How are all diminishing returns calculated in League of Legends?

It was brought up in another question about how two slows would stack.

I am wondering how do diminishing returns work and are calculated.

For instance, if I would stack dodge on a Jax if I was able to get 100% would I actually always dodge?

Slows, dodge, and also ignite, if someone gets double ignited does it stack?

Dodge now been removed from the game.

Dodge items do not stack additively. For example, Jax, with level 5 counterstrike, has 18% dodge chance. If he then picks up ninja tabi (+12% dodge) his total dodge chance is 28% (and not 30%).

It's easiest to simply calculate the highest %dodge first (as they stack multiplicatively, order is actually irrelevant): In our case, the 18% dodge chance from counterstrike is simply added (18% of 100% hit chance is 18%) so Jax's dodge chance is 18%, and his "be hit" chance is 82%. Next, the dodge chance from ninja tabi is added. 12% of 82% "be hit" chance is 9.8%, which then gets added to the previous 18%, for a grand total of ~28% dodge chance.

If there were another dodge item (say, an identical version of Ninja Tabi that stacked with itself), the +12% dodge would be 12% of 72%, or 8.6% increase.

The reason dodge is handled this way is such that the mitigation of dodge as a stat scales linearly; were dodge strictly additive, the more dodge% you had, the more damage further dodge% would reduce.

Ignite

Casting ignite on an already ignited target will reset the duration of the DoT, losing any remaining damage the original ignite would have done.

Speed

I'm just going to quote from the "mechanics FAQ" from the official LoL forum.

Q: How do movement modifiers work? (Credit to Larias)

A: First, you have your base movement of say 300. You add boots first, always boots first, so if you have boots added.

Let's say you get boots 2. That's 370 movement. Then, you get 35% movement speed buff from items or runes or masteries or buffs: that 370 is multiplied by 1.35, or 499.5 movement speed. If this is the only thing affecting your movement speed, the diminishing returns formula kicks in.

Now, let's say you get slowed by 38% (ashe arrows). What happens is the ORIGINAL 499.5 is multiplied by .62, and you get 309.69 movement speed. Because 309 is not above or below diminishing returns, you stay at that speed.

Q: What are these diminishing movement returns? (Credit to Guinsoo)

A: For each point of movement you would have above 490, that amount is reduced by 50%. So if your final movement speed was 748, it would be reduced to 490 + (748-490)*0.5 = 604. For each point of movement you would have above 415, it is reduced by 20%. So if your speed after all mods was 445, you would end with 415 + 30 * 0.8 = 439.

Q: Do slows stack?

A: Yes and no. Slows from items do not stack among themselves (Phage, Frozen Mallet, Rylai's Crystal Scepter). However, all other slows stack.

Just like the diminishing returns for bonus movement speed, being slowed has diminishing returns starting at and below 210.

And one addendum: The strongest slow/speed boost is always applied first.

Lifesteal

Lifesteal has no diminishing returns. If you hit an opponent for 20 damage, and manage 200% lifesteal, you will regain 40 health.

Lifesteal is based on damage done, so it is reduced by Armor (which does not have diminishing returns, see below) and doubled (or more!) by crits.

Attackspeed

+Attackspeed from items is additive and references the base attack speed of the champion. Buying two phantom dancers, for example, gives you 110% additional attacks per second, but because they are additive, the effect doesn't increase due to any other items you may have.

Attack speed has a hard cap of 2.5 attacks per second.

Armor and Magic Resistance

The effectiveness of Armor and Magic Resistance do not suffer from diminishing returns.

Please see this answer for a fully detailed explanation of why.