HP/Mana Balance

In Hardcore where death is permanent, it is quite obvious that having a high hp is very important. However for a sorceress, this poses a problem because a sorceress also needs mana. And a lot of it. So how much hp and mana should a HC sorceress have? This goes back to the basic problem of how to allocate stat points. Where a SC sorceress might throw all 5 stat points into energy per level up, a HC sorceress will have to balance her needs between hp and mana. One also needs to consider the effective hit points one has, after considering the effects of energy shield. Below are information that will give you a greater insight into building a HC sorceress.

More often than not, players in hardcore will try to maximise their hp, and only invest just enough Str and Dex to use their best/desired equipment, and throw the rest into Vit. For a sorceress, the Str required is 75 in order to use a 3D-tower shield. To use a Shard, you will need 51 Dex, but it is often better to leave Dex untouched at all at its base 25 and use a wand/scepter with fastest cast and mana.

In the first 30 levels, it is advisable to pump Str/Vit/Ene in a 2/2/1 ratio until you reach 75 Str, and thereafter Vit/Ene in a 3/2 ratio. Opinions will differ on this, and depending on how twinked the sorceress is, one can even go all out for 75 Str first before ever touching Vit and Ene. More of this issue will be discussed in the Leveling Up 1-30 section.

It is good to plan ahead what equipment you want to use in the future. For example, if you plan to use Twitchtroe which adds 10 Str and 10 Dex, you would only need to increase your Str to a base of 65, and even less should you have other hand-me-down equipment from previous characters and friends.

The common practice is to obtain 75 strength after items to wear a 3D-tower shield, leave Dex alone at its base of 25, and after that put points in Vit and Ene as desired. How much of each is discussed in greater detail below, along with how much Energy Shield a sorceress should have. 80 Str is also acceptable to wear a Goldskin. Also, it is advisable to get 75 Str before you enter Nightmare difficulty and suffer resist penalties.

You need to get energy early in the game or you will keep running out of mana. The best ratio of Vit to Ene is probably somewhere between 1:1 and 1:2, lean more towards Ene if you find you keep running out of mana and more towards Vit if you find yourself going below 2/3 hitpoints often.

Once you have enough mana to solo Act 4 Hell comfortably, feel free to pump Vit for the rest of that character's life. Or perhaps you might prefer to think like Psycho, where once you get enough hp to withstand most one-hit kills (Heph, at least 3 waves of MSLE bolts, etc), you pump mana all the way since you are guaranteed a death should you ever disconnect while soloing, whether you have 100 more hp instead of 100 (165 with one SOJ and Frostburn) mana.

Many sorceress including me have no less than 200 Vit by level 75. Of these people, some put everything in Ene thereafter while others maintain a 2/1 ratio for Vit/Ene. Many other sorceress differ in opinion and instead have a 1/2 ratio for Vit/Ene. Usually, this will also depend on the equipment. Suppose a sorceress wears a Frostburn and one SoJ, one point in Vit gives 2 hp while one in Ene gives 1.65 mana. A +20 hp ring would give 20 hp while a +20 mana ring would give +33 mana. Given such a situation, if a sorceress decided to use equipment that concentrated on adding hp, then 1/2 ratio for Vit/Ene would work, while another sorceress concentrating on mana equipment would then prefer a 2/1 ratio of Vit/Ene. Both sorceress would then end up with roughly the same amount of hp and mana even though their Vit/Ene ratio is drastically different, typically about 650-700 hp and 850-900 mana.

Energy Shield (ES) is an important skill because it extends the hp of a sorceress by using her mana as part of her hp. For the ignorant people out there, ES takes double mana damage, meaning that if your Energy Shield is at 40%, and you take 100 damage, you will suffer 60 hp and 80 mana (not 40 mana as you might have imagined). This is the high cost of using your mana as part of your hp. Just how much high should a sorceress' ES be then? If it is too high, you will run out of mana quickly when you take damage, while if it is too low, you are not maximising your effective hp.

