Debuffs

There are 2 types of Debuffs in the game: **Slow** and **Damage Amplification**.
These are obtained by building Towers from the Category:Debuff\_Towers.

All debuffs can stack on a **different** debuff, but will not stack/amplify on itself.
Debuffs are multiplicative but suffer from  Diminishing Returns - an effect which further degrades stacking multiple debuff effects.

## Diminishing Returns

*For every unique Slow/Damage Amp Debuff on a creep, their effects will be diminished by 5% \* (# of Debuffs - 1).*

**NOTE: The below math was done when the diminishing returns values were 5%. They are 12% as of patch 1.7 - adjust your math accordingly.**

###  Polar Tower

Unlike the other 3 amp towers ( Jinx Tower,  Corrosion Tower,  Incantation Tower) the  Polar Tower is not affected by  Diminishing Returns - so it will always remove 11%/22% of the creeps hp regardless of Diminishing Returns stacks - however it will still contribute to Diminishing Returns and will add a stack.

See the examples below to see how it gets applied exactly.

# DiminishingReturns

0.95

Num Of Debuffs
−
1

{\displaystyle \text{DiminishingReturns}=0.95^{\text{Num Of Debuffs}-\text{1}}}

Slow
i

=
(
1
−
(

Strength
i

∗
DiminishingReturns
)
)

{\displaystyle \text{Slow}\_i=(1-(\text{Strength}\_i\*\text{DiminishingReturns}))}

Amp
j

=
(
1
(

Strength
j

∗
DiminishingReturns
)
)

{\displaystyle \text{Amp}\_j=(1+(\text{Strength}\_j\*\text{DiminishingReturns}))}

# TotalSlowMult
1
−

∏

# i
1

Slow
n

Slow
i

{\displaystyle \text{TotalSlowMult}=1-\prod\_{i=1}^{\text{Slow}\_n}\text{Slow}\_i}

# j
1

Amp
n

Amp
j

−
1

{\displaystyle \text{TotalAmp}=\prod\_{j=1}^{\text{Amp}\_n}\text{Amp}\_j-1}

TotalSlow and TotalAmp get rounded to the nearest integer for percent calculation before beeing applied.

## Examples

### Example 1: 2 Lvl1 Slows

 Root Tower +  Nova Tower

Each of them solely slows for 16%, but when both slows hit the same creep, diminishing returns takes action (note: because of the multiplicative behaviour of slows it would already be less than 32% [-> ~29.44% to be exact], but diminishing returns even further degrades the slow effect):

# DiminishingReturns

0.95

2
−
1

=
0.95

{\displaystyle \text{DiminishingReturns}=0.95^{2-1}=0.95}

So the slow of the  Root Tower is (with a strength of 16% so 0.16):

Slow
Root

=
(
1
−
(
0.16
∗
0.95
)
# )
0.848

{\displaystyle \text{Slow}\_\text{Root}=(1-(0.16\*0.95))=0.848}

Same goes for the  Nova Tower (with a strength of 16% so 0.16):

Slow
Nova

=
(
1
−
(
0.16
∗
0.95
)
# )
0.848

{\displaystyle \text{Slow}\_\text{Nova}=(1-(0.16\*0.95))=0.848}

So the total slow is:

# TotalSlow
1
−
(

Slow
Root

∗

Slow
Nova

# )
1
−
(
0.848
∗
0.848
# )
1
−
# 0.719104
0.280896

{\displaystyle \text{TotalSlow}=1-(\text{Slow}\_\text{Root}\*\text{Slow}\_\text{Nova})=1-(0.848\*0.848)=1-0.719104=0.280896}

Calculating the total slow: *0.280896* -> 28.0896% which gets rounded to the nearest integer: 28% - as seen in the screenshot above.

### Example 2: 2 lvl1 Amps

 Corrosion Tower +  Incantation Tower

Corrosion increases damage by 20%, incantation does 10%/32% depending if the creep is alone or more creeps nearby. For this calculation we will assume that the creep is not alone, so incantation will amplify the damage by 10%.
Because of the multiplicative behaviour amps will buff each other, only degraded by  Diminishing Returns.

# DiminishingReturns

0.95

2
−
1

=
0.95

{\displaystyle \text{DiminishingReturns}=0.95^{2-1}=0.95}

Amp of lvl1  Corrosion Tower is 20%:

Amp
Corrosion

=
(
1
(
0.2
∗
0.95
)
# )
1.19

{\displaystyle \text{Amp}\_\text{Corrosion}=(1+(0.2\*0.95))=1.19}

Amp of lvl1  Incantation Tower hit with nearby creeps is 10%:

Amp
Incantation

=
(
1
(
0.1
∗
0.95
)
# )
1.095

{\displaystyle \text{Amp}\_\text{Incantation}=(1+(0.1\*0.95))=1.095}

So the total amp is:

# TotalAmp
(

Amp
Corrosion

∗

Amp
Incantation

)
−
# 1
(
1.19
∗
1.095
)
−
# 1
1.30305
−
# 1
0.30305

{\displaystyle \text{TotalAmp}=(\text{Amp}\_\text{Corrosion}\*\text{Amp}\_\text{Incantation})-1=(1.19\*1.095)-1=1.30305-1=0.30305}

Calculating the total amp: *0.30305* -> 30.305% which gets rounded to the nearest integer: 30%.

