You don't have to look too far at all to find mention of what alchemy is or to find people asking for the fastest way to level up alchemy in Skyrim, but what does leveling up the skill actually do for you? I'm not asking about the perks associated with it - What is it that actually sets a level 29 alchemist apart from a level 20 alchemist? Why bother leveling the skill up (other than for fun), if you're not going to bother with alchemist perks?
2 Answers
There are two things that change on what you create the higher the level: How strong the potion is, and how much it's worth. Three ingredients make stronger and more worth potion as well. If I'm not mistaken, duration and level change with level too, making a buff potion last longer, and a debuff potion\poison able to be used on higher level mobs.
When you alchemy level increases then the potions you create will become stronger. The Elder Scrolls Wiki has this table describing the levelling.
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OP is quite specifically not asking about perks. As such the table is valueless for his purposes.– tjdCommented Apr 1, 2015 at 14:33
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1Well, the first sentence is still fairly informative though. Commented Apr 7, 2015 at 0:18
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I can't find a page that actually lists the formula that's used, but that's probably because it's effect-dependent. But... this page will calculate everything, and if it's correct, it shows how your skill level affects the potion strength and value independent of any perks: garralab.com/skyrim/alchemy.php Commented Jun 24, 2020 at 15:26
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From en.uesp.net/wiki/Skyrim:Alchemy - "Each level in the alchemy skill increases the effectiveness of crafted potions and poisons by 0.5% for +50% effectiveness at level 100 compared to level 0." Commented Jun 6 at 16:19