progression-systems

name

progression-systems

description

The math of growth over time: power curve shapes, XP formulas, the flow channel, felt versus actual power, the difficulty sandwich, adaptive difficulty, and unlock pacing. Use when designing XP curves, level-up formulas, difficulty ramps or unlock schedules, deciding what to gate, or when players say the game is 'too easy', 'too hard', 'grindy', or 'I don't feel like I'm getting stronger'. This is the math; for the psychology of why players respond to it use motivation-design, and where the curve IS the whole game use incremental-design.

Progression Systems

Purpose: Tools for designing how players grow in power, skill, and access over time. Good progression makes every session feel rewarding. Bad progression creates grind, frustration, or trivialized content.

Sources: The flow channel is Mihaly Csikszentmihalyi, Flow (1990), as applied to games by Jenova Chen ("Flow in Games," MFA thesis, 2006). Accessibility-and-depth as independent axes follows the standard "low floor, high ceiling" formulation. XP-curve shapes and pacing values here are working heuristics with no external source — apply the Numbers Policy in game-design and treat every figure as a starting value with a test plan.

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Core Model: Accessibility and Depth

Two independent axes that progression systems must serve:

Depth (high ceiling)
    |
    |   +-----------+
    |   | The Goal  |   ← Easy to start, deep to master
    |   +-----------+
    |
    +-------------------→ Accessibility (low floor)

• Accessibility (low floor) — Can a novice play and have a good time?
• Depth (high ceiling) — Is there room for an expert to keep improving?

These are NOT opposites. The best systems score high on both. Techniques:

Technique	How It Works	Example
Layered complexity	Simple surface, deep internals	Chess: easy rules, infinite strategy
Optional complexity	Advanced systems exist but aren't required	Type matchups you can ignore if you over-level
Skill-based progression	The player improves, not just the character	Combo execution, map knowledge, timing

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Power Curves

How player power grows over time. The curve shape determines how the game feels.

Curve Types

Power
  |          Exponential        S-Curve (often ideal)
  |         /                  _____
  |        /                  /
  |       /                  /
  |      /                  /
  |     /                  /
  |    /              ____/
  |   /              /
  |  /              /
  | /           ___/
  |/___________/
  +----------------------------------→ Time

  Linear                    Logarithmic
  /                         ___________
  /                        /
  /                       /
  /                      /
  /                     /
  +-------------------→  +-------------------→

Curve	Feel	When to Use	Risk
Linear	Consistent, predictable	Tutorial sections, first hour	Boring over long spans
Exponential	Dramatic, accelerating	Short games, power fantasies	Unmanageable late game
Logarithmic	Diminishing returns	Realistic simulations	Feels unrewarding as ceiling approaches
S-Curve	Slow start → rapid middle → plateau	Most progression systems	Requires careful inflection point placement

Felt vs. Actual Power

Players need to feel stronger even when mathematical power growth slows.

Techniques for maintaining felt power at diminishing actual power:

• New abilities that look dramatic even if numerically modest
• Visual upgrades (armor appearance, particle effects, screen presence)
• New types of interaction rather than bigger numbers
• Areas of the world that were previously inaccessible
• AI enemies that react more dramatically to the player's attacks

Template: Power Curve Spreadsheet

| Level | XP Required | Cumulative XP | Power Rating | Felt Power | New Content |
|-------|-------------|---------------|--------------|------------|-------------|
| 1     | 0           | 0             | 10           | Low        | Tutorial    |
| 2     | 100         | 100           | 15           | Growing    | Ability A   |
| 3     | 150         | 250           | 19           | Growing    |             |
| 4     | 225         | 475           | 22           | Moderate   | Area B      |
| 5     | 340         | 815           | 25           | Moderate   | Ability B   |

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XP and Level Math

Common XP Formulas

Linear scaling: xp_for_level(n) = base * n

• Simple, predictable, gets grindy fast

Polynomial: xp_for_level(n) = base * n^exponent

• Exponent 1.5-2.0 is common
• Gradually increasing time between levels

Exponential: xp_for_level(n) = base * growth_rate^n

• Dramatic acceleration, use sparingly
• Works when matched with exponential reward scaling

Practical approach:

1. Decide how long each level should feel in play time
2. Estimate XP gain per minute of intended play
3. Back-calculate the required XP per level
4. Plot and smooth the curve
5. Playtest and adjust — the math is a starting point, not the answer

Level Count Rule of Thumb

Target a level-up every 10-30 minutes of play in the early game, stretching to 30-60 minutes in mid/late game. Work backward from intended game length to determine level count. Short games (2-5 hours) need fewer levels (10-15); long games (50+ hours) need more (50-100) but risk grind at scale.

