How do the PCs' magic items factor into challenge ratings?

Question

Everyone knows that a CR 10 monster is meant to be a perfectly balanced challenge for a party of four 10th level PCs. But does that mean it's balanced for a party of four PCs with no magically enhanced items? Or does that mean a party of full-blown +3 magic longswords and +3 magic armors? Or something in-between?

I ask because I'd like a more informed way of determining how often to award magic items, what quality of magic items to award, and which CRs to present accordingly.

Because of the way that hit rate and AC translate to proficiency, a +3 magic item easily equates to a difference of a dozen levels or more, which can greatly impact the outcome of a fight. It is worth stating that a +3 item is certainly a plausible treasure to find in a hoard by level 10, but it is not a guarantee. This seems to create a lot of ambiguity as to exactly when and which magic items must be awarded.

So, to rephrase the question: To what extent do these variables interact, and is there a right way to juxtapose them?

Answer 1

What is Challenge Rating?

To begin, "perfectly balanced" is not how challenge ratings are intended to work. Challenge rating is described in the SRD as:

A monster’s challenge rating tells you how great a threat the monster is. An appropriately equipped and well-rested party of four adventurers should be able to defeat a monster that has a challenge rating equal to its level without suffering any deaths. For example, a party of four 3rd-level characters should find a monster with a challenge rating of 3 to be a worthy challenge, but not a deadly one. (Emphasis mine)

Challenge rating is defined by two factors: offensive CR and defensive CR. Offensive CR is determined by the maximum amount of damage a monster can put out in one round if it goes full nova and uses everything at its disposal, while defensive CR is a measure of highest possible AC and maximum hit point total, if all buffs available have been applied. These values are adjusted by any other effects the monster might have (resistances and immunities for defense, status effects, poison, or other effects for offense). Once the offensive CR and defensive CR have been calculated, they are averaged to determine the overall CR. Then, once the monster has been play-tested, the CR is adjusted to match the appropriate party level.

For example, if you calculate the CR for an ogre using the rules in the DMG, you might come to a result of CR1, but in play-testing the 5e designers found that a single ogre was too much for a group of 4 level 1 PCs, so the CR was adjusted to 2, because even though the calculations show it would be a CR1, it has high enough damage output that it could one-shot most level 1 PCs.

Why does this matter?

Now, there are, of course, many factors that come into play when looking at a party and determining what CR it can handle, but the most important are called out in the description for Challenge Rating: an appropriately equipped and well-rested party.

When you consider that magic items are entirely optional (see the DMG chapter on Treasure for details on this), it brings into question what appropriately equipped might actually mean.

For example, a CR 3 werewolf (a "subtype" of lycanthrope) has damage immunity to "bludgeoning, piercing, and slashing from nonmagical attacks not made with silvered weapons."

CR 3 is the measure of a medium-difficulty challenge for a party of 4 level 3 adventurers who are well-rested and are well-equipped for the encounter, and in this case, an appropriately equipped party will have access to magical attacks (spells or magic weapons) and/or silvered weapons.

So, you can see that magic weapons themselves do not need to be involved (and they shouldn't be required, since they are an optional mechanic), and the CR is unaffected by that fact. A party of 4 level 3 PCs who have the right gear (silvered weapons/magic) and who are well-rested should be able to handle this encounter, and magic weapons themselves have little impact on the outcome of the encounter.

Magic weapons might increase damage output and ability to hit (increased % chance to-hit and +3 DPR at most), but only slightly. However, because CR is based on the monster's AC, resistances, immunities, and damage output, it makes little difference what magic weapons the PCs have available to them (if any at all), so long as they have the means the mitigate any defenses a monster might have.

Also, note that the DMG random treasure tables contain guidelines for the types of treasure that should be awarded for an encounter of a given CR. As the party increases in level and encounter CRs increase, the tables should increase the party's power accordingly. These tables can also be used to gauge if a given item is too powerful and would change the game for the party as its current level. A +3 magic weapon at level 5 is going to have a much more noticeable impact than a +3 magic weapon at level 15, and this is generally reflected in the treasure tables.

Answer 2

So, i'm going to ramble a bit first, but trust me I get to the point.

In 5th edition, Magic items and Weapons are all generally named. I can't recall the page exactly, but it even goes so far as to point this out. We also see a lot of named magic items in the Adventurer's League (in fact, all available magic weapons and armors available are just that - named items).

There's also a catch here: because of how progression works in relation to raw numbers (To Hit and AC) in 5e, magic items are not required during your game and obtaining one should be a climactic moment for a character. As I mentioned above, magic items in 5th edition are meant to be special, once-in-a-lifetime finds. Giving a character a +3 anything is incredibly unbalancing (Given that's literally worth 6 Strength or Dexterity depending on the item!) to the game's natural state. If you give one out as a DM, be prepared to deal with the consequences, namely that everything is about to get its butt kicked.

Since it sounds like you're running a home game, start adding CR to encounters, maybe one or two at first, then try a much harder one at +5 of the recommended "regular" encounter. Again, as i mentioned before magic items aren't required, they're storytelling tools in 5th edition.

So, to answer your original question, hand the items out when it feels right and you're ready as a DM to handle them - for example, when you're going to introduce a number of monsters to the campaign that require magic damage - but be ready to handle the kick in the pants said monsters will take. Its a balancing act, and I wish I could give you "Oh, a +3 is worth 4CR" or something, but unfortunately its not. Watch how combats go after you adjust the CRs up, and start tuning until you find the sweet spot for your characters.

You can also up the difficulty by having enemies that use tactics like disarming (A Dex or Strength save is a great down and dirty way to handle these) characters of their shiny toys, and it can create some awesome role-playing opportunities.

Good luck, and have fun!