damage and burst healing that make him better at diving the back line (which is generally Jax' job in team fights).
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. Learn your builds dude.