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With the release of Patch 2.1.0 for Diablo III and Reaper of Souls, Blizzard also provided a Community Buff:

To celebrate the arrival of this major content update, all players [...] will not only receive a +100% bonus to Gold Find [...] (As with our previous buff, please note that the Gold Find bonus will stack multiplicatively with existing bonuses including those provided by items and Paragon points.)

What does "stack multiplicatively" mean here? If I currently have 25% increased Gold Find, this buff make it 50% (100% more), rather than 125%?

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The key that you're missing is that "increased 25% gold find" means that you have 125% gold find. Stacking multiplicatively with 100% gives you 250%(150% increased), which is better than 225%(125% increased) if you add. When you have 0% increased gold find, you still have 100% gold find. –  Cruncher Aug 28 at 20:15

2 Answers 2

up vote 11 down vote accepted

There are four common sources for gold find:

  1. Your equipment. This is your +X% to gold find.
  2. Shrines. The Fortune Shrine increases your magic find and gold find by +25%.
  3. Paragon Points. Each point will give you +1% to your gold find, to a maximum of +50%.
  4. Difficulty. There's the handy dandy difficulty chart in this answer for how much each difficulty will give you.

The first three sources are added together, to give you your base additional gold find percentage. As of 2.0.5, the difficulty's gold bonus isn't added, but multiplied, to get your final gold find percentage. What this current bonus does is multiply that number.

So the basic formula would be:

(Equipment % + Shrine % + Paragon %) * Difficulty % * Bonus % = End result.

The net effect is that you will find roughly twice as much gold as you were before, no matter what difficulty you play, or how much gold find you have.

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Credit to @pfayze for the info about difficulty being multiplied, not added. –  Frank Aug 28 at 19:26

Your gold income is regularly 100%. When you get the +25% increase, as it is your only bonus, your new gold income is 125%. When you get that +100%, it multiplies instead of adds, like this:

+25% = (1 + 0.25) = 1.25.

+100% = (1 + 1) = 2.0.

1.25 * 2 = 2.5, or a 250% increase in gold.

If you had an additional +75% bonus besides your +25%, it would be like this:

(1.25 + 1.75) * 2.0 = 400%

As it seems in D3 (I do not actually play it) that your bonuses normally are applied additively. If all three of these numbers were to be applied multiplicatively, for example, it would be as follows:

1.25 * 2.0 * 1.75 = 4.375 = 437.5%.

This is a lot more than if you were to add the numbers together for just a 200% increase.

Multiplicative stacking allows for your gold increase to increase much more quickly than with additive.

This is most often used in games for reducing effects though, not increasing. A big example of this would be League of Legends, where things like Crowd Control reductions stack multiplicative as well.

In that case, you have two items that reduce a number by 10%. The formula is like:

-10% = (1 - 0.1) = .9 = 90%.

0.9 * 0.9 = 0.81. (1 - 0.81) = 0.19 = 19% reduction in time, instead of 10+10 = 20%.

As a final note: It would of been much simpler if Blizzard had just said that your total gold find during this period was doubled.

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Your second example is off, actually. An additional +75% would just add to the existing +25%, for a total of +100%. This time-limited bonus going on right now stacks multiplicatively, but other sources are added, not multiplied. Otherwise gold find would be by far and away a super insane stat. –  Frank Aug 28 at 18:21
    
I meant it in the context if you had several bonuses that all stack multiplicatively, not in D3's context, as I have not actually played D3. I will add in D3 specific context though. –  Tylor Aug 28 at 18:42
    
Frank, since 2.0.5 gold bonuses stacks manipulatively. I have updated your answer based on this. –  pfayze Aug 28 at 19:18
    
@pfayze Oh, neat. I hadn't realized that. I did reject the edit, though, because that's a lot of extraneous information that's not needed. I will update the formula info, though. Tylor, we try to ensure information is as specific as possible here. We don't need a general math lesson in how things multiply; we need an answer that explains how it works in the aspect being asked about. –  Frank Aug 28 at 19:23

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