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Oct 1 2008 04:44pm
Mechanics of Life/Mana

- and socketing Jah / Sur or Perfect Ruby / Sapphire


Table of Contents
- [1] Formulae
- [2] Tal Sorc using CtA
- [3] Jah/Sur vs Perfect Ruby/Sapphire


[1] Formulae

The reason for this section is that percentage bonuses to life and mana are available in the game. Without them, we would only have to consider the character specific conversion of Vitality/Energy
points to Stamina/Life/Mana. Furthermore, what some of you may still not know, the game does not just add all your life/mana bonuses together and then apply the percentage boosts to the result.
Some bonuses are "boostable", whereas others are not. And we obviously want as much life and mana as possible with whatever character build and equipment we are aiming for.

(Max) Life and (Max) Mana displayed on your character screen is calculated as follows,

Code

(1)   Max Life = (Boostable Life)*(1 + Life Boost) + Non-boostable Life
(2)   Max Mana = (Boostable Mana)*(1 + Mana Boost) + Non-boostable Mana

Final numbers (Max Life, Max Mana) are truncated.

Source : Things you SHOULD know about Diablo 2 - posted by Ernir @ Battle.net Forums
> http://www.battle.net/forums/thread.aspx?fn=d2-general&t=1312543&p=1&#post1312543 (Question 47)

Stamina, Life, and Mana all follow the same mechanics. Although Stamina is mostly irrelevant in practice, it is included here for the sake of completeness.

Boostable Life/Mana
  • Gained from spent points in Vitality/Energy (hard points as we speak) *)
  • Gained naturally per level-up **)
  • Gained from quest rewards (Act III, "The Golden Bird" quest, +20 to Life)
  • "+X to Life" / "+Y to Mana" from items
Each of these stack with the default Life/Mana on a new character, to form a single number (Boostable Life/Mana) used in (1) / (2).

*), **) Values depend on character class. Refer to the Arreat Summit : http://www.battle.net/diablo2exp/classes/

Life/Mana Boost (%)
  • Battle Orders (+35 % Stamina/Life/Mana @ slvl 1, then another +3 % per slvl)
  • Oak Sage (+30 % Life @ slvl 1, then another +5 % per slvl)
  • Lycanthropy (+20 % Life @ slvl 1, then another +5 % per slvl)
  • Werewolf (+25 % Stamina/Life and synergised by Lycanthropy)
  • Werebear (+50 % Life and synergised by Lycanthropy)
  • Jah/Sur Rune (+5 % Life/Mana, only when socketed into Helms or Body Armor)
  • "Increase Maximum Life/Mana X/Y %", e.g. Doombringer (20 % Life), Hoto (15 % Mana)
Each of these stack to form a single percentage (Life/Mana Boost) used in (1) / (2).

Non-boostable Life/Mana
  • Gained from Vitality/Energy on items (soft points as we speak)
  • Gained from "+Z to Vitality (Based on Character Level)", e.g. Infinity
  • "+X to Life (Based on Character Level)" / "+Y to Mana (Based on Character Level)", e.g. Harlequin Crest, Wizardspike
Each of these stack to form a single number (Non-boostable Life/Mana) used in (1) / (2).

Stamina benefits from Vitality. Level-ups and hard Vitality points count towards Boostable Stamina. Soft Vitality points count towards Non-boostable Stamina. Refer to the Arreat Summit link above.


[2] Tal Sorc using CtA

We will be using my level 89 Tal Sorc to check (1) and (2) as well as Max Stamina. Additionally, I want to compare the Life and Mana when swapping Tal Rasha's orb + mask for Harlequin Crest + Ocu.

Code
{clvl 1 - Sorceress}

Vitality: 10,  Energy: 35
Stamina: 74,  Life: 40,  Mana: 35

Each Vitality point: +1 Stamina, +2 Life
Each Energy point: +2 Mana
Level-up: +1 Stamina, +1 Life, +2 Mana


Numbers in () below are BASE values. That is, bonuses from equipment and charms are excluded.


{clvl 89 - Setup 1, complete Tal Rasha's set}

Vitality: 397 (355),  Energy: 87 (35)
Stamina: 549 (507),  Life: 1 376 (878),  Mana: 665 (211) [unbuffed]
Stamina: 863 (507),  Life: 2 177 (878),  Mana: 981 (211) [slvl 10 BO]


{clvl 89 - Setup 2, Harlequin Crest + Ocu}

Vitality: 419 (355),  Energy: 99 (35)
Stamina: 571 (507),  Life: 1 286 (878), Mana: 704 (211) [unbuffed]
Stamina: 915 (507),  Life: 1 983 (878), Mana: 978 (211) [slvl 12 BO]

Those were the values read in-game. Note that Setup 1, using the entire set, yields more Life and Mana with CtA than Setup 2, using 3 set pieces and Harlequin Crest + Ocu.

