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This Mod is out of date!
Go here for the current version. More Natural Encumbrance 2.0

INTRODUCTION:
This is my first mod. I was looking for a mod that does this, but when I couldn't find one I decided to make it myself. After lots of tweaking and testing, I finally have it working the way I want it to. Like the title suggests, this mod aims to make the over encumbrance system feel more natural/gradual while still keeping it balanced and in line with Bethesda's original intent, which is to hinder you if you become over encumbered.

WHAT THIS MOD DOES:
This mod allows you to run while over encumbered, but drains your stamina while doing so. There are 5 tiers of over encumbrance, each one draining your stamina more based on the percent you are over encumbered.  There are two main versions of this mod, each with a regular, medium or light variation. In short, the medium variations drain your stamina less than the regular, and the light variations drain your stamina even less. This will be explained in detail below under STATS. The medium or light versions will be easier on low level characters.

The main file: This version will temporarily raise your carry weight limit by 10,000 when you become over encumbered, allowing you to run. If you are carrying more than 25% of your original carry weight, it will be returned to normal and you won't be able to run anymore. Also, if you let your stamina get below 10% you will have to wait 30 seconds before you can run again, forcing you to rest. With this version you can technically sprint while over encumbered, but this drains your stamina A LOT. Also you still won't be able fast travel if you're over encumbered.

Version 2, the speed version: This version will significantly increase your speed when you become over encumbered so that your walk speed is slighty slower than the vanilla run speed. For each increased tier your speed will be slighty reduced. With this version you can't sprint. Your stamina drains the same.

Both versions are affected by buffs from potions or enchanted items. In version 1 For example, let's say your carry weight is 300 and your inventory weight is 310. This mod will increase your carry weight limit to 10,310, but If you drink a strength potion or equip an item that increases your carry weight by 20, your carry weight will be set to 320, you won't be over encumbered and your stamina won't drain any more.

This mod also changes the "You are carrying too much to be able to run" message to "You are over encumbered" for obvious reasons. Also, when you're not over encumbered anymore it will display a message saying "You are no longer over encumbered."


STATS:

Speedmult is only for the speed version.
Your stamina will drain as follows:

Regular Variation:
Tier 1: Over encumbered by 0 to 5%, stamina drain while running =15 per second. While sprinting = 215 per second. V2: (+150 speedmult)
Tier 2: Over encumbered by 5 to 10%, stamina drain while running = 30 per second. While sprinting = 265 per second. V2: (+140 speedmult)
Tier 3: Over encumbered by 10 to 15%, stamina drain while running = 50 per second. While sprinting = 315 per second. V2: (+130 speedmult)
Tier 4: Over encumbered by 15 to 20%, stamina drain while running = 75 per second. While sprinting = 365 per second. V2: (+120 speedmult)
Tier 5: Over encumbered by 20 to 25%, stamina drain while running = 100 per second. While sprinting = 415 per second. V2: (+110 speedmult)

Medium Variation:
Tier 1: Over encumbered by 0 to 5%, stamina drain while running = 10 per second. While sprinting = 165 per second. V2: (+150 speedmult)
Tier 2: Over encumbered by 5 to 10%, stamina drain while running = 20 per second. While sprinting = 215 per second. V2: (+140 speedmult)
Tier 3: Over encumbered by 10 to 15%, stamina drain while running = 35 per second. While sprinting = 265 per second. V2: (+130 speedmult)
Tier 4: Over encumbered by 15 to 20%, stamina drain while running = 50 per second. While sprinting = 315 per second. V2: (+120 speedmult)
Tier 5: Over encumbered by 20 to 25%, stamina drain while running = 75 per second. While sprinting = 365 per second. V2: (+110 speedmult)

Light Variation:
Tier 1: Over encumbered by 0 to 5%, stamina drain while running = 5 per second. While sprinting = 115 per second. V2: (+150 speedmult)
Tier 2: Over encumbered by 5 to 10%, stamina drain while running = 10 per second. While sprinting = 165 per second. V2: (+140 speedmult)
Tier 3: Over encumbered by 10 to 15%, stamina drain while running = 20 per second. While sprinting = 215 per second. V2: (+130 speedmult)
Tier 4: Over encumbered by 15 to 20%, stamina drain while running = 35 per second. While sprinting = 265 per second. V2: (+120 speedmult)
Tier 5: Over encumbered by 20 to 25%, stamina drain while running = 50 per second. While sprinting = 315 per second. V2: (+110 speedmult)

REQUIREMENTS:
Just the latest patch of Skyrim, that's it.

COMPATIBILITY:
It was pointed out to me that the main version, the one that increases your carry weight limit, won't be compatible with other mods that rely on your carry weight, or the relationship between your inventory weight and carry weight limit. Your game won't break but such mods won't behave properly with this one, which is why I made the speed version as an alternative. Side note, I recommend using the main version of this mod with Athletics Training (which is one of my favorite mods, you should definitely check it out), as it has a fatigue option which lowers your speed when your stamina drains too much. If you use these mods together remember to turn the encumbrance option OFF in the Athletics Training MCM menu.

The speed version won't be compatible with other mods that affect your speed after you become over encumbered. Again your game won't break because this mod adds unique spell abilities to your player to affect your player's stats, but other mods that also do this won't behave properly. Most likely if the other mod uses ModActorValue SpeedMult you won't really notice the difference as this mod increases your speed a lot. If they use SetActorValue SpeedMult this mod won't work at all. If you want to change the speeds from this mod, in the CK search under magic/spells/abilities for NaturalEMOD spells and tweak to your liking.

INSTALLATION/UPATING:

If installing for the first time simply unzip the file and move the contents to your Skyrim/Data folder. Only check one version in your load order at a time, (regular, medium or light.)

If updating from the older version, or switching between the speed and carryweight versions:
1 First, load your game and make sure you’re not over encumbered. 
2 Search in the console for the NaturalEncumbrance Quest.
3 Type in the consol "stopquest" followed by the quest ID. Should look something like: stopquest  BF00894D
4 Make a new save
5 Uncheck or delete the old esp
6 Install this mod by extracting to the Skyrim/Data folder and checking it in your load order.

If you are switching between the regular, medium and light variations in the same version you don't need to make a clean save as they use the same script.

UNINSTALLATION:
1 First, load your game and make sure you’re not over encumbered. 
2 Search in the console for the NaturalEncumbrance Quest.
3 Type in the consol "stopquest" followed by the quest ID. Should look something like: stopquest  BF00894D
4 Make a new save
5 Uncheck or delete the old esp

ISSUES/BUGS/FAQS:
I've tested this quite a bit and have fixed a lot of bugs, but if you find one let me know! I've included the source file for the script in case you want to mess around with it.

While perusing your inventory you may find a note called Encumbrance Note. This is added to force the mod to update after you are forced to rest or when equipping/unequipping an item. Wait a few seconds and this should be removed automatically but if it's not feel free to drop it.

For the main version, If your carry weight is already at or above 10,000 this mod won't work properly, but if this is the case, you probably don't need this mod.

Sometimes if you drop or pick up multiples of the same item at once, say 10 dragon bones, sometimes this mod won't update. I'm not sure why this is, or how to fix it, but it doesn't seem to happen very often. If this happens simply remove or add another item to your inventory.