The Game Designer Reference Library – Math & Balancing — Quick Reference Tables

1. XP Progression Curve Models

ModelFormulaGrowth BehaviorTypical Use CaseDesign Notes
LinearXP = Base × LevelConstant increaseCasual / short gamesPredictable pacing
ExponentialXP = Base × Rate^LevelRapid late growthRPGs / live serviceControls late-game lifespan
QuadraticXP = Multiplier × Level²Smooth scalingMost modern RPGsBalanced grind curve
LogarithmicXP = Base × log(Level+1)Fast early, slow laterSkill systemsReduces early friction
HybridXP = Level² × Mult + BaseControlled scalingLong progressionMost flexible

Typical exponential rates:

RatePerceived Pace
1.05Very gradual
1.1Smooth
1.15Noticeable grind
1.2Hardcore

2. Damage Calculation Models

ModelFormulaScaling StabilityCommon GenresNotes
Flat ReductionDamage = ATK − DEFPoor late scalingClassic RPGCan cause zero damage problems
Percent ReductionDamage = ATK × (100 / (100 + DEF))Very stableAction RPG / MMOIndustry standard
MultiplicativeATK × Mods × Buffs × CritComplex scalingARPG / StrategyRequires careful tuning
Armor CurveDamage = ATK × (1 − Armor%)PredictableShootersEasy readability

3. Time-to-Kill Benchmarks

GenreTarget TTKCombat Feel
Tactical FPS0.2 — 0.8 secHigh lethality
Arena Shooter1 — 3 secReactive
Action RPG5 — 20 secAbility driven
MOBA3 — 12 secTactical bursts
MMO20 — 60 secRotation based
Survival2 — 10 secTension focused

4. Health Regeneration Models

ModelFormulaTypical RangePlayer Perception
Flat RegenHP/sec = Fixed1–10 HP/secSimple
Percent RegenMax HP × Rate0.5–2%Scales with progression
Delayed RegenAfter delay3–7 sec delayModern standard
Combat RegenReduced in combat25–50% normalTactical pacing

5. Loot Drop Rate Benchmarks

TierProbabilityPlayer Expectation
Common40 — 70%Frequent
Uncommon20 — 40%Regular
Rare5 — 15%Exciting
Epic1 — 5%Memorable
Legendary0.1 — 1%Event level

Pseudo-random adjustment range: +0.5% to +2% per failure


6. Critical Hit Standards

ParameterTypical RangeImpact Level
Crit Chance5 — 25%Baseline
High Crit Builds30 — 60%Volatile
Crit Multiplier1.25x — 2xStandard
Burst Multiplier2.5x — 3xHigh variance

Expected damage formula:

Damage = Base × (1 + CritChance × CritMultiplier)


7. Economy Flow Ratios

MetricHealthy RangeRisk if Exceeded
Income vs Spending1 : 0.9Inflation
Sink Coverage80 — 95%Currency hoarding
Reward VelocityStablePlayer burnout
Inflation Growth<5% per weekEconomic collapse

8. Cooldown Design Ranges

Ability TypeTypical CooldownDesign Intent
Core ability3 — 8 secRotation
Utility10 — 30 secTactical choice
Ultimate60 — 180 secPower spike
Charge regen10 — 30 secFlexibility

Cooldown reduction formula:

CD = Base × (1 − Reduction%)


9. Reward Timing Cadence

Reward ScaleIntervalPurpose
Micro reward30 — 90 secEngagement loop
Small reward5 — 15 minRetention
Medium reward30 — 60 minSession satisfaction
Major reward2 — 6 hrsLong goals

10. Power Growth Multipliers

Game ScopeTotal Power Increase
Short campaign2x — 5x
Mid length10x — 50x
RPG100x — 1000x
MMO / live service10,000x+

11. Difficulty Scaling Models

ModelBehaviorBest Use
StaticFixed difficultyCompetitive
Level scalingMatches playerOpen world
Soft scalingPartial adjustmentHybrid RPG
Dynamic (DDA)Performance basedCasual accessibility

Common performance metrics: deaths, accuracy, completion time


12. Stat Allocation Benchmarks

Stat CategoryAllocation Range
Offense35 — 45%
Defense25 — 35%
Utility15 — 25%
Luck / variance5 — 10%

13. RNG Influence Targets

GenreRNG Influence
Competitive5 — 15%
Action15 — 30%
RPG30 — 60%
Roguelike50 — 80%

14. Risk vs Reward Scaling

Standard heuristic:

Reward ∝ Risk²

Risk LevelSuggested Reward
Low1x
Moderate2–3x
High4–6x
Extreme8–10x

15. Progression Milestone Targets

Session LengthExpected Progress
10 minMinor upgrade
30 minSmall milestone
1 hrLevel gain
3 hrsMajor unlock

Quick Design Heuristics

PrincipleGuideline
Early progression speedFast first hour
Feedback loop timing<60 sec
Economy healthMaintain sinks
RNG fairnessUse PRD
Player power curveSmooth ramp
Complexity introductionGradual
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