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orb suggestion: cost reduction
#11
Are you sure exp isn't multiplicative, I was told it was. I guess you would probably know though. I'll have to test it out at some time.
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#12
The way the xp orb is applied is by taking ((eventrate)*(1+OctoberBonus)*(1+ExpOrb))

That being said, the event rate is like (EventExp%+SupportExp%+AccountExp%+Etc.+Etc.)

I'm sure yall can figure it out.
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#13
In that example it is multiplicative. Doesn't matter if it's multiplied inside parenthesis or outside as long as it's never added. For example 3*3*3 is the same as 3*(3*3) but 3*(3+3) and 3+(3*3) are different. If it was included in the event rate additions then it would not be multiplicative.
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#14
(10-11-2015, 11:13 AM)Void Wrote: The way the xp orb is applied is by taking ((eventrate)*(1+OctoberBonus)*(1+ExpOrb))

That being said, the event rate is like (EventExp%+SupportExp%+AccountExp%+Etc.+Etc.)

I'm sure yall can figure it out.

Close enough.

It looks like this:

BaseExp*(1+eRate)*OtherMultipliers,

where

eRate=(1+orb%)*(1+global%)*(event*+support+account%+etc%).
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#15
(10-11-2015, 11:27 AM)Aaron Storm Wrote: In that example it is multiplicative. Doesn't matter if it's multiplied inside parenthesis or outside as long as it's never added. For example 3*3*3 is the same as 3*(3*3) but 3*(3+3) and 3+(3*3) are different. If it was included in the event rate additions then it would not be multiplicative.

This is incorrect.

When two bonuses of +x% and +y% stack mutliplicatively, the total bonus is given by
(1+x%)*(1+y%) = 1+x%+y%+xy%% (i.e. 1+x/100+y/100+xy/10,000),
for a total percentage bonus of (x+y+xy/100)%

It's called multiplicative because you multiply the ratios together to get the result.  You have a 2% increase stacking multiplicatively with a 3% increase?  The result is a ratio of (1.02)*(1.03).

When two bonuses stack additively you don't multiply the ratios, you add the differences.  A 2% increase stacking additively with a 3% increase yields 2%+3%=5% increase.

Or, more generally an x% and y% increase stacked additively yield an (x+y)% increase.

The situation with the experience and gold orbs is more complicated.  The stacking is neither multiplicative nor additive with any other factor.  Rather it is a percentage increase on the eRate Brouwer described.

[NOTE: Brouwer describes eRate=(1+orb%)*(1+global%)*(event*+support+account%+etc%).  Not to confuse things, but in what follows i have written
erate% =(1+global%)*(event%+support%+account%+etc%), without the (1+orb%).  If we can agree on terminology i can replace my erate% with a more suitable term.]

At first glance it may appear to be multiplicatively stacking with the erate, but that in fact would look like
(1+orb%)*(1+erate%), whereas what we actually have is (1+(1+orb%)*erate%).

To calculate the true effect of the xp orb we should examine the ratio of the experience with an orb to the experience with no orb:
[1+(1+orb%)*(erate%)] / (1+erate%) = (1+erate%+orb%*erate%)/(1+erate%) = 1+orb%*[erate%/(1+erate%)]

So we can see that the actual impact on our xp is not an increase of orb% (which is what we would expect from true multiplicative stacking, i.e. if it were independently mulitplicative with each other factor, the way party boost is), but instead has a coefficient of [erate%/(1+erate%)].

In other words, a 2% xp orb will not increase our xp received by 2%, but rather by 2*[erate/(1+erate)]%, or if you prefer, 2*[1 - 1/(1+erate)]%.  As erate becomes quite large, this value will approach 2%, but if we have very little erate (e.g. if we have low account upgrade for experience), the value of the experience orb will be greatly diminished.
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#16
(10-11-2015, 11:27 AM)Aaron Storm Wrote: In that example it is multiplicative. Doesn't matter if it's multiplied inside parenthesis or outside as long as it's never added. For example 3*3*3 is the same as 3*(3*3) but 3*(3+3) and 3+(3*3) are different. If it was included in the event rate additions then it would not be multiplicative.

When in the hell did I say it wasn't multiplicative?

I was just listing the formula.

And if I know the formula...I'm quite sure I know it's multiplicative.
(10-11-2015, 02:07 PM)Brouwer Wrote:
(10-11-2015, 11:13 AM)Void Wrote: The way the xp orb is applied is by taking ((eventrate)*(1+OctoberBonus)*(1+ExpOrb))

That being said, the event rate is like (EventExp%+SupportExp%+AccountExp%+Etc.+Etc.)

I'm sure yall can figure it out.

Close enough.

It looks like this:

BaseExp*(1+eRate)*OtherMultipliers,

where

eRate=(1+orb%)*(1+global%)*(event*+support+account%+etc%).

I was leaving out the other part of the formula :|
So I'm quite sure it's right.
If you want the full formula, it is:

(monsterlevel*(1+(monsterlevel*0.003))*(1+RestBonus)*(partyMod)*(1+eRate)
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#17
(10-10-2015, 02:15 PM)Brouwer Wrote:
(10-09-2015, 11:44 AM)Aaron Storm Wrote: All orbs are multiplicative right now.

Exp isn't. And assuming gold orb works the same way as exp, gold isn't either.

I was replying to this comment void, not the one you wrote.

(1+y)*(1+x) is still multiplicative because the 1 is simply a way of simplification because it's easier than having x = 102% instead of just 2%. Makes it a lot easier in programming so you don't have to subtract 100% when you pull it up for other things, such as saying what your current percentage is in the orb screen.

To test it you just have to look at the comparison between ((1+y)*(1+x))-1 versus the additive which would be y+x. When Y equals 2% and X equals 3% the multiplicative equals 5.06% versus the additive which is 5%. Doesn't make much difference with those numbers but with larger numbers it does. For instance if X = 50% and Y = 70% then the multiplicative would be 155% versus additive of just 120% that is a 35% difference.

Since we already have some large numbers in play for exp and gold, specifically the 120% account upgrade, it's important whether something is multiplicative or additive. A 8% add to that 120% would be a mere 128% whereas a multiplication of it would be 137.6% nearly a 10% difference. And that doesn't include the event points and support level.
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