Original Answer: Lots of Guesswork
I don't think any currently-published materials address the effect of magic items on encounter difficulty, but the rules assume a certain volume of magic items-per-level, and the difficulty calculations and monster challenge ratings probably take that into account. However, if your PCs are exceeding the daily recommended allowance of magic items (very vaguely defined, but see addendum below), XP thresholds based on their true experience levels are almost certainly useless.
That being said, it's possible to compare the powers of magic items to the bonuses players get by gaining experience levels. A weapon that confers +1 to attack and damage rolls is functionally the same, in-combat, as gaining 2 points in the relevant ability score. An item that lets you cast a certain spell once per day is "the same as" gaining a spell slot.
Combat-oriented magic items denoted by the DMG as uncommon or rare have effects that amount to a fraction of the increase in power received by gaining a single level, at least in the low-level tier for which they're recommended (per DMG 135). At level 4, the Druid gets an ability score improvement (combat-equivalent to that +1 weapon), another 2nd-level spell slot (roughly combat-equivalent to that spellcasting item), some more hit points, and another hit die. So if you give both those items to a level 4 Druid, that PC is almost level 4, for combat purposes. You might want to calculate two different XP thresholds, treating the PC as level 3 and then as level 4, or you might want to split the difference between them.
This approach can't account for the versatility that magic items provide. To a Wizard who already can cast scorching ray, a circlet of blasting is a fairly disappointing reward, but to a hammer-oriented Champion Fighter it opens up a world of hands-free blasting possibilities.
Combat-oriented items denoted by the DMG as very rare or rarer provide bonuses that far outstrip the benefits of ascending from experience level 3 to experience level 4, and may even be equivalent to a full experience level or more for PCs at level 15 or above. I have no experience with high-level 5e and can't really speak to that. It's not hard to guess, though, that if you provide your players with a lot of very rare-rated magic items, your hopes of accurately calculating combat difficulty will fly out the window.
Addendum: Lots of Rolling on Tables
On close inspection, the DMG is actually fairly specific about how many magic items a party should get. It just happens to establish this in an extremely roundabout way. On page 133: "Over the course of a typical campaign, a party finds treasure hoards amounting to seven rolls on the Challenge 0-4 table, eighteen rolls on the Challenge 5-10 table, twelve rolls on the Challenge 11-16 table, and eight rolls on the Challenge 17+ table."
Rather than reproducing the Challenge 0-4 table and the many tables it references, I'll present here only a few relevant values. A treasure horde generated for CR 0-4 has:
- 36% chance of no magic items.
- 24% chance of 1d6 items from Magic Item Table A.
- 15% chance of 1d4 items from Magic Item Table B.
- 10% chance of 1d4 items from Magic Item Table C.
- 12% chance of 1d4 items from Magic Item Table F.
- 3% chance of 1 item from Magic Item Table G.
Now, Table G is a level 4 adventurer's dream. You have a 10% chance to get a +2 weapon, which is categorically overpowered for this tier. If that's not broken enough, you might end up with a mace of disruption or a wand of wonder. A 3% chance of rolling on this table at this tier seems like a bit much to me, but I'm no wizard of a coast.
This is what the guidelines tell us, though, so let's pretend to roll 7 times on the Challenge 0-4 table. If we apply my liberal arts degree's understanding of the law of averages, I predict we'll end up getting no magic items twice, roll a total of 2d6 times on Magic Item Table A, and roll 1d4 times each on tables B, C, and F.
Table A is 98% consumables and a couple of fairly mundane utility items. Rolling 7 times, we'd probably get 3 or 4 potions of healing, 3 or 4 low-level spell scrolls (hopefully from the spell list of a caster in your party!), and maybe—if you're really lucky—a driftglobe.
Table B is 64% consumables, a few somewhat more interesting utility items, and a very few items like mithral armor with fairly remote combat applications. We'll probably get a couple of fun potions, but let's say we picked up that mithral armor. I won't tell if you don't.
Rolling twice on Magic Item Table C, we might pick up a necklace of fireballs, but far more likely we'll get a couple rare-ish potions.
On Magic Item Table F, we're looking at stuff like a +1 weapon, a circlet of blasting, or some gauntlets of ogre power. That is, a couple of those "combat-equivalent to gaining part of a level" items described above.
By the end of the level 1-4 tier, we've amassed (and likely consumed) quite a few potions and scrolls. Their effect on combat isn't nothing, but it's not really enough to impact any combat difficulty calculations.
