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Just a few things I would like to point out with this build:
***This math is done from the perspective of level 20 with full build and full stacks, and is intended to showcase the possibilities of this build.***
Before penetration and mitigations, with a full build Khepri should have 144 Physical Protection, and 128 Magical Protection. With the passives from Sovereignty, Heartward Amulet, and all 10 stacks of Hide of the Urchin, that makes his total protections 204 and 178 respectively.
Damage, before penetration, is determined as such: Damage * (100 / 100 + Protection) = Damage Dealt
This means that, again before penetration, our physical protection means we are only taking about 33% of physical damage, while magic protection allows us to take only about 36% of magical damage. As you can see, an extra 26 physical protection only gives us about 3% damage mitigation, while 100 protection actually gives us 50% damage mitigation (do the math), so we have effectively hit diminishing returns for both types of protection.
The rest of this build is focused around sustainability. Without taking any passives into account, including being out of combat or his build in ability passive, we have a base HP5 of 84 with full build at level 20... While this typically caps at 100, the passives on Mail of Renewal, Stone of Gaia, and his own built in passive ability, allow you to push past this cap in the form of percentages, which is calculated seperately. (If anyone can provide conclusive evidence that this has been changed, please let me know. As of right now, you can break the 100 HP5 cap using percentages like this).
Because we have built Sovereignty, and this passive aura is also applied to ourselves (hence why we calculated the added protections from it above), our actual HP5 is already at the max of 100 by the time we have full build. Traveler's shoes serve only as increased movement speed and gold at this point. Due to the diminishing returns already explained above, changing to the reinforced shoes later in the game still does not seem worth giving up the extra gold as support or the additional movement speed to get in and out or rotate effectively. I still recommend keeping Traveler's due to these two aspects of the build.
So, with a health pool of 3710 at level 20 with this full build, the increased health regeneration from your Stone of Gaia passive would be an additional 74.2 health every 5 seconds. This is also the same amount of additional SHIELD (not HP5 or healing) you receive from your passive every 5 seconds (every 10 seconds if in combat), which is separate from your health pool, this will cap at an additional 371 health shield after 25 seconds of being out of combat. Now take into account the Mail of Renewal, which can proc on a kill or assist on an enemy god OR an objective (Fire Giant, Bull Demon King, Gold Fury, etc.) - that is an additional 15% of your health over 5 seconds - or 556.5 health regenerated.
So, taking all of this extra information into account and rounding our numbers up, lets look at a particular scenario. You just helped the team kill the fire giant. This means that in the first 5 seconds you will be restoring 731 health... You will also be receiving a passive for an additional 75 points of shield in that 5 seconds. In other words, when you achieve an assist, due to the way smite calculates different values seperately, you just gained basically over 800 health in 5 seconds.
Obviously, your HP5 is not like this all the time, this is an extreme example that shows just how strong this build CAN be in certain situations.
Updated for Season 4 Patch 4.7
Guide is still viable. Thebes is now a better option than Mail of Renewal. Also added Mantle of Discord in possible replacements for item #4. Gets you nearly same protections, but a lot faster, and has a built-in stun which is great for team fights. Would recommend this for all modes except conquest.
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