My current strategy for Desktop Dungeons is to collect potions and save them up for the last battle. I only attack monsters if I can defeat them without using a potion, and then heal by revealing more parts of the map. But I've started wondering, would it be more advantageous to use potions earlier to help me defeat creatures that are above my level and therefore get experience faster, rather than just using them for the boss fight?
Health potions heal 40% of your max health. Comparatively, tiles recover 1 health per level per tile. Your base health is 10 per level, so without enhancements it takes 4 tiles of exploration to account for one potion. Consuming a potion also doesn't trigger enemy regeneration.
Mana potions heal 40% of your max mana. Tiles only recover 1 mana per tile, and your base mana does not increase without picking up mana items.
Vlad is very correct in that using potions just to speed up leveling is not very useful, especially if that level isn't going to make you survive the final conflict. But, excellent planning and luck may make an early potion very potent.
The main reason to use a potion in the early game is to maximize damage output while minimizing resource use. This isn't just for the immediate gains of what tiles you don't explore, but capitalizing on the position you're left in that will make future exploration less necessary. Maximizing damage output means using potions in the capacity such that their health or mana contribution is towards the destruction of your target. Using a health potion to survive killing foes for a mid-battle level up or a mana potion to afford a secondary casting of APHEELSIK is fairly wasteful.
For example, imagine a scenario where you've revealed a third of the dungeon so far. There are no monsters left you can defeat without potions, but there are many monsters that are 2 levels above you, some of which you could handle without a potion if you leveled up once. If you don't drink a potion, you could end up having to reveal a large portion of the dungeon looking for something to level up on. But if you can use a potion to defeat one of the 2 levels above you monsters and level up, you give yourself many more advancement opportunities which should far exceed the loss of that one potion.
Also, shoot to drink potions early game when you have a high maximum health. If you haven't found any health items, haven't bought a pendant of life, and otherwise do not have a lot of health, just stay away from big enemies and rely on exploration. As your health increases, the level of opponent you can take down using a single potion increases significantly.
Which leads to my next point: unless it's a requirement of a ridiculous chain assault you setup for victory that would make Rube Goldberg proud, you should probably never drink more than one potion of each kind to take out a single non-boss monster. The cost of using a potion impacts your ability to face all higher level foes, and the level catapult you may get for a single monster will still leave a large number of higher level foes. So if you must use a potion to take on a high level foe early on, figure out whether you can get it done in just one potion and some exploration. If that isn't enough, you should seek other opponents.
Mana potions are much less useful in the early game on their own. Even with wizard types, it usually takes 2-3 potions just to get a single spell slot back, and in the early game this won't really make a dent.
Their fault is their strength, however, because their lack of scaling with level makes them very useful if drinking a single mana potion saves you more than just a health potion. If you can drink a mana potion to pull off the BYSSEPS + GETINDARE combo that defeats a high level foe, it's actually more worth it. Just, as mentioned before, make sure you quaff the potion to contribute to damage.
The wonderful list of exceptions, where we assume you have enough money
This is not a comprehensive list, but just a couple class- or luck-specific strategies.
If you find a keg store early on, this can make it a lot more viable to take on a good number of high level enemies, leaving a lot of ripe opportunities for future mid-battle level ups.
In the free version of the game, the Glowing Guardian offers the equivalent of 2 full heals. These are excellent against bosses, so discovering early on that you have this option may allow early potions much easier.
For obvious reasons, Halflings and Gnomes have a similar advantage that finding a keg store provides.
Thieves have a trait that lets both forms of potion heal both attributes. If you have a spell like BURNDAYRAZ or GETINDARE or HALPMEH, you can probably get some very early nice kills by taking advantage of this trait, as it effectively doubles your potion stock.
Assassins have a trait that instantly kill any enemies of a lower level, which means that a potion-induced level catapult is significantly more useful to them than other classes. They are pretty much the leaders of mid-battle leveling.
Priests have a trait that makes health potions heal 100% health. This makes it a lot easier to spend only a single potion when taking on significantly stronger foes, but remember to still stick with "1 potion per non-boss".
A Sorceror is usually better off using HALPMEH or CYDSTEPP than quaffing health potions.
Bloodmages have a trait that makes mana potions heal 100% mana at the cost of some health. This makes them actually much less suited to using mana potions during the early game, because the mana gain is simply not worth it. So you'll probably be drinking later with them.
Warlords have a very interesting synergy with potions that makes their potion strategy exceptionally complex. To give a peek, one who gets some mana items early on may prioritize the utility of early game Mana potions, but others may prioritize late-game to utterly crush foes. I will also note that you should probably save the bonus damage for the target, not for a mid-battle level.
It's better to use potions when it's really needed to survive(like the boss fight). If it's just for speeding up leveling a little then you better wait because the amount of monsters is limited anyway so it's just a matter of time before you become stronger anyway. When it's a boss fight, you can't wait to became stronger(because it's probably the last monster, if not, go kill the rest If you can..) so there the potion would save you.
So your tactic is good and changing it is not recommended.