Within the field of game design, game balance can best be described as a black art. It is the process by which game designers make a game simultaneously fair for players while providing them just the right amount of difficulty to be both exciting and challenging without making the game entirely predictable. This involves a combination of mathematics, psychology, and occasionally other fields such as economics and game theory.
Game Balance offers readers a dynamic look into game design and player theory. Throughout the book, relevant topics on the use of spreadsheet programs will be included in each chapter. This book therefore doubles as a useful reference on Microsoft Excel, Google Spreadsheets, and other spreadsheet programs and their uses for game designers.
FEATURES
- The first and only book to explore game balance as a topic in depth
- Topics range from intermediate to advanced, while written in an accessible style that demystifies even the most challenging mathematical concepts to the point where a novice student of game design can understand and apply them
- Contains powerful spreadsheet techniques which have been tested with all major spreadsheet programs and battle-tested with real-world game design tasks
- Provides short-form exercises at the end of each chapter to allow for practice of the techniques discussed therein along with three long-term projects divided into parts throughout the book that involve their creation
- Written by award-winning designers with decades of experience in the field
Ian Schreiber has been in the industry since 2000, first as a programmer and then as a game designer. He has worked on eight published game titles, training/simulation games for three Fortune 500 companies, and has advised countless student projects. He is the co-founder of Global Game Jam, the largest in-person game jam event in the world. Ian has taught game design and development courses at a variety of colleges and universities since 2006.
Brenda Romero is a BAFTA award-winning game director, entrepreneur, artist, and Fulbright award recipient and is presently game director and creator of the Empire of Sin franchise. As a game director, she has worked on 50 games and contributed to many seminal titles, including the Wizardry and Jagged Alliance series and titles in the Ghost Recon, Dungeons & Dragons, and Def Jam franchises.
Author(s): Ian Schreiber, Brenda Romero
Publisher: CRC Press
Year: 2021
Language: English
Pages: 806
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
List of Case Studies
Acknowledgments
Preface
Authors
Part I: Game Balance
1 The Foundations of Game Balance
What Is Game Balance?
Kinds of Game Balance
Mathematical Balance
Balanced Difficulty
Balanced Progression
Balanced Initial Conditions
Balance between Multiple Strategies
Balance between Game Objects
Balance as Fairness
How Do We Know If a Game Is Balanced?
How Do You Balance a Game?
Designer Experience
Small-Scale Playtesting
Analytics
Mathematics
Balance between Types of Balance
A Note about Math
Discussion Questions
Rogue’s Main Quest, Part 1: A Mini Expansion Set
Fighter’s Main Quest, Part 1: Analysis of an Epic Journey
Wizard’s Main Quest, Part 1: Creating a TCG
2 Critical Vocabulary
Understanding the Possibility Space
Affecting the Possibility Space
Determinism
Transitivity and Intransitivity
Information
Symmetry
Feedback Loops
Curves
Solvability
Types of Solvability
Solving Non-deterministic Games
Solving Intransitive Games
The Metagame
Metagame Balance: Benefit or Bane?
Discussion Questions
Sidequests
Sidequest 2.1: Balance Intuition Log
Rogue’s Main Quest, Part 2: Find the Exemplars
Fighter’s Main Quest, Part 2: Fast Parts, Slow Parts
3 Where to Start—Systems
Where to Start: Put It All on the Table
Critical and Fuzzy Thinking about Systems
Types of Resources
Time
Currency
Game-Specific Objects
Hit Points/Lives
Experience and Levels
Establishing Relationships between Resources
Discussion Questions
Sidequests
Sidequest 3.1: Make a Resource Flow Diagram
Fighter’s Main Quest, Part 3: Grinding for Loot
4 The Components of Progression—Curves
The Importance of Numerical Relationships
Types of Numerical Relationships
Tradeoff Relationships
Progression Relationships
Types of Game Curves
Identity Curve
Linear Curve
Exponential Curves
Logarithmic Curves
Triangular Curves
Custom-Crafted Curves, Formulas, and Outcomes
Cost Obfuscation Curves
Curve Summary
Everything in Moderation
Discussion Questions
Sidequests
Sidequest 4.1: Level Curve
Sidequest 4.2: Level Curve Fitting
Sidequest 4.3: Machinations
Sidequest 4.4: Optimizing Idle Game Play
Sidequest 4.5: Detangling the Obfuscation of an F2P Game
Rogue’s Main Quest, Part 3: Identifying Key Resources
5 Finding an Anchor
Establishing an Anchor
Finding an Anchor
Scaling an Anchor with Curves
Finding an Anchor in Skill-Based Games
Finding a Comparative Anchor
Giving Value to Extras
Interactions between Systems
Example 1: Rocket Jumping and Bunny Hopping
Example 2: How to Nuke Your Income
Granularity
Completing a First Pass
Discussion Questions
Sidequests
Sidequest 5.1: Arcade Analysis
Wizard’s Main Quest, Part 2: Building Intuition
6 Economic Systems
What Are Economic Systems?
