You open a chest and get two rings. One has +12% crit rate. The other has +30% crit damage. The game shows both in the same gold font and offers no help.
Most players pick on instinct, or whichever number is bigger. That works surprisingly badly, because RPG stats do not add up the way they look like they should. Some multiply each other. Some lose value the more you stack them. Some are wasted past a cap.
The good news is that the arithmetic underneath is simple. Once you see it, a lot of gear and build choices stop being guesswork. This guide walks through expected damage, crit maths, additive versus multiplicative stacking, and how defence changes the picture.
Expected Damage: The Only Number That Matters
Games show you individual hits. What actually kills enemies is **average damage over time**. Everything below is about estimating that number.
Most RPG damage follows the same basic shape:
damage per second = base damage x bonus multipliers x crit multiplier x attacks per second, then reduced by the enemy's defence
The rest of this article is about what sits inside each of those terms.
Crit Maths
A critical hit is a hit that deals extra damage. Two stats control it:
- Crit rate: the chance any hit is a crit, for example 25%
- Crit damage: how hard a crit hits. Games display this differently. Some show the total (a crit deals 150%). Others show only the bonus (+50%). Check which one yours uses
Using the bonus version, your **average multiplier from crits** is:
1 + crit rate x bonus crit damage
A few examples:
| Crit rate | Bonus crit damage | Average multiplier |
|---|---|---|
| 5% | +50% | 1.025 |
| 25% | +50% | 1.125 |
| 25% | +150% | 1.375 |
| 60% | +120% | 1.72 |
| 100% | +50% | 1.50 |
Look at the first row. With a low crit rate, crit damage is almost irrelevant. This is the single most common mistake: stacking huge crit damage numbers while critting one hit in twenty.
The Two Rules
1. **Raise whichever is lower relative to the other.** Because they multiply, the gain from one stat is proportional to the size of the other. When rate is low, rate is worth more. When damage is low, damage is worth more
2. **Never go past the crit rate cap.** Most games cap crit rate at 100%. Every point beyond that does nothing, so a build sitting at 110% has wasted gear
Where the 1:2 Ratio Comes From
You will often see advice to keep crit damage at about twice crit rate. That is not a law of RPGs. It falls out of one specific situation: **when gear prices one point of crit rate the same as two points of crit damage**, which is true in some popular games.
Under that exchange rate, if you have a fixed budget to split, the product of rate and damage is largest when damage is about twice rate. Change the exchange rate and the ideal ratio changes with it. If your game gives crit rate and crit damage at one to one, the balanced point is roughly one to one.
Additive vs Multiplicative: Why Bonuses Lose Value
This is the idea that explains the most confusing stat behaviour.
Additive bonuses
Many games group bonuses into a single pool and add them together before applying them. Three separate +50% damage bonuses become +150%, a **2.5x** multiplier.
The trap is that each new bonus is worth less than the last **relative to what you already have**:
| Total additive bonus | Next +20% adds |
|---|---|
| +0% | 20% more damage |
| +100% | 10% more damage |
| +300% | 5% more damage |
Going from 1.0x to 1.2x is a 20% increase. Going from 4.0x to 4.2x is a 5% increase. Same item, very different value.
Multiplicative bonuses
Other bonuses apply separately, each multiplying the result of the others. Three separate 50% multipliers give 1.5 x 1.5 x 1.5, about **3.4x**. Each one keeps its full value no matter how many others you have.
Path of Exile makes this distinction explicit in its wording, using "increased" for additive bonuses and "more" for multiplicative ones. Most games are less helpful and you have to infer it from testing or the community.
What This Means for Choices
- Early on, almost any bonus is good, because your pools are small
- Later, diversify. If you already have a huge additive damage pool, a bonus that sits in a different bucket (crit, attack speed, a separate multiplier) is usually worth more than another +% damage
- Permanent multiplicative bonuses matter most in long games, because they compound with everything else
How Defence Changes the Picture
Enemies reduce your damage, and how they do it matters.
Subtractive defence
The enemy's defence is subtracted from each hit. A 100 damage hit into 40 defence deals 60.
Under this model, **big hits beat many small hits**. A 50 damage hit into 40 defence deals only 10. Fast, weak attacks get punished hard, and crit damage becomes more valuable because it lifts single hits above the defence floor.
Percentage defence
The enemy takes a percentage less from every hit, often through a formula like damage x 100 / (100 + defence). Each hit is reduced by the same proportion regardless of size.
Under this model, attack speed and many small hits are no worse than slow big ones. Most modern games use some version of this, partly because subtractive defence makes balancing so hard.
Diminishing returns on your own defence
The same formula usually applies to you. With a 100 / (100 + defence) shape, going from 0 to 100 defence halves the damage you take. Going from 100 to 200 only cuts it from 50% to 33%. Each point of defence protects you a bit less than the one before, though it never stops helping entirely.
Attack Speed
Attack speed multiplies the number of hits, and every hit carries your crit chance, your on hit effects and your bonuses. That is why it often feels stronger than its number suggests. It scales with everything else you have.
Two things can limit it: a hard cap on attacks per second, and subtractive defence, which punishes the smaller hits fast builds tend to make.
Common Traps
- Stacking crit damage with a tiny crit rate. Fix the rate first
- Going past a cap. Crit rate over 100%, attack speed over a hard limit, cooldown reduction at its maximum
- Comparing raw numbers across stats. +12% crit rate and +30% crit damage are not on the same scale
- Ignoring which pool a bonus goes into. One more additive +% damage is often the weakest choice late game
- Judging a build by its biggest hit. Big crit numbers are satisfying to watch. Average damage is what clears floors
Where Pixel Heroes Fits
Pixel Heroes is a retro idle RPG for iPhone where these choices are most of the game. Combat is automatic, so the skill lives in the build.
Each level up offers a choice from more than 30 cards, plus class exclusive ones for the Sword Master, Archer and Mage. Gear fills 4 equipment slots across 6 rarity tiers up to Unique, with set bonuses and enhancement. Over a long climb, rebirth trades your run for shards, and Ascension adds a multiplicative bonus on top with no level cap. As the section above explains, that kind of compounding bonus is exactly what keeps paying off as everything else grows.
To be clear about what this article is not:
- It is not a datamine of Pixel Heroes. It describes the maths common to RPGs in general. The game does not publish its internal formulas, and individual games differ in the details
- Use the principles, not a fixed ratio. Check how the game prices stats, watch for caps, and compare builds by how fast they clear floors rather than by the biggest number on screen
If you are new to the genre, the idle RPG guide explains offline progress, rebirth and ascension, and roguelike vs roguelite covers where build cards came from.
The Short Version
- Judge stats by average damage over time, not by the size of a single hit
- Average crit multiplier = 1 + crit rate x bonus crit damage, so the two stats multiply each other
- Raise whichever crit stat is lower relative to the other, and never go past the crit rate cap
- The 1:2 ratio only applies when gear prices one point of rate the same as two of damage
- Additive bonuses lose relative value as they stack. Multiplicative ones keep it
- Subtractive defence favours big hits. Percentage defence treats all hits equally