Cure Formula Changes

[Economizer]

I'm not exactly sure what you are thinking, but a few thoughts.

I read your previous numbers post that you linked back when you posted it, and reread it recently (to be completely honest, I couldn't really make sense of the second half whenever you talked about "scaling" - that is to say, I didn't know where you were applying the numbers.

I linked all my sources that I've been using previously, but I'll link them again more clearly, you seem to have a better head for numbers then I do, so the tools would probably help more.

• Furen's FFXI Cure Calculator
• Furen's FFXI Cure Guide
• FFXI Calculator

FFXI Calculator is better for getting the true caps on spells, but does not show some of the finer workings that Furen's Cure Calculator does (plus Furen's is online), and you can see all Furen's notes on his guide, which explain cures quite well. I can only assume you've probably used/read one of these before, if not all of them, but I want to be sure we have the same resources.

That implies a hard power cap of 1240. Adding that to my spreadsheet for personal reference.

I checked the formula that FFXI Calculator had on this, and while Cure V does hit its hard cap at a power of 1240, the lower tier cures do not cap at any level, at least according to the calculator. I only remember people confirming the top cure amounts for Cure V and Cure VI on the FFXI Calculator forums, so we'd either have to be suspicious of the numbers given for Cures I-IV, or test it.

The easiest way to test this would be to pop a Primevel Brew and start curing people with lower tier cures, or possibly stack enough stats to get over the 1240 power amount, which again, only really seems possible in Abyssea. If anyone with access to the test server is reading this, perhaps you could test maximum possible cure amounts with a Primeval Brew for us?

Because of the way they've built it (now that I have a pretty complete picture of things), I can see how they might be hesitant to change it. For example, I don't know why the specific value of 1240 is used as a max power, but if it's hardcoded into various places, or there's other code that depends on that particular value, it could be very troublesome to change (and easily break stuff if they don't go through everything very carefully).

Blue Mage spells use the same formulas that White Mage spells do, with a bit added on or taken off. Changes to ours would probably changes theirs. Then mob power calculations come in - if mobs can heal more they would be more difficult, and so on. Or at least that's two reasons they might not want to change the formula.

At this point I'm doing some rethinking of my proposed revisions based on these limitations (ie: min cured, 3 defined caps, max of 1240 power).

When you do get a proposal to post, be sure to post something like an average cure amount. For example, I've been using the same stat block over and over for my displayed numbers when making points or answering questions so far.

[Motenten]

I'm not exactly sure what you are thinking, but a few thoughts.

I read your previous numbers post that you linked back when you posted it, and reread it recently (to be completely honest, I couldn't really make sense of the second half whenever you talked about "scaling" - that is to say, I didn't know where you were applying the numbers.

I linked all my sources that I've been using previously, but I'll link them again more clearly, you seem to have a better head for numbers then I do, so the tools would probably help more.

• Furen's FFXI Cure Calculator
• Furen's FFXI Cure Guide
• FFXI Calculator

FFXI Calculator is better for getting the true caps on spells, but does not show some of the finer workings that Furen's Cure Calculator does (plus Furen's is online), and you can see all Furen's notes on his guide, which explain cures quite well. I can only assume you've probably used/read one of these before, if not all of them, but I want to be sure we have the same resources.

Furen's calculator doesn't include a true hard cap. I likewise was not aware of it until you linked to the BG thread on Cure 6 testing.

I actually used Furen's javascript code to verify the formulas I derived based on what's on the wiki.

Furen's formulas are the same that I'm using, with a couple modifications. For example, he uses:

(Power / 2) / rate

Where rate is what I call 'scale', except that I don't use Power/2, so my values would be the equivalent of

Power / (2*rate) == Power / scale

Then obviously my 'scale' values are twice his 'rate' values. His main page also indicates that only even values of Power cause a change in cure, and may be why he uses Power/2, but I don't see an indication that Power itself is divided and floored. There's tons of values where changing Power by 1 point won't change the amount cured, even in my setup.

I also simplified his [3 * Mnd + Vit + 3 * (Skill/5)] to be [3 * (Mnd + Skill/5) + Vit].


