What is True random distribution?

True Random Distribution (TRD) is a type of probability where each trigger is calculated independently of previous attempts. This approach doesn't use pseudo-random logic and is entirely based on pure chance. TRD in Dota 2 can be divided into two subtypes: flat distribution and discrete distribution.

Flat distribution:

Some mechanics roll a random value between 0 and 1 and scale it along the minimum / maximum gradient. For example:

• Chaos Knight — Chaos Bolt: min/max stun duration and min/max damage. Damage and stun duration are correlated inversely.
• Phantom Lancer — Doppelganger: random positions within the target area. Calculation might be in polar coordinates with 0-360° angle and 0-325 distance units as min/max gradients.
• Crystal Maiden — Freezing Field: min/max explosion distance: 195-785. Angle within the four 90° sectors may be random.
• Last hit gold bounty, if a minimum and maximum range is given.
• Roshan's respawn timer.
• Attack damage of units, if they have a minimum and maximum attack damage range (the game interface shows the average attack value; to see the hero's attack range, hover over their icon).

Discrete distribution:

A couple of random events have discrete states that have similar probability:

• Powerup Runes with a discrete clamping over the 6 types and 2 locations.
• Neutral camps can spawn different creeps for each of the small, medium, hard and ancient camps.
• Chaos Knight — Phantasm, Naga Siren — Mirror Image, Manta Style: the position of the caster and the illusions within the formation is random.