Copied straight from where I made it.

Much of this information came from

http://www.dota-allstars.com/wiki/Pseudo_Random_Distribution

I made some readjustments and rephrased most of it so that it actually makes sense.

This system applies to the following skills

• Naga Siren's Critical Strike

• Chaos Knight's Critical Strike

• Bounty Hunter's Jinada

o Based on Drunken Brawler

• Juggernaut's Blade Dance

• Phantom Assassin's Coup de grâce

• Skeleton King's Critical Strike

• Pandaren Brewmaster's Drunken Brawler

o Based on Drunken Brawler

• Crystalys

• Buriza-do Kyanon

• Troll Warlord's Bash

• Slardar's Bash

• Faceless Void's Time Lock

• Dwarven Sniper's Headshot

• Monkey King Bar

• Tidehunter's Anchor Smash

• Infernal's Flaming Fists

• Earth (Primal Split)'s Pulverize

• Maim

• Maelstrom

• Mjollnir

• Stout Shield

• Vanguard

Normally when we think of percentages of chanced attacks such as maim or critical strike all we know is the percentage, and that is all. For example Mortred’s ultimate has 15% changes to deal 4x damage. But what does that really mean? If it is truly 15% then there is a horrible glitch to the game.

Let’s think of this scenario: Mortred’s critical strike

If we just use the static 15% method, then that would basically mean every time you attack, the computer rolls out a 1~100 number and if that number is below 15 then you get a nice red number flashing behind her. This doesn’t sound too bad right?

This could potentially mean that you could never ever cirt in the entire game, or in fact if you are really lucky and crit every time you attack.

Now, I know that will probably not happen but you do see the flaw in the logic there right?

Therefore the smart Blizzard techs developed the pseudo random distribution system.

The advantage of using this pseudo distribution is that you will never "not" have maim and never "always" maim.

The equation for this is distribution is really quite a simple linear equation

P= Probability of occurring an attack modifier

N= Number of attacks, minimum of 1.

C= Is a constant that represents the initial probability of the percentage and how much it increases each time.

P is what we are trying to find so that isn’t need to be explained.

N is also quite simple, it is basically how many attacks you have ordered or received

C is the only one that is tricky.

Basic algebra shows this N value to be equal to 1 / C. The value of C in turn depends on the probability stated in the World Editor for that skill. This effectively means that if we had “infinite” number of attacks the number of attack modifiers divided by the total number of attacks should give us what our “ideal” C equals right?

P(infinite) / N (number of attacks) = C ideal

However we do not have “infinite” and so therefore not possible to get a perfectly exact number for C. Actually according to the Blizzard Techs to even calculate a rounded “C” ever time an attack is issued will eat up so much CPU that we will just be constantly lagging.

Therefore Blizzard has done the work for us. They took the easy way out, instead of calculating the actual value of C every time they simply imbedded a single constant multiple to all of the attack modifying skills.

5%

That’s right, 5% everything is rounded to the nearest 5%.

That is why all these Pseudo Random Distribution skills are rounded to the nearest 5th of a percent. What does that mean for us? Well if we just plug all the numbers in…

I skipped from 50~65 because well... there isn’t anything in between.

For those that like graphs here is a graphical interpretation of 10% crits

Why am I telling you all this? Well basically, the next time you use some hero with this distribution ability, maybe before you go into a battle hit a few creeps first based on the statistics shown above. This might cost you some time, but really if you were someone like Mortred 1 crit can make all the difference.

**Pseudo Random Distribution Explained- By Flodian**Much of this information came from

**Dota Wiki**http://www.dota-allstars.com/wiki/Pseudo_Random_Distribution

I made some readjustments and rephrased most of it so that it actually makes sense.

This system applies to the following skills

**Critical Strike**• Naga Siren's Critical Strike

• Chaos Knight's Critical Strike

• Bounty Hunter's Jinada

o Based on Drunken Brawler

• Juggernaut's Blade Dance

• Phantom Assassin's Coup de grâce

• Skeleton King's Critical Strike

• Pandaren Brewmaster's Drunken Brawler

o Based on Drunken Brawler

• Crystalys

• Buriza-do Kyanon

**Bash**• Troll Warlord's Bash

• Slardar's Bash

• Faceless Void's Time Lock

• Dwarven Sniper's Headshot

• Monkey King Bar

**Pulverize**• Tidehunter's Anchor Smash

• Infernal's Flaming Fists

• Earth (Primal Split)'s Pulverize

**Orb**• Maim

• Maelstrom

• Mjollnir

**Hardened Skin**• Stout Shield

• Vanguard

Normally when we think of percentages of chanced attacks such as maim or critical strike all we know is the percentage, and that is all. For example Mortred’s ultimate has 15% changes to deal 4x damage. But what does that really mean? If it is truly 15% then there is a horrible glitch to the game.

Let’s think of this scenario: Mortred’s critical strike

If we just use the static 15% method, then that would basically mean every time you attack, the computer rolls out a 1~100 number and if that number is below 15 then you get a nice red number flashing behind her. This doesn’t sound too bad right?

**WRONG**!This could potentially mean that you could never ever cirt in the entire game, or in fact if you are really lucky and crit every time you attack.

Now, I know that will probably not happen but you do see the flaw in the logic there right?

Therefore the smart Blizzard techs developed the pseudo random distribution system.

The advantage of using this pseudo distribution is that you will never "not" have maim and never "always" maim.

The equation for this is distribution is really quite a simple linear equation

**P(N) = C * N**P= Probability of occurring an attack modifier

N= Number of attacks, minimum of 1.

C= Is a constant that represents the initial probability of the percentage and how much it increases each time.

P is what we are trying to find so that isn’t need to be explained.

N is also quite simple, it is basically how many attacks you have ordered or received

C is the only one that is tricky.

Basic algebra shows this N value to be equal to 1 / C. The value of C in turn depends on the probability stated in the World Editor for that skill. This effectively means that if we had “infinite” number of attacks the number of attack modifiers divided by the total number of attacks should give us what our “ideal” C equals right?

P(infinite) / N (number of attacks) = C ideal

However we do not have “infinite” and so therefore not possible to get a perfectly exact number for C. Actually according to the Blizzard Techs to even calculate a rounded “C” ever time an attack is issued will eat up so much CPU that we will just be constantly lagging.

Therefore Blizzard has done the work for us. They took the easy way out, instead of calculating the actual value of C every time they simply imbedded a single constant multiple to all of the attack modifying skills.

5%

That’s right, 5% everything is rounded to the nearest 5%.

That is why all these Pseudo Random Distribution skills are rounded to the nearest 5th of a percent. What does that mean for us? Well if we just plug all the numbers in…

I skipped from 50~65 because well... there isn’t anything in between.

For those that like graphs here is a graphical interpretation of 10% crits

Why am I telling you all this? Well basically, the next time you use some hero with this distribution ability, maybe before you go into a battle hit a few creeps first based on the statistics shown above. This might cost you some time, but really if you were someone like Mortred 1 crit can make all the difference.