In this part of the guide, I will introduce the EHP (effective HP) concept and form the basis framework allowing for comparisons to be made between equipment that add various amounts of hp and mana. The EHP concept will be used throughout the rest of the guide, so read carefully.

First, some terminology:

Next, I'll state some obvious formulas. Suppose a monster hits you for D amount of damage:
You will suffer (2ES%)(D) mana.
You will suffer (1-ES%)(D) hp.

Ideally, my EHP is highest when my ES% is such that when D damage is done to me, both my hp and mana reaches zero at the same time. Thus M/H = (2ES%)(D) / (1-ES%)(D). Simplifying the equation (the D is cancelled, and the ES% is brought to the same side), you get ES% = M/(2H + M). Your EHP = H/(1-ES%). Substituting ES% into the EHP formula, you get EHP = H + M/2.

What happens if my ES% is higher than the ideal ES%? I'll introduce a new variable ES2% where ES2% > ideal ES%. Since my ES2% is higher, my mana will be drained out completely first, before my HP drops to zero. After which ES automatically deactivates and whatever hp I have left after that is the remaining damage I can take.

Maximum damage I can take to reduce my mana orb to zero is M/(2ES2%). Taking M/(2ES2%) damage, I will suffer M/(2ES2%)*(2ES2%) = M mana and (1-ES2%)(M/(2ES2%)) hp. I will be left with H - (1-ES2%)(M/(2ES2%)) hp and zero mana after taking M/(2ES2%) damage. Hence my EHP = H - (1-ES2%)(M/(2ES2%)) + M/(2ES2%). Simplifying this, EHP = H + M/2, the ES2% cancels each other out. Thus is the prove that your EHP is the same no matter what your ES% is above the ideal value of M/(2H+M).

What does this imply? Suppose James the Sorceress has 310 hp and 800 mana. His ideal ES% = 800/(2*310 + 800) = 0.563 and his EHP = 310 + 800/2 = 710. As long as his energy shield is 56.3% or higher, his effective hitpoints is always 710. (Suppose his ES is 60%, he will take 666.66 damage before his mana reaches zero, and he will have 43.33 hp left = 710 EHP).

Now suppose he was soloing and fighting monsters, his hp is still full, but his mana orb is about half full and he suffers a timeout. He has 310 hp and 400 mana. At these values, his ideal ES% = 400/(2*310 + 400) = 0.392 and his EHP = 310 + 400/2 = 510. No matter what his ES% is above 39.2%, his effective hitpoints is 510 in this case. However, his mana orb isn't always half full, it could be full when he suffers a disconnect! Thus his ideal ES% is still 56.3%. When his mana orb is half full, whether his ES% is 56.3% or 39.2%, his EHP is still 510.

The flaw in all the above is that it does not take into account mana regeneration. I assume all the damage is dealt to you in ONE hit or over a extremely short period of time. This is realistic (from playing experience as well) as the only damage that really matters happens in very short intervals. If I was dying slowly, I would drink a potion and teleport/TP away. Dying quickly, by definition happens very abruptly. Such events include being hit by Hephaesto or Might enchanted monsters, waves of MSLE bolts and more. Hence time and mana regeneration is irrelevant in these cases.

The one case where time becomes a factor is during a timeout, a disconnect. Mana would regenarate over the course of the timeout. Suppose I take 15 seconds to timeout (the widely believed value), my ideal ES% would be then ES3% = M2/(2H + M2), where M2 here is equal to the max mana you have plus a little bit more from regeneration in 15 seconds. And where M2 > M, ES3% is obviously larger than ES%. In the above example, James ideal ES% is 56.3%, in order to compensate for mana regeneration in a timeout, I would add a few more % to this value, maybe to at most 60%. M2 can be estimated quite easily if you wanted to calculate ES3%.