### Example 3: 2 lvl2 Debuffs vs. 4 lvl1 Debuffs

A little realistic example: you got a base setup of ++, all 3 on lvl3, so 2 points left to spend - you could now spend both points on  for lvl2  Root Tower and lvl2  Incantation Tower, or 1 on  and 1 on  for lvl1  Nova Tower, lvl1  Jinx Tower, lvl1  Root Tower and lvl1  Incantation Tower.

Lets do the math:

Setup1 (lvl2  Root Tower + lvl2  Incantation Tower):

# DiminishingReturns

0.95

2
−
1

=
0.95

{\displaystyle \text{DiminishingReturns}=0.95^{2-1}=0.95}

Slow
Root

=
(
1
−
(
0.32
∗
0.95
)
# )
0.696

{\displaystyle \text{Slow}\_\text{Root}=(1-(0.32\*0.95))=0.696}

Amp
Incantation

=
(
1
(
0.2
∗
0.95
)
# )
1.19

{\displaystyle \text{Amp}\_\text{Incantation}=(1+(0.2\*0.95))=1.19}

So a total slow of 30% and damage amplification of 19%.

Setup2 (lvl1  Nova Tower + lvl1  Jinx Tower + lvl1  Root Tower + lvl1  Incantation Tower):

# DiminishingReturns

0.95

4
−
1

=
0.857375

{\displaystyle \text{DiminishingReturns}=0.95^{4-1}=0.857375}

Slow
Nova

=
(
1
−
(
0.16
∗
0.857375
)
# )
0.86282

{\displaystyle \text{Slow}\_\text{Nova}=(1-(0.16\*0.857375))=0.86282}

Slow
Root

=
(
1
−
(
0.16
∗
0.857375
)
# )
0.86282

{\displaystyle \text{Slow}\_\text{Root}=(1-(0.16\*0.857375))=0.86282}

Amp
Jinx

=
(
1
(
0.08
∗
0.857375
)
# )
1.06859

{\displaystyle \text{Amp}\_\text{Jinx}=(1+(0.08\*0.857375))=1.06859}

Amp
Incantation

=
(
1
(
0.1
∗
0.857375
)
# )
1.0857375

{\displaystyle \text{Amp}\_\text{Incantation}=(1+(0.1\*0.857375))=1.0857375}

# TotalSlow
1
−
(
(
1
−
(
0.16
∗
0.857375
)
)
∗
(
1
−
(
0.16
∗
0.857375
)
)
# )
0.2555416476

{\displaystyle \text{TotalSlow}=1-((1-(0.16\*0.857375))\*(1-(0.16\*0.857375)))=0.2555416476}

# TotalAmp
(
(
1
(
0.08
∗
0.857375
)
)
∗
(
1
(
0.1
∗
0.857375
)
)
)
−
# 1
0.16020823512

{\displaystyle \text{TotalAmp}=((1+(0.08\*0.857375))\*(1+(0.1\*0.857375)))-1=0.16020823512}

So a total slow of 26% and damage amplification of 16%.

however the second setup gives a few more options for Quad Element Towers - namely on top of only  Nuclear Tower, it adds:  Doom Tower,  Rage Tower,  Life Altar Tower and  Shredder Tower. Also another lvl1 buff tower option:  Blacksmith Tower gets available. Also lvl1 debuff towers cost less than a third (1500 gold vs 5000 gold) than lvl2 debuff towers - money which can be spent into more damage towers. However you'll need a few more spots for building the debuff towers.

### Example 4: 6ele

a 6 ele setup with all except earth on lvl 2:
lvl2  Nova Tower + lvl2  Jinx Tower + lvl2  Windstorm Tower + lvl1  Polar Tower + lvl2  Corrosion Tower + lvl1  Root Tower + lvl1  Incantation Tower + lvl1  Muck Tower

# DiminishingReturns

0.95

8
−
1

=
0.69833729609

{\displaystyle \text{DiminishingReturns}=0.95^{8-1}=0.69833729609}

0.73509189062

Slow
Nova

=
(
1
−
(
0.32
∗
0.69833729609
)
# )
0.77653206525

{\displaystyle \text{Slow}\_\text{Nova}=(1-(0.32\*0.69833729609))=0.77653206525}

Slow
Windstorm

=
(
1
−
(
0.32
∗
0.69833729609
)
# )
0.77653206525

{\displaystyle \text{Slow}\_\text{Windstorm}=(1-(0.32\*0.69833729609))=0.77653206525}

Slow
Root

=
(
1
−
(
0.16
∗
0.69833729609
)
# )
0.88826603262

{\displaystyle \text{Slow}\_\text{Root}=(1-(0.16\*0.69833729609))=0.88826603262}

Slow
Muck

=
(
1
−
(
0.16
∗
0.69833729609
)
# )
0.88826603262

{\displaystyle \text{Slow}\_\text{Muck}=(1-(0.16\*0.69833729609))=0.88826603262}

# TotalSlow
1
−
(
0.77653206525
∗
0.77653206525
∗
0.88826603262
∗
0.88826603262
# )
0.52422140736

{\displaystyle \text{TotalSlow}=1-(0.77653206525\*0.77653206525\*0.88826603262\*0.88826603262)=0.52422140736}