The Language of Economic Systems
Common Economic Systems
Mechanical Characteristics of Economic Systems
Supply and Demand
The Supply Curve
Gameplay Effects of Scarcity
The Demand Curve
Marginal Supply and Demand
Supply and Demand with Multiple Resources
Market Price
Fixed Economies
Player-Dynamic Economies
The Invisible Hand
Free-To-Play (F2P) Economies
Analyzing Historical Data
Testing the Market
Targeting the Market
Keeping Prices Flexible
Prestige Economies
Inflation
Supply-Side Inflation
Demand-Side Inflation
Adding Negative-Sum Elements to the Economy
Removing Positive-Sum Mechanics from the Economy
Economic Resets
Open and Closed Economies
Player Trades in Open Economies
Discussion Questions
Sidequests
Sidequest 6.1: Fixing Monopoly
Sidequest 6.2: Fixing TCG Expansion Sets
7 Trading Systems
What Are Trading Systems?
What’s a Trade?
Mechanics of Direct Trades
Establishing Limits
Prolonging Play
Preventing Exploitation
Preventing Kingmaking
Reducing Complexity
Limited Information
Costs
Futures
Mechanics of Gifting
Strengthening Retention
Promoting Virality
Mechanics of Auctions
Setting Time Limits
Setting Reserve Prices
Setting Buyout Prices
Setting Negative Effects
Limiting Information
Enabling Sellers to Bid
Auction Formats
Quantity of Items Up for Auction
Payment in Auctions
Where Does the Money Go?
Underbidding
How Trading Affects Balance
Players Buy Time
Players Look for Exploits
Players Are Encouraged to Trade
Players Have a Mind of Their Own
How Gifting Affects Balance
Discussion Topics
Sidequests
Sidequest 7.1: Multiplayer Auction Chaos
Sidequest 7.2: The Trading Game
8 Transitivity and Cost Curves
Transitivity
Costs and Benefits
Cost Curves
Peaks and Valleys in the Cost Curve: Deliberately Unbalanced?
Supporting Math
Creating the Cost Curve for PvE Games
Creating the Cost Curve for PvP Games
Creating the Supporting Math
Cost Curves in New Games
Cost Curves in Existing Games
Analyzing and Studying Existing Analog Games
Looking at Trends
Analyzing and Studying Existing Digital Games
Analyzing and Studying Free-to-Play Games
Cost Curve Guidelines
Discussion Questions
Sidequests
Sidequest 8.1: Using the Supporting Math
Sidequest 8.2: Weaponization
Rogue’s Main Quest, Part 4: Finding the Cost Curve
Wizard’s Main Quest, Part 3: Updating the Costs for Harmony
9 Characters and Character Builds
Character Creation Systems
Character Selection
Attributes (or “Stats”)
Skills
Equipment
Character Classes
Levels of Viability
Balancing for Character Progression
God Stats, Dump Stats, and Meaningful Decisions
Balance and Player Perception
Additional Resources
Discussion Questions
Sidequests
Sidequest 9.1: Three Attributes, Three Builds
Sidequest 9.2: Classes for Players
Fighter’s Main Quest, Part 4: Analyze a Combat
10 Combat
What is Combat?
