Tri-Force is such a great item for several reasons. Spellblade can be proc'd really easily, as auto attacking counts as an ability, which means the only real cooldown in between empowered Qs is the 1.5s cooldown on Spellblade. The Threefold Strike also grants 20 MS, which helps stack your passive a bit.


Phantom Dancer is also really good because not only does it give a bit of crit chance, AS, and AD, but it also gives 7% MS. The real power comes in the Spectral Waltz passive. You get to ghost through units and another 7% MS which is crucial for Zeri's kit, which centers around chasing and evading at high speeds.


I like Boots of Swiftness over Berserker's Greaves. Zeris AS is capped at 1.5, with access converted to AD. However since she is a caster, she doesn't need insane AD scalings, so its best to put that into your MS. Keep in mind Zeri's full-charge Zaps generate faster with faster MS (you move more units, quicker) which at mid-game, level 11, does 12% MAX health damage, which is A LOT


I like BOTrK because its Mist Edge passive helps with dueling and its Siphon passive steals and grants you 25% of enemy champion MS.


Wit's End is also good for a similar reason, its Fray passive gives an impressive 20 MS on-hit, which means you can gain charges easily before engaging in champion combat.


I also like Rageblade because it converts that 20% crit from PD into usable. reliable on-hit damage, giving you in total (PD + Rageblade) an extra 80 damage on hit.


Horizon Focus is an interesting choice I have, but hear me out. I mentioned that Zeri has good AP scaling on her Q, W, and R, which means 85 AP goes a long way, additionally, Fully charged Zaps, and Ws both slow, applying the Hypershot passive


Divine Sunderer: Sunderer is good versus tanks, it gives mixed penetration on its Mythic Passive, which is good for Zeri because she does mixed damage. You do lose out on that precious MS and AS, but in return you get reliable sustain in fights if you are alternating AAs with Qs.


Black Clever: Black Clever is secretly a great item on Zeri. Her un-ulted Q applies 7 instances of damage, totaling to 10-30+(110%) AD, which means you can get all 6 Carve stacks in one Q. If that wasn't enough to sell you, get 3 MS for each stack of Carve up to 18 MS.


Mejais: Its pretty self explanatory, if you have 10 stacks, upgrade your Seal, and sell it to complete the build.


Rylais: This item is another interesting one, AAs count as abilities on Zeri, so you can apply the Rimefrost slow almost permanently if you are weaving in AAs and Qs


Mortal Reminder: This is pretty straightforward. As a side note, this item actually bundles all the stats Zeri loves including MS + some anti-heal. Build it if someone is healing.


Navori Quickblades: I only recommend this if you are going for a full crit/ Infinity Edge build. Your abilities and full Zaps already reduce the E cooldown by 1.5s for each champion hit. This can be useful to reset your E very quickly to dash more and keep the Q pierce.