Multiplier
A multiplier is a modifier that scales a numeric value either up or down by some magnitude via multiplication (as the name would imply).
Multipliers are often expressed is terms of a percentage change, i.e. 50% haste, 20% slow, etc., or as a direct multiplier (x1.5, x0.8); either case has some significant UX issues for designers when different multipliers for the same value stack and/or oppose.
Stacking multipliers
Example: Price Discounts
Players are familiar with real-world examples of multiplier effects, for example a percentage discount at a store (“Everything must go! 80% off!”). Taken in isolation, this is easy to understand - an item that previously cost $100 will now cost $20. What if we also give the buyer a coupon for a 10% discount? How does it combine with the 80% clearance discount? (Note: most stores won’t allow discounts to stack like this…)
Additive stacking: The two discounts are first added together (90%), then applied with a single multiplication (x0.10), for a new price of $10. The 10% off coupon actually reduced the final price by 50%.
Multiplicative stacking: The two discounts are applied separately in two multiplication steps, first x0.20 then x0.90, for a new price of $18. The 10% off coupon reduced the final price by… 10%.
In this case, the buyer would prefer additive stacking, but the seller would prefer multiplicative stacking. Had the coupon been for 20%, the buyer might expect to get the item for free.
Example: Sword Damage Bonuse
Suppose a fighter has a Sword skill that grants a 10% bonus to sword damage for every level of the skill purchased. There are 30 total levels possible, and the player has already bought 29 levels. What happens when they buy the 30th level? How does it combine with the other 29 levels?
Additive stacking: The fighter already had a 10% * 29 = 290% = 3.9x multiplier to damage. The 30th level of the skill raises that to a 4.0x multiplier, for an actual increase of ~2.5%.
Multiplicative Stacking: The bonus from the first 29 stacks is 1.1 ^ 29, or ~15.8x. The 30th level of the skill raises that to ~17.4, for an actual incease of… 10%.
Opposing Multipliers
For a real-world example of confusing opposing multipliers, here is an excerpt from the dot-com bubble article on Wikipedia:
Steel Connect (formerly CMGI Inc.): a company that invested in many Internet startups; between 1995 and 1999, its stock appreciated 4,921%, but declined 99% when the bubble burst. Archive of original article