The Feel of Combat
The Camera
The Sound
The Look and Feel of the Weapons
The Look of the Impact
The Celebration
Clarity
The Timing
Feel vs. Solution
The Pillars of Combat
Genre
Time
Pacing
Feel
Participants
Progression Type
Volume
The Constraints of Combat
Length of Game
Length of Combat and Number of Combatants
Frequency of Combat
Number of Combatants
Number of Hits
The Variety of Combat
Variety of Visuals
Variety of Numbers and Numbers within Levels/Areas
Variety of Behaviors
Variety of Counters
Variety of Players, Player Characters, and AI Characters
Time Outside of Encounters
Genre Specialization and Player Pressure
Calculating Player Power vs. Enemy Power
Play is Required (and Required (and Required))
Difficulty Levels
Response to Player
Pay-To-Win
Melee vs. Ranged Combat
Managing for Degenerate Strategies
The Illusion of Winnability—Chris Crawford
Additional Resources
Discussion Questions
Sidequests
Sidequest 10.1: Roll-and-Move Combat
Sidequest 10.2: RPG Asset Budget
Rogue’s Main Quest, Part 5: Create a New Mechanic
Fighter’s Main Quest, Part 5: Combat Simulator
11 Progression in PvE Games
Balance in PvE
Resistance to Progression
Actual vs. Perceived Progression
The Four Elements of Perceived Difficulty
Progression Arcs and Loops
Velocity and Acceleration
Regression and Loss
Juiciness
Types of Progression
Motivations for Progression
Desire for Agency → Stat-Gain Loop → Virtual Skill
Desire for Mastery → Difficulty/Complexity Loop → Player Skill
Curiosity → Discovery Arc → Player Knowledge
Desire for Closure → Accomplishment Arc → Completion
Social Progression
False Progression
Reward Schedules
Common Problems in PvE
Increasing Player Skill
Differing Player Skill Levels
The Commander Problem
The Elder Game
Progression as Artificial Gating
Difficulty Appropriateness for Audience
Additional Resource
Discussion Questions
Sidequests
Sidequest 11.1: Removal of Level Caps
Sidequest 11.2: Reward Schedules
Sidequest 11.3: Modeling Rewards
Fighter’s Main Quest, Part 6: Reward Schedules, Revisited
12 Progression in PvP Games
Why Progression in PvP?
Positive, Negative, and Zero Sum
Feedback Loops
Power Curves
Positive Sum, Positive Feedback
Positive Sum, Negative Feedback
Zero-Sum, Positive Feedback
Zero-Sum, Negative Feedback
Zero-Sum, Positive, and Negative Feedback
Negative Sum, Positive Feedback
Negative Sum, Negative Feedback
Game Length
Revisiting Flow
Common Problems in PvP
Turtling
Killing the Leader and Sandbagging
Kingmaking
Player Elimination
Balancing Asymmetry
Discussion Questions
Additional Resource
Sidequests
Sidequest 12.1: Player Power in Monopoly
Sidequest 12.2: World War III
Rogue’s Main Quest, Part 6: Create a Mini-Expansion
Wizard’s Main Quest, Part 4: Card Balance
13 Analytics
What Is Analytics?