I checked the release notes of the FFXICalculator and noted the cap you mentioned. However with no source code available I can't really make any decisions based on that. Luckily the BG thread you mentioned has plenty of data to allow me to see where he got the values from, and I've incorporated them into my spreadsheet.

I checked the formula that FFXI Calculator had on this, and while Cure V does hit its hard cap at a power of 1240, the lower tier cures do not cap at any level, at least according to the calculator. I only remember people confirming the top cure amounts for Cure V and Cure VI on the FFXI Calculator forums, so we'd either have to be suspicious of the numbers given for Cures I-IV, or test it.

The easiest way to test this would be to pop a Primevel Brew and start curing people with lower tier cures, or possibly stack enough stats to get over the 1240 power amount, which again, only really seems possible in Abyssea. If anyone with access to the test server is reading this, perhaps you could test maximum possible cure amounts with a Primeval Brew for us?

The release notes on FFXICalculator also only list fixes to Cure V/VI, so it's not surprising it doesn't hard cap 1-4. But yes, would be nice if someone could brew on the test server to verify the max cured amounts for each.

Blue Mage spells use the same formulas that White Mage spells do, with a bit added on or taken off. Changes to ours would probably changes theirs. Then mob power calculations come in - if mobs can heal more they would be more difficult, and so on. Or at least that's two reasons they might not want to change the formula.

When you do get a proposal to post, be sure to post something like an average cure amount. For example, I've been using the same stat block over and over for my displayed numbers when making points or answering questions so far.

Fiddling with numbers while keeping these limitations in mind. So far, kind of annoying, as there's a lot of variability to account for (amount cured at various levels, progressive spell efficiency at different power levels, etc).

[SpankWustler]

This thread is really great. I'm actually learning stuff from it, even. It's a lot like reading a Dostoevsky novel.

Every idea is well thought out. Everything is well-written. Most similarly, it's a depressing tale of sad individuals trapped by their own mistakes and misdeeds. True to form, the responsible parties are dragging others down along with them. My favorite part is that nobody among the Development Bros thought to check for a cap on Cure Power before creating Cure VI.

Perhaps the Development Bros could just remove the "Hurt by cures. Ouch!" property of Undead creatures then go ahead with whatever cure changes need to be made with somewhat fewer complications. Cure spells cast on Undead have the rare and distinguished honor of being more useless than the Banish line, so it would hardly be a loss if such a change allowed them to fix the restorative properties of Cure spells more properly.

[Economizer]

Sorry to disappoint, but this post is going to be a bit light on the math.

Perhaps the Development Bros could just remove the "Hurt by cures. Ouch!" property of Undead creatures then go ahead with whatever cure changes need to be made with somewhat fewer complications. Cure spells cast on Undead have the rare and distinguished honor of being more useless than the Banish line, so it would hardly be a loss if such a change allowed them to fix the restorative properties of Cure spells more properly.

To be honest, I would hope that with the formula change, we get the opposite of it getting removed, but rather, we get increased damage against undead. I'm not asking for much really, it isn't like I'm asking for the short period of time White Mages everywhere could nuke down undead with 99999 damage cures (although I am secretly hoping for it). I'm not really even asking for the ability to outnuke a Black Mage on undead.

Still, even something like a hidden trait that somehow reduces the 50% damage reduction of cures on undead for all jobs over level 50 or so would be amazing, since Cures, tier for tier, do not hit as high numbers as elemental magic does, and is still subject to resists. Further, they only work on undead. In deference to offensive magics, Elemental or Divine, I'm not sure a full removal of the damage reduction would be allowable (well, not without a more detailed examination of the math behind it), but any bone thrown would make the spells slightly more viable.

As a bit of a side point, I'd also hope that an enfeebling job, such as Red Mage would get a spell like "Zombie" that would make non-undead mobs weak to cure spells among other effects.

Wandering away from offensive applications of Healing Magic, I recently looked into gear that boosts Healing Magic skill, and unsurprisingly there isn't as much of it as there is of gear like Enhancing Magic skill or Enfeebling Magic skill. I wonder if it is made to be more useful if the amount of boost to this skill will be increased?