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The Flow Channel

Challenge should approximate skill level — the "flow channel" from psychology:

Challenge
    |     Anxiety
    |    /
    |   /  FLOW CHANNEL
    |  /  /
    | /  /
    |/  /
    | /  Boredom
    |/
    +------------------→ Skill

• Above the channel → anxiety, frustration, quitting
• Below the channel → boredom, disengagement
• In the channel → engagement, "just one more try"

Targeting the Channel

• Does difficulty scale with demonstrated player skill (not just time played)?
• Are there multiple difficulty signals? (Speed, accuracy, strategy quality, not just "did they die?")
• Does the channel widen as skill increases? (Experts tolerate more variance)
• Can players self-select difficulty? (Options, optional challenges, difficulty modes)

Adaptive Difficulty

If implementing dynamic difficulty adjustment (DDA):

Do:

• Adjust invisibly (enemy spawn rate, AI aggression, resource availability)
• Base adjustments on multiple signals (death rate + time-to-complete + resource usage)
• Apply gradually — sudden shifts feel unfair

Don't:

• Make it visible — players who notice rubber-banding feel cheated
• Adjust core challenge identity (if the game is about precision, don't make hitboxes bigger)
• Scale only HP/damage (lazy, breaks balance, doesn't change the experience)

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The Difficulty Sandwich

Good progression peels three layers of challenge:

Layer 1 (bottom):  Mechanical skill     (can I physically do this?)
Layer 2 (middle):  Cognitive challenge   (do I understand what to do?)
Layer 3 (top):     Strategic depth       (can I optimize my approach?)

Progression phases:

• Early game: Layer 1 only — learn controls, build muscle memory
• Mid game: Layer 1 + 2 — learn systems, understand interactions
• Late game: All three — master strategy, optimize builds, find efficiencies

Anti-pattern: Introducing Layer 3 challenges before Layer 1 is comfortable. Don't ask for strategic thinking while the player is still fumbling with controls.

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Content Pacing

New content (mechanics, enemies, zones, abilities) should arrive at inflection points on the power curve.

Rules of thumb:

• Introduce new content when the player has just mastered the previous content
• Each new element should change how the player plays, not just what they fight
• Space unlocks so there's always something recent to explore and something to anticipate
• The longest stretch without new content should be shorter than the player's patience — and that's shorter than you think

Unlock Pacing Checklist

• Is there a meaningful unlock or new mechanic every 15-30 minutes? (Adjustable per genre)
• Do unlocks change player behavior? (New ability that opens new tactics > +5% damage)
• Is there always a visible "next milestone" to work toward?
• Does the pacing slow down as the player's investment deepens? (Acceptable late-game)
• Are early unlocks front-loaded to hook new players?

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Common Pitfalls

• Flat difficulty that doesn't respond to player growth (level 50 feels like level 5)
• Rubber-banding that's visible and feels unfair ("the game cheated")
• Difficulty modes as HP/damage scaling (lazy, breaks balance, doesn't change experience)
• Punishing experimentation in the learning phase (deaths should teach, not just frustrate)
• Power creep in sequential content releases (each new thing must be "better" to sell)
• Grind without purpose — repetition is acceptable when each cycle teaches something; it's toxic when it's just time-gating

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Cross-References

Three tight links. Everything else routes through the map, so adding a skill touches one file rather than twenty: references/routing-map.md (in game-design).

• motivation-design — Why players respond to any of this
• incremental-design — When progression is the game
• player-ux — Onboarding is the first phase of the curve