Despite several opportunities to pick up some overpowered weapons or equipment, our permanent acquisitions are probably limited to two or three rare-grade items. And these we have to split among the whole party! Only a very greedy and very lucky PC will be carrying enough magic items to be treated as one experience level higher for combat purposes. It might not be a bad idea, though, to calculate your XP thresholds as if one PC is one level higher, if the efficacy of one additional experience level is spread out across the entire party.
I will spare you my "calculations" for your campaign's treasure horde yields in the level 5-10 tier and above, but I notice those tables continue to draw a lot from magic item tables A, B, and C. Following the guidelines on page 133, PCs can't really rely on these treasure hordes to contain permanent magic items until the level 17+ tier. Suddenly the limit on attunement to a maximum of three items doesn't seem like a huge deal!
Of course, relying exclusively on these tables is going to make for one boring campaign. So many potions of giant strength! Magic items are used best as storytelling props, hand-picked for their roles in the scenarios you create. But the printed guidelines clearly intend for a given PC to pick up only a small collection of permanent magic items over his or her career. I can conclude with some confidence that the intended magic item distribution is so sparse as should not affect encounter difficulty calculations.
But that conclusion answers a different question! For present purposes, the upshot to this excess of analysis is that we now have a benchmark for what the 5e rules consider the correct number of magic items ("not very many"), and can gauge by our distance from that figure how overpowered our party is for purposes of encounter difficulty calculation.
Glib Extra Answer
If your PCs have so many magic items that the monsters you pit against them are no longer a challenge, try giving some magic items to the monsters.
"Not from 'round here"
I've used "you were practicing in your master's keep, when there was a blue flash. When you woke up, the moon above was wrong... wrong color, wrong mare, wrong size, and wrong phase."
This works quite well for players who don't have history and religion skills... for the religion skill, finding that the local gods have the same myths and similar names, well, it solves that. History remains utterly borked, but one skill that can be "regained" by spending downtime in study... for the proficiency itself is as much in learning how to learn history as it is knowing the ins and outs of a specific world.
No History but what comes up in play.
I find it quite a bit easier in the long run, and a good bit richer, as well, to let players invent history and jot down whether their roll was "truth" or not... if it's "truth" (they made their History roll), it's true for the game world. If they fail, it may or may not be true, and I'll leave it for later.
Failure isn't always «No Truth»
Failure on a knowledge roll doesn't need to be «No Truth»...
It can also be:
- «Some Truth» Give them parts of the truth, but leave out the most important bit.
- «Too Many Truths» give them 2-3 different and incompatible «truths»...
- «True... From a Certain Point of View» (also called "Obi-wan style deception"). It's a lie based upon wilful manipulation of the facts. "Duke Fred Murdered your Father!" (leaving out that your father had challenged him to that drunken duel...)
- «Irrelevant Truth» - Sure, it's nice to know about the origin of the Castle... but I need to know who the prior duke's enemies were, not who the Building Baron's Friends were...
- «Inconvenient Truth» Sometimes, you can give them information that's true and helpful, but making use of it implicates them or their employer in something else...
It's fine to occasionally have it be «No Truth»
Best Answer
The same way(s) you keep any other combat from getting boring.
First, I'm going to point you to DDAL03-04 "Shackles of Blood" which has an excellent arena scene in it exemplifying some of the advice I'll give below. These are presented in ascending order of complexity. Because in your repeated scenario, you should be adding in these elements and combining them in new ways with each iteration.
Terrain
Just because it's an arena doesn't mean that the ground is flat and featureless. Terrain makes non-arena interesting, right? Put some in your arena. This also encompasses hazards and obstructions, not just topography.
Cover & Visibility
Hand-in-hand with terrain, areas of cover and impairments to visibility make tactical decisions more interesting. A literal fog of war changes everything; most importantly, turning combat from a game of perfect-information tactics to a game of imperfect-information risk and resource management. Whether it's weather, terrain, or magic, your ranged attakers should never have the ability to target all points from any one point.
Objectives
Outright slaughter of the opposing side is the least interesting possible setup, yet is too often the go-to. "King of the hill" or "capture the flag" scenarios, a task to be completed while defending an asset, and splintered priorities all spice things up. Is your arena-runner diabolical enough to offer individual rewards to characters, in ways that might put them at odds? Can they make a friend of the slave-captain by comporting themselves in one way, though their safety is dependent on a different behavior?
Time
A ticking clock makes every decision more impactful. Do bridges give way every round, threatening to strand characters far from their allies? Does a new foe enter every N rounds, turning the slower-but-low-risk strategy into a riskier one? Are terrain elements changing with time?