Bash mechanics

[LifeDrainer[RO]]

Whenever you hear this, what it means is that a certain effect has an increased percentage, but not directly increased. If you have 20% of something, and an item or skill that gives another 20% of that something, if it stacks diminishingly, it will not equal 40%!

The way to work out diminishing returns is to use this formula:

T = C/100 + (100-C)/100 * E/100

T is the Total percent, C is the Current percent, and E is the Extra percent.

For example, if you have a melee hero with 25% bash and buy the item Cranium Basher, the extra 15% bash stacks diminishingly. To work out the total percent, use the formula:

T = 0.25 + (100-25)/100 * 0.15
= 0.25 + 0.75 * 0.15
= 0.25 + 0.1125
= 0.3625

The total bash percent would be 36.25%. If you added another Cranium Basher, to work out the bash percentage, again apply the formula. Note that the Current Percent is changed to 36.25%

T = 0.3625 + (100-36.25)/100 * 0.15
= 0.3625 + 0.6375 * 0.15
= 0.3625 + 0.095625
= 0.458125

Here are two other passive skills which can stun for a short duration. The first is Sniper's Headshot, which has a 40% chance to stun for 0.1 seconds. The second is MKB, which has a 30% chance to stun for 0.1 seconds. It is important to note that these skills will not stack with each other; for example, if you bash a target with the bash from a cranium basher, and then the short bash from the MKB occurs, the stun from the basher will be cancelled.

For easy reference:

On heroes without bash -

1 Cranium Basher : 15% bash
2 Cranium Bashers : 27.75% bash
3 Cranium Bashers : 38.5875% bash
4 Cranium Bashers : 47.79937% bash
5 Cranium Bashers : 55.62946% bash
6 Cranium Bashers : 62.28504% bash

On heroes with 25% bash (Timestopper, Slithereen Guard) -
1 Cranium Basher : 36.25% bash
2 Cranium Bashers : 45.8125% bash
3 Cranium Bashers : 53.94062% bash
4 Cranium Bashers : 60.84953% bash
5 Cranium Bashers : 66.7221% bash
6 Cranium Bashers : 71.71378% bash

On heroes with 10% bash (Troll Warlord) -

1 Cranium Basher : 23.5% bash
2 Cranium Bashers : 34.975% bash
3 Cranium Bashers : 44.72875% bash
4 Cranium Bashers : 53.01944% bash
5 Cranium Bashers : 60.06652% bash
6 Cranium Bashers : 66.05654% bash

This Excel file is dedicated to those that knew the formula but are to lazy to count by themselves and also to dota-freaks that wanna know precise numbers on most dota situations.

The Spreadsheet contains these sheets:

* Bashes
* Stout or Vanguard?
* Criticals stacking (Average damage with criticals and innate crits and images)
* Buriza vs MKB DPS (damage per second) based on IAS & Damage
* DPS based on IAS & Damage
* Reaper-Scythe Exact Kill Zone (for the derivation see my guide in dota-allstars.com Mechanics>Guides&Lists)
* Sunder

Enable Macros as they serve functionality and i assure and guarantee you that the file is clean. (code and formulas aren't protected, you can see them)