Metrics
A Question of Ethics
The Process of Balance through Analytics
Finding the Key Questions
Strength of a Claim
Data Visualization
Additional Resource
Discussion Questions
Sidequests
Sidequest 13.1: Analytics Plan
Rogue’s Main Quest, Part 7: Playtest, Iterate, and Finish
Fighter’s Main Quest, Part 7: Analytics Plan for Remake
14 Metagame Systems
Rankings and Ratings
Rating Systems
Harkness
Elo
Glicko
TrueSkill™
Online Rating Systems
Masterpoints
Common Problems with Rating Systems
Encouraging Activity
Luck and Skill
Matchmaking
Rating Inflation and Deflation
Handling Draws
Multiplayer Games
Disconnection
Cheating
Ratings as Outcome Prediction
Additional Predictors of Outcome
Proving the System
Ranking Systems
Granularity
Community
Permanence
Subjectivity
Progression
Tournament and League Play
Round Robin
Single Elimination
Double Elimination
Swiss
Hybrid
League and Season Play
Handling Dropouts
Metagame Reward Systems
Discussion Questions
Sidequests
Sidequest 14.1: Elimination
Sidequest 14.2: The Alpha Rating System
Sidequest 14.3: Elo with Luck
Sidequest 14.4: Swiss Deathmatch
Wizard’s Main Quest, Part 5: Harmony Ratings
15 Production and Playtesting
Balance throughout Development
Early Development
First Playable
Pre-Alpha
Alpha
Beta
Post-Launch
Playtesting for Balance
Additional Resources
Discussion Questions
Sidequests
Sidequest 15.1: Cheat Codes
Sidequest 15.2: BattleBattle
Wizard’s Main Quest, Part 6: Playtest Your Cards
16 Beyond Balance
Wrapping Up
Perfect Imbalance
Counters All the Way Down
Balance and Fun
Imbalance in We Didn’t Playtest This At All
Imbalance in The Great Dalmuti
Imbalance in Betrayal at House on the Hill
Balance in Story-Heavy Games
Balance, Fairness, and Expectations
Numbers Aren’t Always Balance
What’s Next?
Additional Resource
Part II: The Mathematics of Balance
17 Independent Randomness
Non-deterministic Mechanics
Die Rolls and Independence
Probability, Odds, and Chance
Computing-Independent Probability
Rolling One Die
Rolling Two Dice
Rolling Far Too Many Dice
Rolling Dice in Sequence
Negation: the Probability of Failing
Combining Results
Expected Values
Permutations
The Law of Large Numbers
Summary
Additional Resource
Discussion Questions
Sidequests
Sidequest 17.1: Bad Player
Sidequest 17.2: Kill the Elf, Redux
Sidequest 17.3: Horse Race, Redux
Sidequest 17.4: Pig AI
Sidequest 17.5: The Amazing +1 Bonus
Sidequest 17.6: Meanwhile, Back At The Inn…
Sidequest 17.7: Collecting Dragon Eggs
Sidequest 17.8: Rare Loot Drops
18 Dependent Randomness
Dependent Events
Card Draws and Dependence
Computing Dependent Probability
Drawing Two Cards
Drawing Two Cards with Uneven Distribution
Permutation and Combination
Counting Shuffles
Discussion Questions
Sidequests
Sidequest 18.1: Really Big Flush
Sidequest 18.2: Multiple Turns in a Row
Sidequest 18.3: Three and Three vs. Four and Two
Sidequest 18.4: War Lite
Sidequest 18.5: Magic Redux
Sidequest 18.6: Hearthstone Opening
Sidequest 18.7: Battleship AI
19 Managing Luck and Skill
Beyond Randomness
A Series of Paradoxes
Opportunities for Skillful Play
Frames of Reference
The Double Axis
Kinds of Skill
Kinds of Luck
Kinds of Uncertainty
Kinds of Information
Skill vs. Luck
Do These Distinctions Matter?
Modifying Skill and Luck
Additional Tradeoffs
Discussion Questions
Sidequests
Sidequest 19.1: Experiments with Input and Output Randomness
Sidequest 19.2: Depth of Strategy in the Land of Candy
20 Probability and Human Intuition
Probability Isn’t Always Intuitive
Expected Value and Utility
Cognitive Biases and Fallacies
Selection Bias
Self-Serving Bias
Dunning–Kruger Effect
Attribution Bias
Anchoring
The Gambler’s Fallacy
Hot-Hand Fallacy
Design Solutions to Deal with Human Idiocy
Exploitation
Dealing with Biases
A Question of Ethics
An Honest Solution
Additional Resource
Discussion Questions
Sidequests
Sidequest 20.1: A Monopoly on Fairness
Sidequest 20.2: Exploitification
Sidequest 20.3: Evil Gambling Game
21 Pseudorandom Numbers
Analog Randomness
Pseudorandomness
Saving and Loading
Pseudorandom Shuffling Algorithms
Discussion Questions
Sidequests
Sidequest 21.1: Test Your RNG
Sidequest 21.2: Another Card Shuffling Algorithm
Sidequest 21.3: Large Deck Shuffling
Sidequest 21.4: Cracking Your Own RNG
Sidequest 21.5: Exploiting the Save System
22 Infinite Probability
An Infinite Problem
Matrices
State Machines
Converting State Machines to Matrices
Yahtzee
Risk
Discussion Questions
Sidequests
Sidequest 22.1: Thunderstorm
Sidequest 22.2: Hi Ho! Chery-O
Sidequest 22.3: Mordenkainen’s Magical Rubber Band
Sidequest 22.4: Kill the Elf as a State Machine
Sidequest 22.5: Horse Race, Exact Solution
Sidequest 22.6: Two in a Row
23 Situational Balance
What Is Situational Balance?
