Artificer battle smith wants to make magical armor, we're trying to figure out the borders

Question

We're using the 2019 UA Artificer (from the DND Beyond site).

Situation

I am the DM. The PC is level 3 (getting to level 4 pretty soon) and he wants to start going into crafting magical armors because he feels its part of his class identity.

Now, I understand its generally up to me to decide what is suitable and what is not, but we try to figure a balanced way to handle this, in which he can have creative ideas and magic items still feel wondrous.

The examples I gave him, from what I understood from the PHB and DMG books, is that he either finds a formula, or creates one.
I mostly understand the other parts, we are discussing the creation of a formula. We're trying to understand the basics and go up from there for our understanding's sake with creating a common magic item.

We're trying to be as true to the "original" world of D&D as we're both pretty new and he really likes trying to "outfigure" the system; not by cheating it, but by thinking of clever ways in which to use it.
He offered two examples:

1. One is trying to infuse a piece of armor with Heroism spell, in a way that once a day a humanoid who wears it and expresses bravery (judged by the piece itself) it gives it 1d4 temporary hit points, or something like that.
   Which sounded cool and okay with me.

2. The second example was infusing a pair of boots (Leather worker's tool?) with Expeditious Retreat. Which sounded really bad with me. He couldn't describe how it will do it, just that its infused with the magic and is "cast" the same way normal Expeditious Retreat is cast, which just says "This spell allows you to move at an incredible pace." He said he wants the boots to have the spell active at all times, and I figured it would make it a rare or very rare item? (which he can't create).

We're trying to go for a as "realistic" to the world approach as we can. How would you approach this?

Answer 1

By default, artificers are capable of making magic items in three main ways. Certain subclasses gain additional methods for making specific magic items (e.g. the Artillerist gains the ability to make a specific variety of magic wands with their Wand Prototype class feature) detailed in their class features, but these are applicable to all Artificers:

First, they can simply use the explanation of "I created a temporary magic item" as an explanation for how they cast a spell with a Tool as their Arcane Focus. For instance, casting Cure Wounds with an Alchemist's Tool could be explained as creating a temporary healing potion and immediately feeding it to someone before the magic on it wears off. The explanation for this is found in the "The Magic of Artifice" sidebar in the 2019 Artificer Unearthed Arcana articles.

Second, they are capable of creating temporary magic items using their Infuse Item class feature. This works in accordance with the rules of that feature, with them only knowing a set number of Infusions for their level, only being able to create one item for any given Infusion at a time, and only being able to create a set number of magic items with that class feature at a time. The rules for this are explained in the relevant class feature in the 2019 Artificer UAs.

Third, they are capable of creating permanent magic items using the rules for the Crafting A Magic Item downtime activity in the Dungeon Master's Guide and Xanathar's Guide to Everything. This allows them to create magic items that, by default, are limited to magic items listed in the relevant sections of the Dungeon Master's Guide and other published books.

This is the mode where possessing formulas for the magic items is required; there are no rules for the acquisition of these, so it largely falls into the realm of DM fiat - the PCs might be able to create them themselves (possibly with a non-magical item crafting check), they might need to go on adventure to find one, they might find them as treasure while on adventures for other reasons, or, if you simply don't want a PC to be able to craft a certain item, you can simply say that PCs aren't able to find the formula they want. Effectively, they allow you, as a GM, to filter what items you want to allow PCs to craft.

If you wish to allow them to create homebrewed magic items with the last option, you would simply assign the item a Rarity based on your evaluation of its power level and then he would simply follow the rules for creating an item of that Rarity level. For the specific items you're mentioning, there are two published magic items that are broadly analogous to the items your player wants to make: for the first, there is the Boros Guild Signet from Guildmaster's Guide to Ravnica, and for the second, there are the Boots of Striding and Springing from the Dungeon Master's Guide.

Answer 2

The nuance between these two items is the difference between an item casting a spell and the item having a spell-like effect.

The first effect you bring up is casting the Heroism spell once a day through the armor. This follows all the mechanics of Heroism, including duration and requiring concentration as per the spell description.

The second effect you bring up is having boots with a spell-like effect of Expeditious Retreat. Spell-like effects are more powerful than casting the spell because they do not require concentration and, if permanent, don't have a duration. Some spell-like effect items use charges to limit their power.

The mechanics for magic item crafting do not support the creation of either spell casting or spell-like effects without a formula. The artificer knows how to cast the spell using one method. They do not know another method to emulate that effect without further cost. The lack of this knowledge is why I wouldn't allow any item creation without some roleplaying to find that formula.