Name: Skyrim Critical Hits Recalculated by AshAuryn
Version: 1.0
Date: 11/12/2015
Category: Gameplay Effects and Changes
Author(s): AshAuryn
Source:

Summary
===========
This mod recalculates the way critical damage is quantified and applied in Skyrim so that it levels with your character and is appropriate to the weapon being used. In short, this fixes Skyrim's broken Critical Hit system.
**No scripts. Just math. Compatible with all weapons and safe for your save game.**


Description
=======================

I was tired of the broken Critical Hits system in Skyrim. Vanilla critical hits are based on a calculation that uses a weapon's base stats (before leveling, upgrades, or enchantments). After level 10 or so, the system is useless.

Likewise, I found the "ignore armor" perks for hammers and maces and the "extra bleeding" perks for axes to be similarly less-than-useful. I also found errors in the way Bethesda calculates critical hit chance, and decided to adjust the numbers using statistical analysis.

I am a math and science major. I decided to re-work this problem without scripts. Critical Hits are now based on your Stamina level, which should increase as you level up.

**For Mages: There is an optional .esp that makes the same calculation using Magicka instead of Stamina
**For Power Gamers: There is an optional .esp that uses my calculations but doubles the chance of a critical hit

============CHANGES================

--Critical Perks--

Did away with "bleeding damage" and "ignore armor" system for axes and hammers. Now all weapons (including daggers, hammers, and axes) have a chance of a critical hit and a perk to go along with it. Perks adjusted: Bladesman, Bonebreaker, Deep Wounds, Hack & Slash, Limbsplitter, Skullcrusher, and Critical Shot.

--Critical Chance--

For the three perk levels of each critical perk, chances of making a critical hit range from an average of 1 in 100 for rank 1, 1 in 80 for rank 2, and 1 in 60 for rank 3. Occasionally you will get lucky and get crit hits in quick succession, but your crit strikes will average out to these numbers. Two-handed weapons have a higher chance than one-handed, and Bows/Crossbows have a much higher chance ranging from 1 in 50 for rank 1, 1 in 25 for rank 2, and 1 in 15 for rank 3.

--Critical Damage--

Critical Damage is now based on your stamina level. This was the only way to synthesize "leveling up" without using scripts. The more points you have in stamina, the more damage your critical hits will do. Daggers do the least critical damage and Warhammers do the most. The better type of weapon material you have, the more critical damage it will do. (An iron dagger does less critical than a daedric one).

Critical Damage in this mod is calculated as: Weapon Crit effect Multiplier * (Fixed Percent) * Stamina = Extra Damage Applied.
(How I determined the fixed percent, if you are interested, is explained at the end of this document)

Example #1: An Iron Dagger has a base critical effect multiplier of 2, base damage of 4. In order for you to get the first perk in Bladesman, you would need to have a One-Handed skill of 30 and be a minimum of level 3. This will give you a 1 in 100 chance of getting a critical strike with a dagger at level 3. Let's say your stamina at level 3 is 110. Your damage for your critical strike will be 2 * .0825 * 110 = 18.15. That's (dagger's crit effect mult * my calculation * your stamina) = 18.15 extra damage.

Example #2: Now you are level 30. You have the rank 3 Bladesman Perk, and you have put half of your bonuses into stamina making your stamina 240. Your iron dagger still has a crit multiplier of 2. It's damage has leveled up to 5.8, but as far as vanilla skyrim's critical system is concerned it's still at 4. Fortunately, you have this mod! You now have a 1 in 60 chance of getting a critical hit, and your damage from a critical strike will now be 2 * .0825 * 240 = 39.6. Your vanilla critical damage would have been only 1.82 (.455 * base damage).

Example #3: You are level 50. You have rank 3 Deep Wounds, and your stamina is 350 because you decided to be badass and put half your points into stamina. Your Daedric Greatsword's leveled damage is 36 without smithing or enchantments or perks, and its crit effect multiplier is 12. According to Vanilla Skyrim, its base damage is still 24, and with Vanilla Skyrim, you would be fighting trolls with 400 health and you would be doing a measly 22.5 critical damage. With AshAuryn's mod, you now have a 1 in 50 chance of doing (12 * .1429 * 350) = 600.18 critical damage. Troll is decapitated, mammoth takes a big hit, and Dragon pretends it didn't hurt but it really did.

=======Breakdown===========

(let's assume iron weapons and long bow, level 40, and a stamina of 200 for our "character" in this breakdown example)

Bladesman: Daggers are now included as well as swords.
Dagger crit damage = 33, Sword crit damage = 75
Rank 1: 1 in 100 chance
Rank 2: 1 in 80 chance
Rank 3: 1 in 60 chance

Hack & Slash: War Axes do critical damage
War Axe crit damage = 120
Rank 1: 1 in 100 chance
Rank 2: 1 in 80 chance
Rank 3: 1 in 60 chance

Bonebreaker: Maces do critical damage
Mace crit damage = 150
Rank 1: 1 in 100 chance
Rank 2: 1 in 80 chance
Rank 3: 1 in 60 chance

Deep Wounds: Greatswords do critical damage
Greatsword crit damage = 200
Rank 1: 1 in 90 chance
Rank 2: 1 in 60 chance
Rank 3: 1 in 50 chance

