Background

Protection, Fire Protection, Blast Protection, and Projectile Protection are all mutually exclusive enchantments in survival Minecraft. I just need some clarification of some comments in the official wiki to understand what happens when these are mixed and matched in multiple pieces of armor.

Conflict

In the wiki it states under each of these 4 enchantments

If multiple pieces have the enchantment, only the highest level's reduction is used.

The way I read the wiki it sounds like it is a waste to have 2 of the same protection enchantments.

However multiple posts claim that protection stacks with multiple pieces of armor. Example from minecraft wiki. Example from Stack Exchange.

Is the wiki wrong? Are the blog posts just old and no longer true? Am I misunderstanding the statement in the wiki?

Question

As protection reduces damage by 4% per level which of these is true?

1. Protection IV on 2 pieces of armor will reduce the incoming damage by 16%
2. Protection IV on 2 pieces of armor will reduce the incoming damage by 32%
3. Neither, please explain my error in understanding.

I am asking in the context of Bedrock edition (Windows 10, Pocket Edition, Xbox). Though would be interested in hearing how it differs in java if at all.

Solution 1:

The test

I hit my friend with different weapons, who is equipped with full diamond armor, but with different enchantment combinations. (e.g. Only Helmet is enchanted; Helmet and Chestplate; Only Leggings; etc.) I also wrote a tiny plugin that outputs the raw, adjusted damage received by a person and conducted multiple tests to determine the effects of enchantments on armor.

This is the plugin deployed on a Minecraft Java version server running on PaperSpigot 1.10.2 with API version 1.10.2.-R0.1-SNAPSHOT.

package com.fivefourdee.damagenotifier;

import org.bukkit.Bukkit;
import org.bukkit.event.EventHandler;
import org.bukkit.event.Listener;
import org.bukkit.event.entity.EntityDamageEvent;
import org.bukkit.plugin.java.JavaPlugin;

public class DamageNotifier extends JavaPlugin implements Listener{
    @Override
    public void onEnable(){
        Bukkit.getPluginManager().registerEvents(this,this);
    }
    @EventHandler
    public void onEntityDamage(EntityDamageEvent event) {
        event.getEntity().sendMessage(event.getCause().toString()+" > "+event.getFinalDamage());
    }   
}

The results

A Diamond Sword is used for the tests below.

Test 1.0: Base damage test

Gear                                            Raw damage / damage compared to base

Helmet
Chestplate
Leggings
Boots                                                 1.8899998664855957  /  100.00%

Test 1.1: Multiple armor pieces owning the same Enchantment

Gear                                            Raw damage / damage compared to base

Protection IV Helmet
Chestplate
Leggings
Boots                                                 1.5875999927520752  /  84.000%

Protection IV Helmet
Protection IV Chestplate
Leggings
Boots                                                 1.2851998805999756  /  68.000%

Protection IV Helmet
Protection IV Chestplate
Protection IV Leggings
Boots                                                 0.9827998876571655  /  52.000%

Protection IV Helmet
Protection IV Chestplate
Protection IV Leggings
Protection IV Boots                                   0.6803998947143555  /  36.000%

Test 1.2: Same armor pieces owning different levels of same Enchantment

Gear                                            Raw damage / damage compared to base

Protection IV Helmet
Protection I Chestplate
Leggings
Boots                                                 1.5119999647140503  /  80.000%

Protection IV Helmet
Protection II Chestplate
Leggings
Boots                                                 1.4363999366760254  /  76.000%

Protection IV Helmet
Protection III Chestplate
Leggings
Boots                                                 1.3607999086360005  /  72.000%

A Bow with minimum pull before release is used for the tests below. Minimum pull is used due to fluctuation of data if maximum pull is used instead, as seen below:

Test 2.0: Base damage test

Gear                                            Raw damage / damage compared to base

Helmet
Chestplate
Leggings
Boots                                                 0.20999997854232788 /  100.00%

Test 2.1: Multiple armor pieces owning the same Enchantment

Gear                                            Raw damage / damage compared to base

Projectile Protection II Helmet
Chestplate
Leggings
Boots                                                 0.17639999091625214 /  84.000%

Projectile Protection II Helmet
Projectile Protection II Chestplate
Leggings
Boots                                                 0.1427999883890152  /  68.000%

Projectile Protection II Helmet
Projectile Protection II Chestplate
Projectile Protection II Leggings
Boots                                                 0.10919998586177826 /  52.000%

Projectile Protection II Helmet
Projectile Protection II Chestplate
Projectile Protection II Leggings
Projectile Protection II Boots                        0.07559999823570251 /  36.000%

Test 2.2: Same armor piece owning different levels of same Enchantment

Gear                                            Raw damage / damage compared to base

Protection II Helmet
Chestplate
Leggings
Boots                                                 0.1931999772787094  /  92.000%

Protection II Helmet
Projectile Protection I Chestplate
Leggings
Boots                                                 0.17639999091625214 /  84.000%

Protection II Helmet
Projectile Protection II Chestplate
Leggings
Boots                                                 0.15959997475147247 /  76.000%

The conclusion

In Java version, Protection Enchantments stack, and the mechanism is less complicated than you think. For each Protection Enchantment, the added damage reduction is linearly added to the total percentage (+4%). For each specific damage type Protection Enchantment, the added damage reduction is also linearly added to the total percentage (+8%).

Feel free to come up with more "what if" situations so I can directly test it and update the results here.