Now for the calculations. First, the inherent bonuses
  • 88 level-ups, 345 Vitality points spent, 3 x 20 life from "The Golden Bird" quests
Hence,
  • Base Stamina = 74 + 88*1 + 345*1 = 507
  • Base Life = 40 + 88*1 + 345*2 + 3*20 = 878
  • Base Mana = 35 + 88*2 = 211
confirming the base values read in-game. Next, consider all external bonuses
  • +57, 60, 50 to Life from Tal Rasha pieces and +150 to Life from the full set
  • +77, 30, 30, 42 to Mana from Tal Rasha pieces
  • +97 to Life from inventory charms, excluding Annihilus + Hellfire Torch
  • +120 to Mana from Raven Frost + mana ring
  • 10 % to Mana Boost from Lidless
  • +32 Vitality from Anni + Torch
  • +10 Vitality from War Traveler
  • +10 Energy each from Tal Rasha's orb and Lidless
  • +133 (= 89*1.5, truncated) Life and Mana from Harlequin Crest
  • +22 (20 + 2) Vitality and Energy from Harlequin Crest + Ocu
From these we calculate the following,

Code
{Setup 1, complete Tal Rasha's set}

Boostable Life = 878 + (57 + 60 + 50 + 150) + 97 = 1 292
Boostable Mana = 211 + (77 + 30 + 30 + 42) + 120 = 510

Life Boost = (35 + 3*9)% = 62%
Mana Boost = (35 + 3*9 + 10)% = 72%

Non-boostable Life = (32 + 10)*2 = 84
Non-boostable Mana = (32 + 10 + 10)*2 = 104

Max Stamina = (507)*(1 + 0.62) + (32 + 10) = 863
Max Life = (1 292)*(1 + 0.62) + 84 = 2 177
Max Mana = (510)*(1 + 0.72) + 104 = 981

Final values are truncated.


{Setup 2, Harlequin Crest + Ocu}

Boostable Life = 878 + (50) + 97 = 1 025
Boostable Mana = 211 + (30 + 42) + 120 = 403

Life Boost = (35 + 3*11)% = 68%
Mana Boost = (35 + 3*11 + 10)% = 78%

Non-boostable Life = (32 + 10 + 20 + 2)*2 + 89*1.5 = 261
Non-boostable Mana = (32 + 10 + 20 + 2)*2 + 89*1.5 = 261

Max Stamina = (507)*(1 + 0.68) + (32 + 10 + 20 + 2) = 915
Max Life = (1 025)*(1 + 0.68) + 261 = 1 983
Max Mana = (403)*(1 + 0.78) + 261 = 978

Final values are truncated.

again confirming the values read in-game.


[3] Jah/Sur vs Perfect Ruby/Sapphire

Here is another application of (1) and (2). Suppose we have decided to socket either a Jah/Sur Rune or a Perfect Ruby/Sapphire in our helm (or body armor), for the additional Life/Mana they provide.
Now, which one is best ... Jah or Pruby ? Sur or Psapp ?

Consider (2) first.

Since we are comparing Sur (+5 % to Mana Boost) and Psapp (+38 to Boostable Mana), Non-boostable Mana is clearly irrelevant here. And we may disregard all of our equipment for the same reason.
Hence, it suffices to consider Base Mana (our Mana without any bonuses from equipment and charms) which is part of Boostable Mana.

Setting X = Mana Boost (excluding Sur), then we have to compare
  • (Base Mana)*(1 + X + 5%) icon_pointl.gif "Sur"
  • (Base Mana + 38)*(1 + X) icon_pointl.gif "Psapp"
Most terms are equal except "Base Mana * 5 %" and "38*(1 + X)". Dividing by 5 % leaves us with
  • Base Mana
  • 760*(1 + X)
and these are easy to compare,

Code
(Sur Rune vs Perfect Sapphire)

(3) IF Base Mana > 760*(1 + X) THEN Sur is better
(4) ELSE IF Base Mana = 760*(1 + X) THEN Sur and Psapp are equally good
(5) ELSE Psapp is better

In particular by (5), if Base Mana < 760, then Psapp is better.

The exact same reasoning applies to Jah vs Pruby. Simply replace Mana with Life everywhere.

I hope some of you found it useful. Any relevant comments or suggestions ?
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Oct 1 2008 04:51pm
what is the meaning of life
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Oct 1 2008 04:56pm
Part 3 answers a commonly asked question.

Good work on that again.
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Oct 1 2008 06:55pm
Quote (P00 @ Wed, Oct 1 2008, 10:51pm)
what is the meaning of life


Trust in Faelwen.
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Oct 1 2008 06:58pm
Quote (purpurhare @ Thu, 2 Oct 2008, 02:55)
Quote (P00 @ Thu, 2 Oct 2008, 00:51)
what is the meaning of life

Trust in Faelwen.

happy.gif

Quote (TheUndyingGod @ Thu, 2 Oct 2008, 00:56)
Part 3 answers a commonly asked question.

Good work on that again.

Thanks.

This post was edited by Faelwen on Oct 1 2008 07:00pm
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Oct 1 2008 09:24pm
Might point out that multiple sockets don't change the 760 balance point.


Other than that,

Quote (purpurhare @ Thu, 2 Oct 2008, 03:55)
Trust in Faelwen.
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Oct 1 2008 09:42pm
n1
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Oct 1 2008 09:42pm
Sticky plz
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Oct 1 2008 10:02pm
Definatly sticky this, Very informative smile.gif
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Oct 2 2008 12:13am
I liked #3.
Helped alot.
The rest was way over my head
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