Which configuration of armor enchantments gives maximum protection?

minecraft-java-edition

Prior to 1.4.6 it was a well known fact that the protection enchantment on armor was strictly superior to the other enchantments and that simply having a few pieces with protection III/IV would max out this protection, leading to the best possible set of armor. Now that this has changed, however, I'm curious to see if anyone has analysed what the optimal armor configurations now are?

Presumably it will be some combination of protection enchantments and other enchantments, going by the description of how enchantments work now on the wiki. Or, are we forced to choose one or more types of protection to max out? (This would be the case if there are not enough total enchantments possible to max out all areas). If this is the case, it would be great to see some analysis of how to optimise that choice as well. I've looked around but haven't found any good mathcrafting on this question yet.

Furthermore, beyond protection against taking damage, can someone include some explanation of the hidden utility bonuses? For instance, Blast Protection has been described in wiki sources as reducing the knockback effects from explosions, and Fire Protection is described as reducing burn time. Do these effects scale and max out at some enchantment level, and does Projectile Protection similarly reduce the knockback effect from projectiles?

First note that the Enchanting page on the wiki says that Protection, Fire Protection, Blast Protection, and Projectile Protection are all mutually exclusive, but it looks like you can have Feather Falling on boots with one of the other enchantments.

The Armor page linked in the question has a table of "Enchantment Protection Factors" provided by each enchantment. I have duplicated the relevant parts of the table below:

Armor protection EPF table

Since increasing the level of the enchantment only increases the EPF, when trying to find the "best" protection it is only worth looking at the highest level enchantment. The article also says that in order to maximize protection from a particular kind of damage, you would need 25 points of protection for that damage type.

Since there are 3 different types of damage, one would need 75 effective points of protection, but since each armor can add either up to 11 points to one type of protection or 5 points to each type (which is like adding 15 total), the max is 60 effective points of protection. So, you can't max out everything. And plain Protection can't be maxed out at all. Therefore, the best armor depends on what you are looking for:

If you want to maximize the minimum protection value:

Put Protection IV on each piece of armor. This will give you 20 points in every type of protection. As a side bonus, if you put any level of Feather Falling on the boots, you will max out fall damage protection.

Protection EPF: 20
Fire EPF: 20
Blast EPF: 20
Projectile EPF: 20
Feather Falling EPF: 38 (capped to 25)

If you want to maximize the average of protection values:

Again, put Protection IV on each piece of armor. Adding Protection IV to a piece of armor adds 5 to each protection type, so it adds 5 to the average. Adding any other protection enchantment adds at most 11/3<5 EPF on average.

Protection EPF: 20
Fire EPF: 20
Blast EPF: 20
Projectile EPF: 20
Feather Falling EPF: 38 (capped to 25)

If you want to prioritize a particular protection type:

Plain old Protection:

Put Protection IV on all 4 pieces of armor.

Protection EPF: 20
Fire EPF: 20
Blast EPF: 20
Projectile EPF: 20
Feather Falling EPF: 38 (capped to 25)

Projectile Protection then Blast Protection:

Put Projectile Protection IV on two pieces of armor, Blast Protection IV on one piece of armor, and Protection IV on the last piece of armor.

Protection EPF: 5
Fire EPF: 5
Blast EPF: 16
Projectile EPF: 27 (capped to 25)
Feather Falling: 23

Projectile Protection, then Fire Protection:

Put Projectile Protection IV on two pieces of armor, Fire Protection IV on one piece of armor, and Protection IV on the last piece of armor.

Protection EPF: 5
Fire EPF: 14
Blast EPF: 5
Projectile EPF: 27 (capped to 25)
Feather Falling: 23

Blast Protection then Projectile Protection:

Put Blast Protection IV on two pieces of armor, Projectile Protection IV on one piece of armor, and Protection IV on the last piece of armor.

Protection EPF: 5
Fire EPF: 5
Blast EPF: 27 (capped to 25)
Projectile EPF: 16
Feather Falling: 23

Blast Protection then Fire Protection:

Put Blast Protection IV on two pieces of armor, Fire Protection IV on one piece of armor, and Protection IV on the last piece of armor.

Protection EPF: 5
Fire EPF: 14
Blast EPF: 27 (capped to 25)
Projectile EPF: 5
Feather Falling: 23

Fire Protection, then the other two

Put Fire Protection IV on 2 pieces of armor and Protection IV on two pieces of armor.

Protection EPF: 10
Fire EPF: 28 (capped to 25)
Blast EPF: 10
Projectile EPF: 10
Feather Falling: 28 (capped to 25)

Fire Protection then Projectile Protection:

Put Fire Protection IV on 3 pieces of armor and Projectile Protection IV on one piece of armor.

Protection EPF: 10
Fire EPF: 27 (capped to 25)
Blast EPF: 0
Projectile EPF: 11
Feather Falling: 18

Fire Protection then Blast Protection:

Put Fire Protection IV on 3 pieces of armor and Blast Protection IV on one piece of armor.

Protection EPF: 0
Fire EPF: 27 (capped to 25)
Blast EPF: 11
Projectile EPF: 0
Feather Falling: 18