Percentages

SamuraiWindu

One of my pet peeves in games is when percentages are combined by simply adding or subtracting, rather than compounding them. This is more significant than most people think, especially when calculating inverse percentages, such as evasion chance or damage reduction. Many mathematical exploits in games are the result of this mix-up.
I am curious to know what other people think about percentage calculations.

Kohl

Are you talking about Skill X has 20% evasion. Item X adds 20% evasion. Total evasion is 40%.
And you're saying total evasion should be 24%?

Noaani

There are situations where additive percentages make sense, and some situations where multiplicative percentages make sense.

My hope, rather than they stick to one or the other, is that they make it clear when it is one or the other. Even if they use the actual appropriate terms additive or multiplicative in the effect description.

SamuraiWindu

noaani wrote: »

There are situations where additive percentages make sense, and some situations where multiplicative percentages make sense.

Adding or subtracting pure percentages works once and only once in a calculation. For example, reducing 100% by 40% is truly 60%, but reducing 100% by 20% twice is 64%.

To further complicate things, a percentage can only be calculated in respect to quantities that exist. For example, evasion represents a reduction in chance to hit. In the real world, evasion as a statistic is a non-event. It has to be inverted into hit chance to hold meaning. For example, 20% evasion becomes 80% hit chance. Block chance and parry chance would also have to be inverted into hit chance before calculation can occur.

Kohl wrote: »

Are you talking about Skill X has 20% evasion. Item X adds 20% evasion. Total evasion is 40%.
And you're saying total evasion should be 24%?

In this example you would have 36% evasion.
(1-0.2)*(1-0.2) = 0.64 or 64% hit chance
1-0.64 = 0.36 or 36% evasion
https://en.wikipedia.org/wiki/Percentage#Compounding_percentages

phdmonster

noaani wrote: »

There are situations where additive percentages make sense, and some situations where multiplicative percentages make sense.

My hope, rather than they stick to one or the other, is that they make it clear when it is one or the other. Even if they use the actual appropriate terms additive or multiplicative in the effect description.

I agree with this. The way bonuses are applied should be present in the description of the modifier or as a tag somehow on it.

CaptnChuck

SamuraiWindu wrote: »

noaani wrote: »

There are situations where additive percentages make sense, and some situations where multiplicative percentages make sense.

Adding or subtracting pure percentages works once and only once in a calculation. For example, reducing 100% by 40% is truly 60%, but reducing 100% by 20% twice is 64%.

To further complicate things, a percentage can only be calculated in respect to quantities that exist. For example, evasion represents a reduction in chance to hit. In the real world, evasion as a statistic is a non-event. It has to be inverted into hit chance to hold meaning. For example, 20% evasion becomes 80% hit chance. Block chance and parry chance would also have to be inverted into hit chance before calculation can occur.

Kohl wrote: »

Are you talking about Skill X has 20% evasion. Item X adds 20% evasion. Total evasion is 40%.
And you're saying total evasion should be 24%?

In this example you would have 36% evasion.
(1-0.2)*(1-0.2) = 0.64 or 64% hit chance
1-0.64 = 0.36 or 36% evasion
https://en.wikipedia.org/wiki/Percentage#Compounding_percentages

Solid explanation. You make a good point, we'll see what the devs do.

Aardvark

SamuraiWindu wrote: »

One of my pet peeves in games is when percentages are combined by simply adding or subtracting, rather than compounding them. This is more significant than most people think, especially when calculating inverse percentages, such as evasion chance or damage reduction. Many mathematical exploits in games are the result of this mix-up.
I am curious to know what other people think about percentage calculations.

Math does not cause exploits ...devs not thinking about how their chosen method of math works causes exploits.

SamuraiWindu

phdmonster wrote: »

noaani wrote: »

There are situations where additive percentages make sense, and some situations where multiplicative percentages make sense.

My hope, rather than they stick to one or the other, is that they make it clear when it is one or the other. Even if they use the actual appropriate terms additive or multiplicative in the effect description.

I agree with this. The way bonuses are applied should be present in the description of the modifier or as a tag somehow on it.

I have played games where damage reduction can go beyond 100%, at which point damage actually restores hit points. With multiple damage types, this mechanism can turn combat into a sort of puzzle; with enough fire resistance, that salamander will actually heal you, but that winter wolf’s breath attack may still cause you trouble. This works fine in a single player environment or maybe in a dueling environment with clear counters akin to Pokémon.

The issue comes in balancing a multiplayer open world like in Ashes of Creation. If players can additively combine inverse percentage bonuses, like evasion chance, they will become immune to attacks if it reaches 100%. Some games put hard caps on statistics like evasion chance and block chance to avoid this problem, but if the game compounds percentages the math just works.