If you integrate what you got it won't look like what you're trying to integrate. I'm about 6 years removed from calculus, but I get something like -ln(e^(4*WS-6) + 1) + CONSTANT. Which makes sense to what he's saying since it starts at some value and drops afterwards, the +1 in the log insures positive values. But the log would drop off sharply to start and less sharply later. This would create favorable scaling for very fast weapons. Which actually wouldn't be too bad of a thing since it would favor warrior tank weapons. Maybe it should be more like a sigmoid where it starts at some pretty much constant value then there's a drop for certain values after which it stays constant again. But that wouldn't be too different than just discriminating against 2h with a different formula and easier to understand.

EDIT: take what Rugrud got and evaluate from 0 to WS for the actual formula.

I did the integral manually, I made a stupid mistake somewhere.

However, I don't agree that there's no place for complex formulas to solve scaling problems. It would seem to me like the game would only have to make the calculation once (when you equip the weapon) and again any time you gained or lost a haste effect. It's not like the game has to integrate either, that can be done beforehand. It's also not like it's some processor-intensive system of nonlinear partial differential equations that the game would have to solve for every swing.

It's not that the computer can't do it, but people playing don't understand it. They should know what's better for them. Excel spreadsheets are as far as it gets. Now sure you can put it in excel spreadsheet if you know the equation beforehand, but blizzard doesn't release this stuff. People just assume linearity and it works. If scaling becomes nonlinear modeling will become impossible because getting through to mechanics will not be feasible.

Then perhaps more transparency is required? I seem to recall a post on the official beta forums regarding improving tooltips. I'd venture to say that most players can see that by equipping different speed weapons, and seeing the effects of their tooltip damage number, they'd be able to tell what's at least good (maybe not the best). Although to that end, I agree with you.

I think they've gotten themselves into a mess from day 1 of the game with the introduction of nonlinearly scaling (and also completely nonscaling!) abilities. I'm somewhat concerned also about the scaling of some of our new prot abilities. Since they haven't tested threat at all yet, we can't be sure whether we'll end up with something that's great while starting out, but falls off at the end, or vise-versa.

The most I expect from that end is for the tooltip to show something like "Gains X damage from attack power" or "Gains Y healing from spellpower" values adjusted real time. There are mods that do that, at least were mods that did that. I doubt they'll put the formulas there.

It's not at all unprecedented for Blizzard to have really complicated scaling rules. Armor follows an diminishing returns formula that most players wouldn't figure out on their own. Hit and crit vs. level of target are simply table-functions that no one would know for sure outside Blizzard employees telling us. Go further back and you find really absurd rules, like the original DOT scaling, or Magic Find Percentage in Diablo 2.

If they're going to re-introduce level-based scaling to SoR, for example, (which is something I think they have to do if they want to sort out the current scaling muddle) then the level->SoRdps scaling is pretty much going to have to be nonlinear, since character power doesn't increase linearly with level. (e.g., you gain a lot more power from 60 to 70 than you do from 50 to 60.)

I can't see why you're trying to change the scaling on SoR, when it's quite apparent that there one particular talent which increases its DPS by 60%. That is the one talent that is causing balance issues.

The more I think about it, the more I'm getting sure that the current iteration of Sheath of Light has to go.

The thing you're missing is that talent is completely tangential to the problem. The problem is this: Seal of Righteousness does more damage for a Ret Pally than Seal of Command or Seal of Blood. Now, if you're going to claim that the reason for this is the spelldamage scaling from Sheath, then perhaps your solution is a good one. Others have even claimed (and I somewhat agree with this point of view) that this flatly isn't a problem, that there is no reason Retribution spec Paladins can't simply use Righteousness for PvE DPS, with Seal of Blood being the vague equivalent of a Hunter switching to Aspect of the Viper for mana regen at the cost of DPS and Seal of Command being for PvP.

Now, assuming you disagree with that, the complaint you will hear about your solution is this: It's a huge nerf to Ret DPS. People trying to change the scaling on SoR are trying to find solutions that do not result in as massive a nerf to Ret DPS as simply removing Sheath would entail. And you would have to completely remove it... at any AP->SP coefficient at all Seal of Righteousness as it stands now would scale better than SoB or SoC, and thus at some later gear point become superior.

If they don't give you the formula you'll need more points than two to model it. It's just very easy now. It's not impossible, but you won't be able to model this stuff on a napkin. Yeah ilevels are nonlinear, but this is very far removed from the players. Ultimately blizzard decides what your items will look like, you just have to go by whatever they give you. You don't loot ilevels and make your own items from them with some knobs, you loot whatever they decide to give you.

EDIT: Magic find % in diablo 2... good times I was actually thinking about diablo 2 since there's a lot of nonlinear stuff there, but all those things were independent of each other. For example you had faster cast on diminishing returns, but you didn't have to model fast cast against spellpower because there was no such stat. You balanced fast cast against something totally different like stamina or strength. And you besically went by a table to shoot for discreet values because the game didn't breakdown into 100ths of a second. Here it's all harder because you have SP, AP and weapon speed all contributing and the players can change

EDIT2: zulaa, two points as a figure of speech I guess, point per dimension would be mathematically. To be honest I'm pretty ignorant of the 2.3 regen model. Not a spirit class and quit the game before that.

