*Disclaimer: The following is very rough due to the complexity of LOL. Assume an error margin of 20 percent or more.*
base HP roughly 350 + 100/level.
Effective HP is harder because it actually scales exponentially... Lets go with +150/level from 1-6, +200 per level from 7-11, and +250 per level from 12-18. It starts at around 600 and reaches ~5k by end game. +50% for bruisers, +100% for tanks.
This is most accurate for builds using one MR item and up to one other defensive item. Think a mage with RoA and abyssal scepter, a DPS with QSS or Banshee, or a squishier top.
Its rough, but here is where the numbers come from:
Base HP: 375-475 + 80-120 per level
Base Armor: 30+3/lvl
Base MR: 30 + one ~40 mr item
At late game, most builds have 70-120 armor and MR. This is ~40-60 percent damage reduction, so effective health is about double base health at late game. Early game, its only about 50 percent more. Most builds also have about 400 bonus health, from a rylais, a RoA, a banshees, or something like that.
Adding the base health in, we get around 2500 base health and 50 percent damage reduction, leading to around 5k effective health.
Overall, these are still very rough numbers. A single giant belt or other defensive item can increase a champions health by a huge amount in the mid-game. Likewise, armor/mpen items and runes mess everything up.
Edit: improving estimates
One important factor to keep in mind for getting kills without position advantage is what I am going to call the timing attack, a la starcraft. The timing attack is attacking right when your champion hits a relative strength. Some examples:
- The moment you finish a 4k item like IE, Deathcap, or TF.
- The levels 6-7/11-12/16-17 as a champion with a standard ult
- The levels just before your opponent hits their next ult (4-5, 9-10, 14-15) as someone with a nonstandard/no ult: Karma, Teemo, Udyr, etc.
- When you are about to level up and have a catalyst
- When your short-CD ult is up but your opponents long-CD is down.
If you have one or more of these factors on your side, you have a good chance of scoring the kill. Try to predict these and act to enhance them, for example, by going back to shop at the moment when you can barely afford IE, to ensure it gives you the biggest advantage.