Limbsplitter: Battle Axes do critical damage
Battleaxe crit damage = 240
Rank 1: 1 in 90 chance
Rank 2: 1 in 60 chance
Rank 3: 1 in 50 chance

Skullcrusher: Warhammers do critical damage
Warhammer crit damage = 300
Rank 1: 1 in 90 chance
Rank 2: 1 in 60 chance
Rank 3: 1 in 50 chance

Critical Shot: Bows do critical damage
Long Bow crit damage = 100
Rank 1: 1 in 50 chance
Rank 2: 1 in 25 chance
Rank 3: 1 in 15 chance


Critical Hit damage will vary depending on the weapon you use and its material. Dragonbone weapons do more critical damage than iron weapons. These values are all based on Skyrim's vanilla weapon critical effect multipliers, so I only had to change the perks. No scripts were used. No weapons were altered.

====Calculations====

For those interested, I will explain my calculations:

As far as critical chance, I found that while Bethesda gave a description in the perk of "10% chance of critical hit" and while the value they used in the math was "10" in the code, a statistical analysis using a modified weapon and thousands of strikes showed that calculation to be false. I re-calculated based on my analysis and now the numbers I use are closer to the truth. For example, a "1" will actually give you about a 1 in 60 chance of a critical hit, or 1.667% chance. While a "4" will actually give you a 1 in 15 or 6.7% chance. You can see how Bethesda's interpretation of "25" (for Rank 3 Bladesman) would be both ridiculous and annoying, since they hard-coded the "Critical Strike" and "BOOM" sound to appear on your screen every time you land a hit. sigh.

As for the fixed crit percentage amount, I based it first off of a multiple of stamina and then worked backwards. I started with a set of weapons that I modified to have a crit damage of 1. Then I set the multiplier fields in the perks to multiples of stamina. (.25 for daggers, .50 for swords, 1.5 for warhammers, so on). I adjusted these numbers until it did what I wanted, which was "my weapon damage plus about 25~50% on a critical hit". Then I needed to account for every weapon having a different crit damage in their critical data field. The tedious and incompatible way would have been to make every weapon have a "1". Instead, I used the iron weapons as a starting point, so that every other weapon would be "more" than an iron weapon. For example, I took the iron sword - it has a crit damage of 3. Turn that into a decimal that when multiplied by 3 will equal 1 -> 100/3/100 = .33. multiply that by the .50 of stamina. you get .1250 of stamina. Now when the iron sword does critical, it will do (your stamina * .1250 * 3). If it's a Daedric Sword, it's critical damage is 7, so with my math it will do (your stamina * .1250 * 7). If you only use iron weapons, you'll end up with a fairly even 25% of your stamina for daggers, 50% of your stamina for swords, 60% for axes, and so on up to 150% for warhammers. The iron crit values are dagger=2, sword=3, waraxe=4, mace=4, greatsword=7, battleaxe=7, warhammer=9, longbow=3. My fixed values are .0825, .1250, .1500, .1875, .1429, .1714, .1667, .1650 respectively. This accounts for 25%, 50%, 60%, 75%, 100%, 120%, 150%, and 50% of stamina, respectively.

Base damage is not part of the equation. Let's take a modified bow as an example. In the "damage" section of its critical data field it says it has 15 crit damage. My original adjustment is based on a bow with crit 3 doing 50% of your stamina on a critical hit. (3 * .1650 * stamina). The .1650 is my "fixed amount" based on a crit of 3. Our modded bow with 15 crit damage multiplier will do 3 times the "normal" amount @ crit 15. If your stamina is 100, a bow that has a crit of 3 will do an extra 50 damage. Our modded bow will do an extra ~250 damage at crit 15. Both bows will do more damage as your stamina increases (as you level up).


Install
=======
1. Extract the files to a temporary location.
2. Examine the folder structure and make corrections where necessary.
3. Copy files to (install folder)\Skyrim\Data\
4. Start Skyrim Launcher, click 'Data Files', place a checkmark beside the .esp file(s).

Optional Mod Organizer install:
1. Open archive with Mod Organizer
2. Select data folder
3. Install
4. Place this mod below any mods that alter perks in your mod order

Uninstall
=========
1. Delete any folders associated with this mod
or
Remove with Mod Organizer.

This mod does not add any scripts and will not affect your save games.


Incompatibility
===============

Will overwrite any mods that alter the following perks:

Bladesman
Bonebreaker
Deep Wounds
Hack & Slash
Limbsplitter
Skullcrusher
Critical Shot

Incompatible with PerMa or any mod that significantly alters the One-Handed, Two-Handed, and Marksman skill trees.*
*Check back in the optional files section for a "friendly" version that will allow you to use this mod in conjunction with other Skill Tree mods.

Known Issues or Bugs
====================

No known issues at this time.

History
=======

1.0: 11/12/15 - Initial release. Calculations have been tested in game using several thousand "swings" per weapon.

Contact
=======

Skyrim Nexus @ AshAuryn

Credits
=======
Thank you to the nexus community for providing this opportunity and to Bethesda for creating a game that I have spent more hours playing than any other game in my life. :)

Tools Used
==========
TES4Edit - http://www.tesnexus.com/downloads/file.php?id=11536

Licensing/Legal
===============
You must contact me and obtain my permission before re-packaging any part of
this mod. I will usually respond within two weeks.