TL;DR because I suck at keeping things short: Cauterize and Rejuvenate both additively affect the healing multiplier. Meaning, 15% Rejuvenate will counter 75% Cauterize, having your healing ultimately be 40% effective instead of 25% effective. 1+0.15-0.75=0.4. Rejuvenate is not applied after cauterize, they counter eachother.

Hi! This is a response to someone's recent 'guide' (https://paladins.guru/guide/qsygjyYa0) showcasing why Rejuvenate is apparently useless.

The assumption he made is that Rejuvenate is applied after Cauterize. However, in truth, all these two items do is affect the healing multiplier on one champion. Say you have Cauterize 1 applied to you and own Rejuvenate 3. Caut 1 drops your healing from 1x to 0.75x, but since you own Rejuvenate 3 it counters 15% of the 25% reduction, bringing you back to a 0.9x multiplier for any healing on your person.

This makes Rejuvenate a lot more useful than it seems, as the incoming healing isn't first reduced by Cauterize's full potential before applying Rejuvenate. Lets demonstrate this with a math!
In his example, he used Furia's heal, healing you for 1000 instantly without Rejuvenate and 1150 with 3 tiers of it. In total, Furia's heal heals you for 1400 health, but in this example I'll just use the instant heal she applies rather than the 400HP heal that applies over 2 seconds after it.

As a base, without any items or healing reduction being applied to you, Furia's heal will heal you for 1000hp.
Once you add Cauterize 2 reducing healing on you by 50%, your healing multiplier becomes 0.5x. 1000*0.5=500. As you add rejuvenate, its addition to the healing multiplier will bump it back up to 0.65x instead of 0.50x. 1-0.5+0.15
To make this a bit easier, let me revisit his examples of Rejuvenate on Furia's heal.

"1150 x.5 = 575 heal. 575 x 1.15 = 661 total (assuming you've purchase rejuv 3)

1150 x .25 = 287.5 heal. 287.5 x 1.15 = 330 heal (an extra 43 heal)."

The thing that's wrong with his calculations is that he first reduces the initial heal with Cauterize, then applies Rejuvenate's increase to healing after. This isn't how it works! All Rejuvenate and Cauterize do, as previously mentioned, is modify your healing multiplier. So then, let's correct his examples!

1150(1+(Rejuv)-(Caut)). 1150(1+.15-0.5) = 747.5. Instead of ending up at 661, we end up at 747. This is 172 extra healing compared to no Rejuvenate.
1150(1+.15-.75) = 460. Again, 130 hp extra restored per heal in comparison to no Rejuvenate. These items are additive in relation to the healing multiplier.

What this means for us as tanks is that ultimately, Rejuvenate 3 counters Cauterize enough that over 3 Furia heals, we're healed for 3(1400(1+.15-.75))=1680 hp. Compare this number to 3 Furia heals without Rejuvenate healing you only for 1050 hp and we have a pretty compelling argument to spend the 900 gold.

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