What if you have already brought your ES% to a level way beyond your ideal ES%? If EHP remains constant no matter what value ES% is above the ideal value, it doesn't really matter right? Wrong, because I'll rather hp and mana both hit zero at the same time, than mana hitting zero before hp, so that in whatever short amount of time I have when I get swarmed, I may still have enough mana to teleport out. And when I do manage to teleport out, I'll want my ES to be still active, because mana is regenerating, and I do not wish to spend that half second recasting ES.

One can argue that with maxed warmth and a bit of lightning mastery, you can regen enough mana to teleport out, even if your mana orb is empty. However, if what is swarming you includes mana drainers (e.g someone tipped the Vizier Seal right on top of you) you will not regenerate any mana at all. On top of that, you are not garaunteed that your very first cast of teleport will succeed, should you get hit and enter hit recovery animation. By the time you cast your second or third, your mana would be dry should ES% be way above ideal ES%. This also applies to waypoint traps and stairtraps you need to teleport away from being swarmed. Saving and Exiting negates all these arguments, but that's a different issue altogether.

Attempting to bring ideal ES% up towards whatever ES% we already have means to get more mana. But on the other hand, looking at the EHP formula, EHP = H + M/2, you notice that our EHP increases by 2 per one Vit, and only 1 per one Ene. Suppose a Frostburn and one SoJ is used, adding max mana by 65%, then one Ene will increase EHP by 1.65. Whatever skill points above ES3% is wasted. It is better to just dump all in Vit, once a desired amount of mana is acquired, such as 900, where you'll be able to play comfortably with no mana potions. (Not enough mana? Static more, Orb less, Same result.)

Going back to James' sorceress, does he have enough hp? This topic is about hp/mana balance after all. 310 hp 800 mana gives him a EHP of 710 at 56.3% ES (11 skill points). If he had 400 hp and 650 mana instead, his EHP is 725 at ES% = 44.8% (6 skill points). Here comes the tradeoff: Would you rather have 5 skill points elsewhere at the cost of having less mana to play with?

Still, ES% should not be calculated on current hp and mana values. It should be calculated on your estimated values of hp and mana at level 75, wearing equipment that you plan to get to maximise EHP. The 310 hp 800 mana should not be a current value to base on at say level 40, since he may not actually have found the SoJs he intended to wear yet. In general, ideal ES% tends to fall as one gets higher in level.

Things get slightly more complicated when you consider in the effects of Nightsmoke and Vulpine equipment. Suppose James wears a Nightsmoke. Over the course of the 310 hp damage he will take in order to die, Nightsmoke will generate 310 * 0.5 = 155 mana. In other words, James mana is increased by a virtual amount equivilant to H*C when he takes his EHP amount of damage, where C is the conversion rate in decimal. Hence the new formulas are ES% = (M + H*C)/(2H + M + H*C) and EHP = H + (M + H*C)/2.

Wearing Nightsmoke thus gives you more EHP by H/4. This is as good as extending your HP by 25% of your vitality. Consider the differences using Nightsmoke and a rare plated belt which adds 50 hp 30 mana and 25 fire, 25 lightning resists. Assume the popular one stone, one frostburn combo and that the Sorceress in question has 600 hp without wearing either belt.

The 50 hp on the rare belt gives: 50 EHP
The 30 mana on the rare belt gives: 49.5 mana = 24.75 EHP
The 20 mana on the nightsmoke gives: 33 mana = 16.5 EHP
Nightsmoke gives an additional EHP of (600*0.5)/2 = 150 EHP

EHP given by rare belt = 50 + 24.75 = 74.75
EHP given by Nightsmoke = 16.5 + 150 = 166.5

Thus the nightsmoke gives about 90 more EHP than the rare belt at 600 hp, allowing you to survive possibly one or two more hits. Is this a good tradeoff for having one less row of potions and 16.5 less mana? If a player is able to obtain resists from elsewhere other than the belt, I believe this IS a good tradeoff and Nightsmoke is better, rarely do we use potions to the point where the belt is nearly empty.