[Alkimi]

I think SE believe that giving Cure V to SCH and RDM would 'unbalance the game' and are attempting anything and everything to work around this in a different way.

Personally I believe it wouldn't and given the choice everyone I know would still pick WHM over the other two jobs when required in a healing capacity on tougher mobs. WHM will still remain the superior healer.

All I really want is something to remove Amnesia but that's a whole other subject....

[Daniel_Hatcher]

The release notes on FFXICalculator also only list fixes to Cure V/VI, so it's not surprising it doesn't hard cap 1-4. But yes, would be nice if someone could brew on the test server to verify the max cured amounts for each.

I tried it out, Naked:

Tier -- Amount
I -- 40
II -- 105
III -- 220
IV -- 450
V -- 810
VI -- 1140

If you want me to try with Cure Potency and such, just say.

[Motenten]

I tried it out, Naked:

Tier -- Amount
I -- 40
II -- 105
III -- 220
IV -- 450
V -- 810
VI -- 1140

If you want me to try with Cure Potency and such, just say.

Thanks. Those all exactly match the hard cap predictions, so we can be confident in the formula and limits. Cure potency test won't be needed.

[Economizer]

I'd like to state clearly that this is not the place to discuss who should get Cure V. This is a thread solely for the talk of the cure formula, and how it should be changed, and in the case it is, we're going to analyze it. Thanks to everyone who has been keeping on topic.

Extra big thanks to Daniel_Hatcher for getting us these numbers:

Tier -- Amount
I -- 40
II -- 105
III -- 220
IV -- 450
V -- 810
VI -- 1140

I've went and posted on the FFXICalc forums so the author of that tool can update it as well, we're going to need all the numbers as accurate as possible.

I suspect that Cure VI may cap at 1240 power as well, and may just have the formula be more based on the power calculation (such as PW-100) at higher numbers. This will be hard to verify compared to some what we've verified so far I think.

Thanks. Those all exactly match the hard cap predictions, so we can be confident in the formula and limits. Cure potency test won't be needed.

Good call on the hard cap of 1240 PW.

And yeah, we already know how cure potency affects cure numbers, so we won't need any more testing in that area. If anything, we could use some testing on the Blue Mage cures to see if they suffer the same hard caps, but I don't think this is really neccisary, we have a lot of evidence that they will in fact be affected by the same hard caps as the White Mage cure spells.

[Motenten]

I suspect that Cure VI may cap at 1240 power as well, and may just have the formula be more based on the power calculation (such as PW-100) at higher numbers. This will be hard to verify compared to some what we've verified so far I think.

Cure VI does cap at 1240 power. Its interval size is higher than expected (normal progression of doubling intervals between cure tiers would have put it at 240, but it's actually 300 between min and first soft cap), with min cured of 660 HP, and the first soft cap hitting at 960 HP. The gain rate above the first soft cap is 2.55 power per HP, and going from 780 power (power needed for first soft cap) to 1240 (max power) gives an extra 460 / 2.55 = 180.39 HP cured. 180 + 960 = 1140, the known hard cap healed.

Most likely the interval was intended to be 240, since 660 + 240 + 240 also equals 1140, but someone made a mistake on the first soft cap, and had to adjust the scaling on the upper tier to compensate.

[Motenten]

Ok, I think I worked out why the max power cap is 1240. It's a set value derived from the power formula for a combination of mnd/vit/skill that was deemed well above what players would ever likely reach (at 75 cap).

1240 power is reached with: 250 mnd, 250 vit, 400 skill. 400/5 skill = 80 + 250 mnd = 330 * 3 = 990 + 250 vit = 1240.


My suggested change to the power formula was 3 * (mnd/2 + skill/2) + vit. With the above numbers, that would end up generating a total power of 400/2 skill = 200 + 250/2 mnd = 200 + 125 = 325 * 3 = 975 + 250 vit = 1225. Nearly the same total value. Adding 10 mnd or 10 skill would reach the 1240 power cap. So overall I think it's still good.


