Ok everyone I was wrong. It has come to my attention that Rod of Tahuti's passive only affects gods and objectives but NOT Structures. This means unless im playing Freya or Chronos in the ADC role (So with an AA build) and my team needs objective shred them im unlikely to consider this item as much as before.
Immediate Damage and Pulsing Damage are applying Rod of Tahuti passive correctly because they update on each time they hit, because each time it hits it is considered a unique instance of damage. Damage over Times are an initial hit that stores that information and does the rest of the damage according to the initial stats it had when it hit."
It's obviously clear that a single instance of damage (any single-hit ability) will apply the passive according to the health state of the enemy at the time they're hit.
The difference that needs to be understood is between ticking (pulsing) damage and DoTs. Ticking damage is something that only applies while the enemy is in range of the ability. Using PonPon's example of Grasping Hands, each instance of damage is separate. Why? The enemy can step out of the AOE and not take any further damage, even when the ability is still there. In fact, all of Anubis' damaging abilities fall under this category.
DoTs, on the other hand, apply a set amount of damage once you're hit the first time, and so the total damage is just extended over a certain period of time. In these instances, then, if the enemy is hit by a DoT while above 50% health, Tahuti's passive power boost won't apply throughout the damage application. Other examples of DoTs besides Expose Evil include Kukulkan's Whirlwind, Agni's Path of Flames, Aphrodite's Love Birds, etc.
One distinction of abilities that seem like they are DoTs (but I'm guessing are Pulsing/Ticking), would be abilities such as Nox's Shadow Lock or Ares' Shackles. Why? You can cleanse these with Purification Beads. Use beads on Whirlwind, on the other hand, and you still get the damage.
Just wanted to note that this item provides bonus healing to teammates on healing abilities (and possibly yourself - I need to test) who are under the 50% health threshold. The passive also works against structures and objectives that are under 50% health too, making it a great pickup on Sol and Chronos for splitpushing and objective melting, especially in combination with Polynomicon.
No, Obsidian Shard scales differently and only applies to titan, players and objectives not structures. Won't be that effective for non-AA mages against structures/objectives as it has a low amount of damage for little attack speed (but equates to a large amount after some time, which means it does well with attack speed).
(just the concept that it provides some enhanced damage against structures... Nothing more than that... I understand the mechanics are different and it wasn't meant completely literally... =p)
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Below explains how Rod of Tahuti's passive interacts with the health state of enemies, based on different types of damaging abilities.
Original Reddit post: https://www.reddit.com/r/Smite/comments/8cmtgg/all_rod_of_tahuti_interactions_with_dot_damage/
HiRezPonPon's response: https://www.reddit.com/r/Smite/comments/8cmtgg/all_rod_of_tahuti_interactions_with_dot_damage/dxggrug/
From HiRezPonPon's response (with parapharasing and formatting adjustments by me):
It's obviously clear that a single instance of damage (any single-hit ability) will apply the passive according to the health state of the enemy at the time they're hit.
The difference that needs to be understood is between ticking (pulsing) damage and DoTs. Ticking damage is something that only applies while the enemy is in range of the ability. Using PonPon's example of Grasping Hands, each instance of damage is separate. Why? The enemy can step out of the AOE and not take any further damage, even when the ability is still there. In fact, all of Anubis' damaging abilities fall under this category.
DoTs, on the other hand, apply a set amount of damage once you're hit the first time, and so the total damage is just extended over a certain period of time. In these instances, then, if the enemy is hit by a DoT while above 50% health, Tahuti's passive power boost won't apply throughout the damage application. Other examples of DoTs besides Expose Evil include Kukulkan's Whirlwind, Agni's Path of Flames, Aphrodite's Love Birds, etc.
One distinction of abilities that seem like they are DoTs (but I'm guessing are Pulsing/Ticking), would be abilities such as Nox's Shadow Lock or Ares' Shackles. Why? You can cleanse these with Purification Beads. Use beads on Whirlwind, on the other hand, and you still get the damage.
Im thinking: Book of Thoth, Shoes of the Magi, Demonic Grip, Obsidian Shard, Rod of Tahuti, Polynomicon for objective melting, or for towers replace the Obsidian Shard with either Spear of Desolation or Soul Reaver.