This was only possible in 1.14-1.14.2, which was then reverted due to issues with the enchanting system, (even though allowing different types of Protection on a single piece of armor had nothing to do with getting bad level 30 enchantments; just how Mojang often does things).
In either case, all you need to max out protection from projectile damage is at least 20 EPF points, which will reach the maximum possible damage reduction of 80%, or 20% of original damage, which is easily met with Projectile Protection by itself as each piece with Projectile Protection IV gives 8 EPF, or 32 for a full set and 24 for 3 pieces. You could also have 2 pieces with Protection IV (4 EPF per piece) and a single piece with Projectile Protection IV, or 3 pieces with Protection IV and a single piece with Projectile Protection IV, both of which will exactly reach the cap of 20.
See also:
When a player or mob wearing armor is subjected to damage, the EPFs of all applicable enchantments are added together, capped at 20, and then damage is reduced as damage = damage * ( 1 - cappedEPF / 25 ), giving a maximum reduction of 80% at EPF 20.
Because of the caps in the calculation, it's possible to max out protection against specific types of damage with only three pieces of armor. For example, two pieces of armor with Blast Protection IV (EPF 8 each) and a single piece with Protection IV (EPF 4) would give a total EPF of 20 versus explosions. Any additional EPF would be wasted against explosions (but might be useful against other types of damage, if applicable).
In other words, 1.14 only made it possible to max out protection from all major damage sources at once (fire, explosion, projectile, falling, with anything else only being affected by Protection for a maximum of 16 EPF or 64%, plus armor itself if it reduces the damage source. Note that Feather Falling, which is technically a protection-type enchantment, can be combined with protection in any version, and only needs 2 pieces with Protection IV to max out).
When applied to diamond armor and the damage of a Power V bow, which is a maximum of 25 (the Wiki is misleading about how much damage bows deal, which is 6-10 for unenchanted to 20-25 for Power V, with a uniform distribution; the table here suggests that there is no randomness while here they claim a fully changed bow consistently deals at least 9 damage), and factoring in armor penetration, which reduces full diamond armor down to 13.75 armor points or 55% damage reduction (each point of incoming damage reduces protection by 1%, 2% for other armor. Enchantments are applied after armor, so they reduce the 45% of damage that gets through), you'll receive a maximum of 4 damage with full Protection IV and 2.25 with maxed-out Projectile Protection (or one of the combinations mentioned above).
Also, for general use (singleplayer Survival) I'd just go with all Protection IV; it is impossible for skeletons to spawn with Power V bows and they have a lower base damage than players (max of 5 vs 10, with Power multiplying damage so they should deal up to 12.5 with Power V), or 3 pieces of Protection IV + Blast Protection IV (as with Projectile Protection this will reach the cap for explosion damage; if you play on Hard creepers can still one-shot you unless you have the maximum protection).
Since 1.14 allows you to have all types of protection on armor, I am wondering how much damage a power five bow would do to maxed out diamond armor.
This was only possible in 1.14-1.14.2, which was then reverted due to issues with the enchanting system, (even though allowing different types of Protection on a single piece of armor had nothing to do with getting bad level 30 enchantments; just how Mojang often does things).
In either case, all you need to max out protection from projectile damage is at least 20 EPF points, which will reach the maximum possible damage reduction of 80%, or 20% of original damage, which is easily met with Projectile Protection by itself as each piece with Projectile Protection IV gives 8 EPF, or 32 for a full set and 24 for 3 pieces. You could also have 2 pieces with Protection IV (4 EPF per piece) and a single piece with Projectile Protection IV, or 3 pieces with Protection IV and a single piece with Projectile Protection IV, both of which will exactly reach the cap of 20.
See also:
In other words, 1.14 only made it possible to max out protection from all major damage sources at once (fire, explosion, projectile, falling, with anything else only being affected by Protection for a maximum of 16 EPF or 64%, plus armor itself if it reduces the damage source. Note that Feather Falling, which is technically a protection-type enchantment, can be combined with protection in any version, and only needs 2 pieces with Protection IV to max out).
When applied to diamond armor and the damage of a Power V bow, which is a maximum of 25 (the Wiki is misleading about how much damage bows deal, which is 6-10 for unenchanted to 20-25 for Power V, with a uniform distribution; the table here suggests that there is no randomness while here they claim a fully changed bow consistently deals at least 9 damage), and factoring in armor penetration, which reduces full diamond armor down to 13.75 armor points or 55% damage reduction (each point of incoming damage reduces protection by 1%, 2% for other armor. Enchantments are applied after armor, so they reduce the 45% of damage that gets through), you'll receive a maximum of 4 damage with full Protection IV and 2.25 with maxed-out Projectile Protection (or one of the combinations mentioned above).
Also, for general use (singleplayer Survival) I'd just go with all Protection IV; it is impossible for skeletons to spawn with Power V bows and they have a lower base damage than players (max of 5 vs 10, with Power multiplying damage so they should deal up to 12.5 with Power V), or 3 pieces of Protection IV + Blast Protection IV (as with Projectile Protection this will reach the cap for explosion damage; if you play on Hard creepers can still one-shot you unless you have the maximum protection).
TheMasterCaver's First World - possibly the most caved-out world in Minecraft history - includes world download.
TheMasterCaver's World - my own version of Minecraft largely based on my views of how the game should have evolved since 1.6.4.
Why do I still play in 1.6.4?
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