Now, total amount cured while still using the current cap/interval config:

Cure 1
Current: 10 base, 10 interval, max 40
Revise: 10 base, 15 interval, max 55

Cure 2
Current: 60 base, 15 interval, max 105
Revise: 60 base, 25 interval, max 135

Cure 3
Current: 130 base, 30 interval, max 220
Revise: 130 base, 45 interval, max 265

Cure 4
Current: 270 base, 60 interval, max 450
Revise: 270 base, 90 interval, max 540

Cure 5
Current: 450 base, 120 interval, max 810
Revise: same

Cure 6
Current: 660 base, ~300 interval, max 1140
Revise: 660 base, 240 interval, max 1140 (changing this is optional)



Suppose we keep the first tier scale the same, at 2 power per HP. How would we adjust the remaining parameters to keep everything tidy?

Cure 1 offset: -10
Total power for first tier: 25 - -10 = 35 * 2 = 70
Additional power for second tier: 15 * 4 = 60
Total power for second tier: 70 + 60 = 130
Scale for third tier: (1240 - 130) / 15 = 74

Cure 2 offset: 20
Total power for first tier: 85 - 20 = 65 * 2 = 130
Additional power for second tier: 25 * 4 = 100
Total power for second tier: 130 + 100 = 230
Scale for third tier: (1240 - 230) / 25 = 40.4

Cure 3 offset: 70
Total power for first tier: 175 - 70 = 105 * 2 = 210
Additional power for second tier: 45 * 4 = 180
Total power for second tier: 210 + 180 = 390
Scale for third tier: (1240 - 390) / 45 = 170/9

Cure 4 offset: 165
Total power for first tier: 360 - 165 = 195 * 4/3 = 260
Additional power for second tier: 90 * 3 = 270
Total power for second tier: 260 + 270 = 530
Scale for third tier: (1240 - 530) / 90 = 71/9

Cure 5 offset: 330
Total power for first tier: 570 - 330 = 240 * 4/3 = 320
Additional power for second tier: 120 * 17/6 = 340
Total power for second tier: 320 + 340 = 660
Scale for third tier: (1240 - 660) / 120 = 29/6

Cure 6 offset: 570
Total power for first tier: 900 - 570 = 330 * 4/3 = 440
Additional power for second tier: 240 * 10/3 = 800
Total power for second tier: 440 + 800 = 1240
Scale for third tier: 0



Cure 1
Current second tier cap of 100 power cures 30 HP. 100 power in the above scale would cure 32.5.

Cure 2
Current second tier cap of 170 power cures 90 HP. 170 power in the above scale would cure 95.

Cure 3
Current second tier cap of 300 power cures 190 HP. 300 power in the above scale would cure 197.5.

Cure 4
Current second tier cap of 460 power cures 390 HP. 460 power in the above scale would cure 426.67


Total power to hit the second cap for Cure 5: 660 (generally pretty easy to hit by lvl 82)
Amount cured for each cure tier with 660 power (original, revised):

            Original      Revised      Improvement
Cure 1            34           47              38%
Cure 2            96          120              25%
Cure 3           201          234              16%
Cure 4           405          466              15%
Cure 5           690          690              --

Tentative power at lvl 99: 330 skill, 150 mnd, 80 vit == 800 power.
Amount cured for each cure tier with 800 power (original, revised):

            Original      Revised      Improvement
Cure 1            36           49              36%
Cure 2            98          124              27%
Cure 3           205          241              18%
Cure 4           417          496              19%
Cure 5           739          739              --

MP Efficiency at 800 power:

            Original      Revised
Cure 1          4.50         6.13   
Cure 2          4.08         5.17
Cure 3          4.46         5.24
Cure 4          4.74         5.64
Cure 5          5.47         5.47

Subbing mage won't be as limited as my previous scaling. 150 skill + 150 mnd + 80 vit is 530 power, which hits the second cap for Cure 4, curing 450 rather than the ~500 for someone with (capped) native healing magic skill. However the entire setup is consistent with the current formulations, so should be more viable as a suggestion.