What's the benefits of having a higher skill?

The idea is:

• Every time you level up in Conjuration, it decreases the cost of conjuration spells.
• Every time you level up in One-handed, you increase the damage you do with one handed weapons

And so on. Does anyone knows what are those bonus exactly?

Is there any fix increasing pattern/percentage per level you get on a certain tree?

Solution 1:

Weapon skills (Archery, One-handed, Two-handed) : skill increases damage done. (0.5% per level. 50% increase at level 100)

Armor skills (Light Armor, Heavy Armor) : skill improves armor rating mildly (perks are where it's really at though). (0.5% per level. 50% increase at level 100)

Magic skills (Alteration, Conjuration, Destruction, Restoration, Illusion) : skill reduces magicka cost. Skill also unlocks new spells on spell vendors at 25, 50, 75 and 100. (about 41% reduction at level 100)

Lockpicking : skill broadens the target zone.

Pickpocketing : skill increases success chance to pickpocket

Speech : skill improves prices when buying and selling, and increases chance of success for persuade and intimidate.

Sneak : skill reduces detection radius for sight and sound.

Alchemy : skill improves magnitude of potion/poison effects.

Enchanting : skill improves magnitude of enchanting effects.

Smithing : skill improves armor rating of upgrading armor and weapon damage when upgrading. Does not improve item creation at a forge, only upgrading is affected by skill.

Block : skill increases percent of damage blocked.