Nightsmoke has a handy -2 (physical) damage as well against Diablo, as well as 10% resists all itself compared to the 25% fire and 25% lightning on the rare belt. Of course, these EHP numbers will vary from belt to belt and on the hp of the sorceress. The rare belt used in the above example was a rather good belt described, yet we find it inferior to Nightsmoke in terms of EHP. Suddenly, Nightsmoke isn't all that bad after all. However, using Nightsmoke means the ideal ES% would be about 5% higher than without Nightsmoke, or about 2 levels of ES. The tradeoff here also involves 2 skill points for 90 more EHP, and possibly more if the sorceress has more hp.

But WAIT! There is an insidious flaw in all the above arguments about how Nightsmoke extends EHP by H/4. The above assumes that the mana generated by Nightsmoke (and Vulpine items) are completely used up by ES. At C = 0%, having a ES% higher than the ideal ES% doesn't affect EHP because all the mana is used up completely by ES, but when using Vulpine items, when the ES% is above the ideal ES%, your mana will run out faster first. ES will deactivate for the remaining hp left when mana hits 0 while the Vulpine ability continues to generate mana. This portion of mana that is generated is not used by ES at all! Thus, Nightsmoke doesn't really extend EHP by H/4, but rather a value less than that (and above zero) most of the time.

Restating the obvious formulas, suppose a monster hits a sorceress for D amount of damage:
You will suffer (2ES%)(D) mana.
You will suffer (1-ES%)(D) hp.
You will gain (1-ES%)(D)(C) mana.
So you will suffer (1-ES%)(D) hp and (2ES%)(D) - (1-ES%)(D)(C) mana.

The sorceress' mana will deplete when she takes M/((2ES%)(D) - (1-ES%)(D)(C)) * D = M/((2ES%) - (1-ES%)(C)) damage. The mana that is generated over this damage by the Vulpine ability is equal to M/((2ES%) - (1-ES%)(C)) / D * (1-ES%)(D)(C) = M/((2ES%) - (1-ES%)(C)) * (1-ES%)(C) = M/((2ES%)/((1-ES%)(C%)) - 1). So the EHP is extended by M/((2ES%)/((1-ES%)(C%)) - 1) / 2 = M/((4ES%)/((1-ES%)(C%)) - 2). Let's call this amount of EHP extended by the Vulpine ability VHP. Only when ES% is equal to the ideal ES% of (M + H*C)/(2H + M + H*C) will VHP be at the maximum of H*C/2, and for the case of Nightsmoke only, H/4. The more a sorceress' ES% is higher than his ideal ES%, the nearer his EHP is to H + M/2.

Again, the ability to convert 50% damage to mana lengthens our EHP by up to H/4. While playing the game one will not want to get hit at all, this ability would then be next to useless, but when one does get hit for HUGE damage such as by Hephasto, this ability is more than useful in providing the additional EHP one may need to survive the damage. If such one-hit huge damages does not exist at all, then Nightsmoke is probably the lousiest belt a sorceress can ever have.

But Vulpine items do not respond to just any kind of damage. Vulpine items return mana only from melee attacks. Therefore, Vulpine items will do nothing against Archers, Oblivion Knights, or Diablo's lightning attack. However, since most melee attacks are physical attacks, one could also think of Vulpine items as working against physical attacks only (although you still have to keep in mind that ranged physical attacks would be an exception).

Some people will claim that Vulpine items should be worn because they provide "virtual HP". The idea is that because they return mana, and mana is needed to fuel ES, the mana generated by Vulpine items can be thought of mana that will go towards saving HP through the continued use of ES. In way, this is true. But it needs to understood that Vulpine items do not always activate, but rather, activate only when melee damage is taken. Because it is very difficult to predict what proportion of the damage you will be taking will be melee damage, it is difficult to do any kind of realistic quantitative analysis of the Vulpine effect thought of as "virtual HP". Making such an analysis even more difficult is the realization that only some of your Sorc's mana is meant for use with ES, whereas the rest is used for spells, and there is no clear way to quantitatively differentiate between these two imaginary mana pools. Sometimes you will need all of your mana for your ES to save you from a bad spot, sometimes the Vulpine effect is irrelevant (and thus, of less value) since you did not take enough damage to really need any help from such items. Because there are so many variables involved when using Vulpine items, I will not attempt a quantitative analysis of Vulpine as "virtual HP". It is simpler, and more to the point, to think of Vulpine items as something that helps to keep your ES alive. The ultimate value of Vulpine items in that role is determined by many things.

