Your Savior is here (Arena)

Eh, in Arena there's a reasonable chance you'll come across an Odin. If so, and if you don't want to use your ult specifically on enemies inside (that might be tanky which sucks for the ult's potential) or save your ult to get out, then Phantom is absolutely an option. 100%. Note I also list it in mine.

DB can work out, technically, on Loki, because there's a lot of attack canceling in his combo, so you get opportunities to get that bonus damage. But the biggest consideration is that his first attack has a progression of 0.75. So...where a normal god with a standard progression of 1 (e.g. hunters) would hit for full damage (base damage + physical power - mitigation from enemy protections), Loki's first hit only deals 75% of that potential damage.

With crits, it's a 2x multiplier, so that hunter would get 2x damage. But for Loki, it's only 0.75 * 2 = 1.5x damage. Basically, crits do less for him.

Then, you add the fact that your example build only has 1 crit item, and now you've built a very expensive item and only have a 25% chance of critting...which is fairly low. Crit builds usually want closer to 50% or higher crit chance to make crits somewhat reliable.

Then you consider his full progression, and it's unlikely you get through the full thing before you want to retreat. This is the full series:

0.75 / .5 / .5 / .5 / 1.5x damage and swing time

So the 2nd, 3rd, and 4th hits only deal 1/2 of the general potential damage, and crits would push that to a damage of 1. If anything, if wanted to get better use out of those basics, you'd build into Qin's Sais, which benefits because the bonus damage applies per hit and doesn't change based on progression. Not that Qin's is usually suggested either...Loki is, for all intents and purposes, a pure ability user who gets enhanced damage from attack canceling. This means Hydra's Lament is core, and it's good you have it in there.

Now...can you have success with crits? Sure. Bonus damage in a way is bonus damage. But you just don't get the same benefit when you DO crit as others would.

Not that I fully endorse this, but if you insist on this, and your team is winning and you can afford it, you might go Warrior, Jotunn, Hydra, Rage, DB, Titan's...or Titan's, DB, Malice. Just don't expect it to be very affordable (and thus bad for your power curve), and...well...you're welcome to try that.

Yes. Loki's basic attack progression is: 0.75/0.5/0.5/0.5/1.5x damage and swing time.

Those numbers are percentage of what the full basic attack will be. Activating a ability will reset the chain (or reaching the end of it).

and with Hydra's Lament being the preferred option on Loki, which he uses in combination with auto-attack cancelling with his abilities, a 0.75x scale auto attack is not very good for crit, at all, because you're only getting 0.75x of what the full crit would be. If you decide to senselessly auto attack the enemy consistently with just autos it's even worse, as the auto attack progression has even lower damage for crit for the next 3 auto attacks. On top of that, Loki is an ability based assassin that does better with power and pen, on top of that, Loki would be very unsafe to be built auto attack based, on top of that, Deathbringer is only a small percentage crit chance. On top of that, there are better item choices.

My recommendation, don't get Attacker's Blessing for arena (it does stack from minion damage/kills, but eh...) and instead start tier 2 boots.

For the build go: Warrior Tabi, Jotunn's Wrath, Hydra's Lament, Brawler's Beat Stick, Bloodforge, Heartseeker (or Titan's Bane, or Magi's Cloak/ Mantle of Discord, or Blackthorn Hammer, or Runeforged Hammer).

Now that i look at it i might replace Deathbringer with Bloodforge