Alright, kind of an odd question, math.

[Dwoofie]

Arguing with a fellow saying multipliers do not stack right.

 

Arguing, that the 1.5x boost from pendant, and 2x from a penance horn (doing agility) should stack into 3.5x experience.

 

As in, 200% and 150% = 350% experience.

 

However, them only being 300% experience is "wrong" (Even though 1.5x * 2x = 3x)

 

Also arguing that, a 10% discount coupon, and a 25% coupon in a store would be 35% off. Which is why 200% experience and 150% experience should be 350% experience.

 

I know there's some trickery with the % here. And I am fairly certain I am correct on this matter (2x * 1.5x should be 300%, or if additive, it would turn out as 2.5x experience, not 3.5x experience.)

 

I want confirmation I'm correct. (And that my mind isn't in a bad place today) and, if I'm correct, a way of explaining how he is wrong because I just can't seem to put it into words.

 

 

So I'd appreciate if someone could explain why either he, or I, am a fool.

[Sy_Accursed]

They vary throughout runescape, a few do stack multiplicatively but the vast majority stack additively.

 

Multiplicative ones work in that say an action is 100xp and you have a 2* xp booster, it becomes 200xp. Then a multiplicative booster of say 1.5* xp would do 200*1.5 for 300xp total pay out. As you rightly said 1.5*2 = 3* multiplier.

 

Additive bonuses work thusly:

100xp activity.

You have a 2* xp thingie and a 1.5* xp thingy they both act on the base xp to give the result.

A 2* booster means the end result is twice the base xp (200xp) BUT only 100xp of that is bonus, the other 100 is the xp you got anyway.

A 1.5* booster goes to 150xp but again the 100xp is the original base xp, only the 50xp is the bonus.

Additive stacking means:

100xp base

100xp bonus from the 2*

50xp bonus from the 1.5*

250xp total aka 2.5* xp

1 (base xp) + 1 (bonus from the doubling effect) + 0.5 (bonus from the 1.5 effect) = 2.5* multiplier

 

Where your friend is getting lost is he is forgetting the multipliers include 1.0 for the base xp that you get anyway so you can't just add 2.0 and 1.5 and say it should be 3.5, using that math you've included the 1.0 base xp twice. I mean sure in direct math 2+1.5 is 3.5, but since we are considering multipliers it doesn't work like that the multiplier is just an instruction of how you get from the normal xp to the xp given by using said item and as such 1.0, 100% or 1/1 of that value IS the base xp and cannot simply be duplicated in adding, when adding you have to ONLY add up the parts of the multipliers in excess of 1.0 and then put the extra 1 back in to the multiplier. (Like I said before for the 2* and 1.5* you do 1 + 0.5 + 1 = 2.5)

 

To shortly summarise what this friend is claiming is that doing agility for a 1000xp action the pendant should give 1500xp for 150% and the horn should give 2000xp for 200% and therefore combined should be 3500xp. In reality the action you are doing is giving you 1000xp, the pendant only gives you 500xp and the horn gives you 1000xp for a total of 2500xp.

[Dwoofie]

Thanks a lot! Very much appreciated ^^