But you ignore the new mana regen from spirit model, which is also nonlinear and which definitely players do need to know how to manipulate. And you're right, you do need more than two points to model it, you need four. Since when do you only have two points? If you're varying it by level, you have 80 points. If you're varying it by weapon speed, there are certainly far more than two possible weapon speeds to test. Nobody was going to model it based on two points anyway. And it isn't remotely difficult to generate a reasonable piecewise interpolator. Sure, maybe not on a napkin, but if you were to insist on doing it on paper (instead of, say, simply having Mathematica or MatLab do it for you automatically) it would be only a single sheet.

We're talking DPS modeling here, not building bridges. We don't need an absolute error of 10^-5 or anything. Heck, as long as it's accurate to within 1 it's good enough.

But the point here is very practical. You will have to choose a tanking weapon between two weapons and you have a scaling formula of SoR damage favoring faster weapons. Say you have a 1.5 speed with 30 str or 2.0 speed with 40 str. Which is better? How about 2.6 speed with 80 str? How about 1.1 speed with no stats? Maybe that would work better with a different rotation? Right now as far as SoR in concerned it's very simple. More AP and SP = more threat. Linear. HotR has a preference for slower speed because it isn't (wasn't?) normalized. After it gets normalized it will very slightly favor slower weapons as the weapon damage part doesn't get normalized, so basically, more AP and SP = more threat. Speed isn't part of ilevel itemization, if you have speed add a curve to this you'll have some items clearly better than other items with the same ilevel. Rogues took [Fang of Venoxis] because it used to be 2.0 speed before normalization because speed outweighed any stats. Now I'm not saying something this retarded will happen, but it could get to something resembling this.

Well, first, "gear scaling" is not the same as "AP scaling". Both SoB and SoC scale with your weapon's base dps, while SoR does not. It's all about the strengths of the various scalings. It's possible for SoR to have better AP scaling than SoB/C, but also to have the weapon-scaling dominate that, so that SoB/SoC still scale more strongly overall as you gear up.

Second, how much of a nerf to Ret dps would removing the AP->SD scaling of SoL actually be? If you're using SoB, then SP has no effect whatsoever on the seal dps. It contributes 58% to judgement damage every 8 seconds, which amounts to roughly 7% of spellpower as DPS; hence if you drop the AP->SD from SoL, your dps drops by 2.1% of your AP, times about 1.6 to account for crits. Call it 3.5% of AP lost as dps overall. So, for our hypothetical paladin in T6 gear with 3k AP raid-buffed, this would reduce his dps (with SoB) by about 100.

Now, that is a nerf to dps, no question about it. But the thing about that is that basically everyone who's played Ret in the beta agrees that at present it's ridiculously overpowered. If they can solve the SoR/SoB/SoC scaling problem by removing the AP->SD conversion from SoL and it results in a pretty modest nerf to Ret dps, then that seems like a good thing because they might decide that's all they need to do to balance Ret dps.

The problem of course is that removing the AP->SP conversion nerfs Ret healing, which is the opposite of what the devs wanted to accomplish in WotLK. So, maybe the answer could be for the AP->SP conversion in SoL to apply only to healing spells (and possibly tweak the AP coefficients on Cons/Exo/etc. if necessary).

I keep looking at all the posts about DK design, and one of the things blues says they try to do is balance the complexity with the "things to do" factor. Right now, there are just too many different damage seals, and they don't have clear roles. The scaling problems would be easier to tackle, if they didn't have to be tackled 4 times.

Given all the other changes, and the intent to have things scale, they really need to revisit what Seals are in the game, and what roles they serve. Blizz has shown that there are few sacred cows, so why not take a step back and rethink the whole thing?

For starters, Paladins find them selves in a few different roles, Healing, Tanking, PVE Solo, PVE Group and PVP DPS for example. Ok, there 5 seals for 5 roles.

Healing - SoL (Changed from Live) - Increased healing Spellpower
Tanking - SoR - Bonus damage/hate on hit, 1H only
PVE Solo - SoV - Dot that builds and is judged as a finisher, 1H/2H
PVE Group - SoB - More straight damage at cost of HP
PVP DPS - SoC - Chance to Proc big whack, bonus to stunned peeps, 2H only

Throw in SoJ as a kind of a wildcard, and there you go.

Now, with those decided, then they can go and make them scale and assist the Paladin in those roles. Further, they could add talents that improve those seals deep in the 3 trees to enhance those seals and thus those roles.

Sometimes you find yourself, like a Ret healing, outside your main role, so you use the appropriate seal, like my new SoL above, but get less benefit than a talented person.

Just some thoughts.

