Be warned, this is a long and detailed post. Look for interesting headlines or go to the bottom for the TLDR if you're not all that interested.
A 6 slot Yi at level 18 can kill a squishy a second with his sustained damage. He can kill a tank with Warmogs, Sunfire, Frozen Heart and Randuins in less than 4 seconds. At 4th offensive item, you'll deal over 1000 damage against a Sunfire Cape opponent if you choose any of the top 20 builds.
I've made a spreadsheet including more than 100 item combinations. I've mainly worked with it at 1 Q target with ult on and E up 60% of the time against an average opponent with armor seals, armor masteries and Sunfire Cape. That's the default setting of the sheet, but it's easy to change. The link is at the bottom.
Firstly, Infinity Edge is as mandatory as it's always been for auto attackers, and Last Whisper is as cost effective for physical damage as we remember it. The Life Steal items are not very good for damage, it's actually a significant sacrifice to get that delicious Life Steal early.
Something that surprised me somewhat was the effectiveness of GhostBlade, even assuming only 50% uptime on the active. It was very often among the top builds. Lastly, the new Trinity Force is actually extremely good midgame when paired with Infinity Edge
I'll try to give an overview of the best build paths.
Path of Highest DamageSlot 1
The first item should be IE or GB. GB can be gotten earlier, IE has good parts to build from and is more cost effective once finished.
If you went GB, you go IE now.
If you went IE, adding Tri is the highest damage midgame, but IE+PD transitions better into lategame and is quicker to assemble. Tri also has a fairly shitty build path. But the field is open with IE, it adds just what you need alongside your ulti.
Add a PD if you don't have one, add a LW if you do.
Add a LW if you don't have one, add another PD if you do.
It's worth noting that these builds are the top contenders even when your ult is down.
GhostbladeThe GB build is almost even with the IE PD build against a Sunfire worth of armor, but ahead against no armor opponents. The PD LW build pulls ahead of the GB build at Slot 3, and is almost even again at Slot 4. This is assuming 50% uptime on the active. It is worse off against armor stacking though, as it doesn't gain LW until 4th item. In my experience, it has less relevant uptime, but it does really wreck face when it's up in combination with E. I personally favour the PD build, but I think it's personal preference at this point.
TriforceIf you went IE with Tri in Slot 2 you gain 10% over the PD build, but you lose 22% at Slot 3 against PD+LW and 12% at Slot 4 against LW+double PD.
LifestealIf you want Lifesteal, BT is generally at higher damage output, but only significantly at Slot 1 and Slot 3. BoRK has the advantage of the active, and being better when ult is down. BT does more Q damage and damage to squishies. Note that unlike on most other champions, BoRK does not really give more healing than BT. BT is significantly better against towers.
If you want to rush lifesteal, go Lifesteal->IE->PD->LW. If you went BoRK and they stack several armor items, switching IE and LW is better.
If you're willing to wait for the most opportune time, getting Lifesteal Slot 3 or 4 is where you lose the least.
Hydra is only defensible if the AoE is going to be very very relevant
Personally, I prefer BoRK over BT, but both are entirely defensible.
With Lifesteal, it'll be about 30HPS at Slot 1, 50HPS at Slot 2, 120HPS at slot 3 and 140 at Slot 4.
You'll reach 200HPS at 3 items with IE+BT+BoRK, dealing 30% less damage than top build. At 4th item, adding a PD, you'll reach 250HPS and deal 25% less damage than top build.
Triforce and LifestealWith BT and Tri, you'll lose 9% at Slot 2. You'll lose 34% cost effectivness at Slot 3, and 30% at Slot 4 though.
Last WhisperIf the average armor of your relevant targets surpass 125ish, it's time for LW almost no matter what.
Defensive ItemsIf you want an offense/MR hybrid, go Hexdrinker/Maw over over Wits End. Its damage scales with E and can crit, and it's better against burst damage than WE. If you want offense/armor hyrbid, Atma's is actually not all that bad, even without HP items. If you've stacked a lot of HP (say, your two defensive items are Randuins/Spirit and Mallet), it's actually the strongest Slot 3 item against <150 armor opponents sorting by cost effectiveness.
At Slot 3, Maw loses you 11% compared to strongest build, and Atma's loses you 7% at base HP.
And just to note it, I do not endorse glass cannon Yi in almost any situation. It's simply too volatile and, well, bad against competent opponents. You don't have range, you simply can't make up for squishyness entirely with positioning.
TenacityI'm not much fan of Zephyr for tenacity. As a second item rather than PD, you lose 43% effectiveness. As a third item, you lose 18% effectiveness. The CDR is not worth much on Yi, neither is the movement speed. In my opinion, if you want tenacity, Merc Treads or Spirit is the way to go, and then just return to your regular build path.
RunesI use attack speed runes. And I know that's weird, considering the massive attack speed boost you get from your ult. But you don't get to start with your ult. ASPD runes gives you the most stat per rune compared to gold, and it facilitates the IE rush. AD runes are also fine for last hitting in lane, you only lose a few percentage of effectiveness.
But, if we pretend there is no early game, crit damage runes are absolutely amazingly unfair. At 4 items, it gets you 150 more DPS. But it's a rather silly idea.
TLDR Best BuildsBest build for damage: IE->PD->LW->PD
Best build with Tri: IE->Tri->PD->LW
Best build with Lifesteal: IE->PD->BT->LW
Best build with rushed lifesteal: BT->IE->PD->LW
Best build with both Tri and Lifesteal: IE->Tri->BoRK->LW