Game Balance

Description

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. 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