Well, a solution I would favor goes like this: increase Touched by the Light to 100% of Stamina as spell power, and revert Seal of Righteousness to scaling only with spell power. Restore multiple ranks with flat constant values for leveling purposes. AKA: revert Seal of Righteousness to its current live state but maybe with more scaling from SP. This way it is still useful for tanking and soloing and Holy soloing, but no longer scales out of all proportion for Ret. Prot Pallies will still want "Generic" Plate tanking gear for the Block Value and the fact that AP would still affect Consecration et al (including obviously Hammer of the Righteous).

In a way this is more complicated because it means multiple ranks of SoR... but it's actually simpler since it amounts to "Don't change SoR from what it is on Live."

Just to make sure I understand, the solution to leveling is have a very strong SoR until 60 when holies start getting SP gear? I assume harsh penalties for downranking.

Well, as strong as it is now, on live. If that isn't strong enough and you think leveling a Paladin on live with SoR is too difficult today, then sure, you could buff the static values.

And yes, obviously it would use the same rules for downranking as most (all?) other spells do in WotLK, which entail much harsher penalties than in 2.4.

While your suggestion actually dovetails with mine, I do want to clarify something. In Wrath, every single ability you mentioned except heals scales with both SP and AP not just SP. So that problem, except healing, is actually gone even if they did remove Sheath of Light.

So yes, it's also possible that a workable solution is to cause Sheath to grant only Healing Spellpower instead of generic Spellpower. Though I also think that would be too large of a nerf to overall Ret damage. Just leaving Seal of Righteousness the way it is now on Live and increasing the Stam->SP conversion for Prot I feel is a better solution.

The only problem is, protadins will be sharing their gear with DK and warriors, whichc means they are laden with strength and stamina with mitigation, no spell power. All the spell power a protadin gets comes from TbtL, which compared to SoL, is pretty weak.

It's strong 'enough' with specific gear. I don't think you can grab a suit like that on your way 60 to 70 really. It's pretty painful in greens. Honestly it feels like a lot of work to balance a lot of ranks around the gear that an average player (not a twink) is expected to have at a level. What I was saying about scaling with deep ret talents is something that nobody will miss and I feel it's something that will make a difference. If it won't solve the problem outright it'll sure get you very close. And it's something that should be done anyway.

Baseline, without any talents, SoR dps scales at 5% of AP. SoB dps scales at 2.5% of AP. So baseline, there is an issue.

Sheath then compounds that, bumping SoR dps to 8% of AP, while SoB stays at 2.5% of AP. Technically, you could fix Sheath by adding a SP coefficient to SoB, thus having Sheath affect both Seals equally. (Then tune coefficients to give the right total DPS values.) But this wouldn't affect the baseline scaling.

I'd be absolutely fine with that.

Back to what someone said earlier, I totally agree - when there was Fury, Justice, Righteousness, Light, and Wisdom baseline and Command talented the Seals made sense. Tank, stun on proc, holy damage on proc (consistent), healing on proc, wisdom on proc, and holy damage on proc (kaboom!). Weaved in with the judgements this system made sense. It was horribly boring, RNG driven, and the weaving of judgements and seals had no rhythm, true... but it made sense.

Now we have holy damage on swing, holy damage on swing, holy damage on swing with a dot, holy damage on proc (less pure dps than other seals with weird itemization concerns, talented) heal on proc, wisdom on proc....

They did a good thing with Judgements - all do damage, some have effects, damage is modified based on the effects. I say do the same thing for seals. It's not like we're supposed to be weaving seals now - their cost is high for that - so give us something along the lines of ...

-- All Seals do Base Seal Damage (BSD) on swing. (Holy damage)

Baseline -- Baseline seals cannot crit, but scale equally over ap and sp.
-- Righteousness - BSD. Normalized over all weapon speeds.
-- Wisdom - 70% of BSD, may proc mana. Scales AP and SP
-- Light - 70% of BSD, may proc health. scales AP and SP
-- Justice - 70% BSD, may proc stun.

Talented -
-- Command - talented, Ret - 100% of BSD, can crit, 20% chance to thrash once (not holy on thrash). (no seal damage on thrash).
-- Vengeance - talented, Prot - some % of BSD (not sure how this math would work), adds dot effect.


That gives us -

-- A base seal that only gets replaced for certain specs. It's fully capable for leveling for any spec, though the talented seals will always be more dps.
-- A talented seal for dps that is a clear winner. It uses crit, it scales well with haste and armor pen (good thing), it scales with AP and SP. It can also be used at any level, once you can talent it, and with the judgement it'll be superior in both PVE and PVP.
-- A talented seal for tanking. It can be tweaked in position and scaling to be used for the right purpose, but it scales properly for holy-prot and ret-prot. The stacking and judgement damage makes it superior to Righteousness on all non trivial fights.
-- Three utility seals. But you still do more than just white damage while you're using them. They'll never dps like a pure dps seal, since they only do BJD and they only do 70% of BSD, neither of which can crit.