(Extract from VenomousVixen's Complete Sorceress Guide)

Looking at Act 4 alone, the area most players level up in, the only monsters that deal any significant non-melee damage are Burning Souls, Maw Fiends (Corpulents and Corpse Spitters), Abyss Knights, Oblivion Knights and Diablo. All the rest inflict melee damage, and even then, all the above named monsters do inflict some form of melee damage when in close proximity except Oblivion Knights. Act 2 is another area most players level up in, similarly the only monsters that inflict non-melee damages are Burning Dead Archers (Horror Archers), Burning Dead mages (Horror mages), Radament, Slingers (Spear Cats, Night Slinger, Hell Slinger) and Night Lords (Dark Lords). It can be clearly seen that most monsters in the game inflict melee damage, and those that doesn't can generally be dodged quite easily. Think to yourself how much more often do you suffer melee damages over non-melee damages before considering how useful Nightsmoke is in extending one's EHP; quite often, a solo sorceress would find a Nightsmoke more useful than a party only sorceress would.

However, if you played your sorceress correctly and only level in areas that have slow moving monsters and few ranged/elemental attackers (as what all hardcore sorceress do anyway), then Nightsmoke is quite obviously a better choice over a rare belt. Think of what monsters you usually meet in the Sewers, Far Oasis, Lost City, Ancient Tunnels, Palace and in Act 4.

Similar, using this concept of EHP, one can see that the effects of Frostburn adding 40% to maximum mana effectively increase EHP by an amount equal to half of the mana added by Frostburn. At level 75, Frostburn adds about 200 mana or otherwise (assuming a base of 500 mana after other items) and this equates to roughly 100 EHP.

Below is a summary of all the equations:

Graph made in Graphmatica for Win32 v1.60e
Graph file can be downloaded here (ehp.gr: 961 bytes)

If you are confused by the complicated looking graph, take notice of only the WHITE lines. Since ES is only applicable between 0% and 100%, that's where the white lines lie, between 0 and 1.

Case 1: When damage-to-mana conversion is at 0%, EHP rises up along the curve then becomes flat and parallel to the x-axis (ES%-axis).

Case 2: When damage-to-mana conversion is at 50% (Eg. Nightsmoke equipped), EHP rises up along the same curve, and rises beyond when it was at 0%, up to a tip. EHP then falls along the other white curve.

For those of you who still can't grasp the EHP concept properly, I'll refer you to Dog of Justice's Hardcore Sorceress Guide. Look under Energy Shield in the Lightning Tree section. The same formulas and numbers are there, but explained in a easier to understand form. (Note: The formulas there are essentially taken from my guide, since we both worked on our guides simultaenously. That is also why some sections of my guide are taken from his guide.)

EHP Calculator

Note: I am aware that this EHP calculator does not work in Netscape 4, but I also know for a fact it works in Netscape 6. So if it isn't working for you, go update your Netscape.

Again, as a general guide, the average level 75 HC sorceress has about 650 hp and 900 mana wearing one SoJ and one Frostburns. These are good values for a newbie sorceress to base on and work towards. This gives an ideal ES% of 40.9%, so ES% should be at 43%. If Nightsmoke is used then ideal ES% is 45%, so ES% should be at 46% or 49%. Once you have obtained a comfortable amount of mana to play with, throw everything into hp. The goal is thus to maximise EHP after reaching a nice amount of mana.

The EHP concept relies on the basis that damage that comes slowly does not matter; you'll drink a potion. Damage that comes quickly over an extremely short amount of time is the one that matters, thus EHP is the thing to maximise in HC.