A Simple Example
Implications for Game Designers
Versatility
Complete Inability to Change
Unrestricted Ability to Change
Versatile Objects
Shadow Costs
Sunk Costs
Opportunity Costs
Discussion Questions
Sidequests
Sidequest 23.1: Desktop Tower Defense
Sidequest 23.2: DOOM
24 Statistics
What Is Statistics?
Fundamental Statistical Calculations
Outliers
Statistical Significance
The Z Test
Correlation
Common Mistakes
Anscombe’s Quartet
Sample Size
Sample Bias
Programming
Miscalculation
Correlation and Causality
Frequentism and Bayesianism
Discussion Questions
Sidequests
Sidequest 24.1: Gender in Games
The Applicant Pool
Selection Bias
Sidequest 24.2: The Average Dalmuti
Alternate Challenge
25 Intransitive Mechanics and Payoff Matrices
Intransitive Mechanics
Solving Intransitive Mechanics
Solving Basic Rock-Paper-Scissors
Toward a Steady State
Solving Rock-Paper-Scissors with Costs
Solving Rock-Paper-Scissors with Incomplete Wins and Losses
Solving Asymmetric Rock-Paper-Scissors
Solving Rock-Paper-Scissors-Lizard-Spock
Solving Rock-Paper-Scissors-Dynamite
Solving Rock-Paper-Scissors-Jackhammer
Solving Game of Malkav
Solving Three-Player Rock-Paper-Scissors
Summary
Discussion Questions
Sidequest 25.1: Three-Player Rock-Paper-Scissors with Fewer Draws
Sidequest 25.2: A Fighting Game
Sidequest 25.3: Five Cards Battle
Part III: Spreadsheets
26 Making Lists
Sidequests
Sidequest 26.1
27 Basic Formatting
Sidequests
Sidequest 27.1
28 Formulas, References, and Graphs
Graphing
Sidequests
Sidequest 28.1: Graphing Common Curves
29 Absolute References
Sidequests
Sidequest 29.1: Graphing Supply and Demand
30 Advanced Formatting
Sidequests
Sidequest 30.1: Build a Level
Sidequest 30.2: UI Design
Sidequest 30.3: Cost Curve Formatting
31 Math Functions
Pseudorandom Functions
Statistical Functions
Conditional Functions
Monte Carlo vs. Brute Force
Sidequests
Sidequest 31.1: 4d6 Brute Force Speedrun
Sidequest 31.2: Correlation of Chance
32 Deck Shuffling
Loot Drops
Sidequests
Sidequest 32.1: Shuffling a Deck
Sidequest 32.2: Poker Probabilities
Sidequest 32.3: Automated Game Design
33 Organizational Formatting
Working with Worksheets
Cell Formatting
Data Validation
Long Text
Named Formulas
Sidequests
Sidequest 33.1: Human or Robot?
Sidequest 33.2: Word Cloud
34 Times and Dates
Sidequests
Sidequest 34.1
Sidequest 34.2
35 Iterative Calculations
Sidequests
Sidequest 35.1: Rock-Paper-Scissors AI Pair
36 Fancier Graphing
Graphing Options
Kinds of Charts
Sidequests
Sidequest 36.1: Tiny Graphs
37 Matrix Functions
Implementing a Markov Chain
Calculating a Payoff Matrix
Solvers
Sidequests
Sidequest 37.1: Trust but Verify
Sidequest 37.2: Build a Matrix Auto-Solver
Appendix: Game Genres
Index
