GDEV20-08-Theorycrafting PDF

Complexity More or Less, That is the Question Lecture Time! Complexity: Scapegoat of the Accessibility Argument Meaningful Play: Related to Complexity? Theorycrafting: Overview Case Study: Maze Navigation (program demo) Why do puzzle games tend to get boring really quickly? Review: MD...

Complexity More or Less, That is the Question Lecture Time! Complexity: Scapegoat of the Accessibility Argument Meaningful Play: Related to Complexity? Theorycrafting: Overview Case Study: Maze Navigation (program demo) Why do puzzle games tend to get boring really quickly? Review: MDA Framework Complexity can be found where? Assuming the game is already playable, what is responsible for the answer of the first/above question? What is the relationship between a game’s features and the answer of the second/above question? Features In an ideal world: All games match the design document version Patches add more content without adding bugs, exploits, and other undesirables http://gatherer.wizards.com/Handlers/Image.ashx?multiverseid=2051&type=card Features In reality, some features do get cut; reasons include: No more resources (time, money, manpower, etc.) to implement or maintain the feature The feature is not part of the game and/or it is not fun The feature is complicated enough to require a relatively steeper learning curve Then Why’s It In The GDD? Discuss the differences: SimCity 1 vs Cities: Skylines Call of Duty series vs Unreal Tournament series Legend of Zelda: BotW/TotK vs Genshin Impact World of Warcraft vs Final Fantasy 14 vs Tarisland Granblue Fantasy vs Granblue Fantasy: Versus vs Granblue Fantasy: Relink Fear of Sequels Sequels (and patches/expansions) can be viewed as attempts to refine the core/original game Undesirable features are removed or modified (ex. bugs, auction house) New features added (ex. idle/offline crafting, auction house) More content added to core features (ex. new abilities, raised level cap) Players Are Not That Stupid https://news.blizzard.com/en-us/diablo4/23964909/diablo-iv-patch-notes Players Are Not That Stupid There are complex game series that continue to have a large player audience: The Sims The Elder Scrolls Diablo Final Fantasy The Legend of Zelda Players Are Not That Stupid Complexity is NOT the sole factor to blame for a game’s lack of accessibility Sometimes, adding complexity is necessary Changing flat percent boosts to a rating system (ex. 1% crit chance at lv 60 becomes 14 critical strike rating) Adding rules (ex. strength now affects non-combat interactions such as intimidate)... OK, Sometimes They Are https://kotaku.com/resident-evil-4-remake-design-crate-sign posting-obvious-1850238136 https://www.reddit.com/r/ffxiv/comments/w9j5fb/do_people _really_not_read_their_tooltips/ Games are NOT New! Before video games, we had pen & paper games, board games, etc. And they had rules/features too! Some games had numerous and/or complicated rules RPGs (like Dungeons & Dragons) Wargames (like Advanced Squad Leader) Games are NOT New! With or without assets, electronic games based on or duplicating these rule-dependent games benefited from computers doing the number-crunching and resolving actions like combat Old computers (pre-2000) could still perform millions of operations per second Wait, Back Up a Bit Before video games, we had pen & paper games, board games, etc. And they had rules/features too! Some games had numerous and/or complicated rules RPGs (like Dungeons & Dragons) Wargames (like Advanced Squad Leader) Complex Games What makes a game “complicated”? What makes a rule “complicated”? Can a single complicated rule make the game complicated? https://upload.wikimedia.org/wikipedia/commons/f/f7/Apples_in_a_basket.jpg No Man Rule is an Island Mechanics = rules, including available player actions Mechanics alone do not dictate game complexity, but there is a connection https://upload.wikimedia.org/wikipedia/commons/8/86/Steel_ruler_closeup.jpg No Man Rule is an Island Dynamics = interactions among rules, including those involving player actions with other parts of the system Complexity occurs as a result of these interactions Grand Blues!, episode 1 Meaningful Play VS Complexity Does this mean that complexity equals meaningful play? Increased range of player actions Increased variety of possible situations where players can perform actions Permutations and combinations, anyone? What exactly is “easy to learn, difficult to master”? Meaningful Play VS Complexity Meaningful play deals with the relationship between decision and outcome Casting a fireball on an oil-coated enemy will result in seeing a higher damage number and being able to defeat the enemy that much more quickly So casting it looks like a good decision Meaningful Play VS Complexity Complexity is about the way parts relate to each other in a system, which does not necessarily include player decisions A fireball, as a fire spell, does +X% more damage on an oil-coated enemy, where X is determined by the oil's combustibility No one said anything about you casting it on an oil-coated enemy, but the option to do so is there And It's Worth Repeating Over and Over Complexity is a prerequisite of meaningful play! Complexity Fuels Meaning In games where meaningful play does exist, some aspect of the game system is complex No complexity means no decision-making opportunities Zoku Natsume Yuujinchou, episode 4 Case Study: DPS Some players try to mathematically analyze games to get a better understanding of its mechanics Known in some circles as theorycrafting With the help of math and statistics tools, theorycrafters determine if that “upgrade” is really an upgrade, how much of an upgrade it really is, and if there's a better-but-not-as-obvious upgrade out there Case Study: DPS In MMORPGs, one focus of theorycrafting is damage-per-second (DPS) – being able to output the maximum amount of damage on average What goes into computing this? Let’s find out! Simple Start Consider a weapon that does 100 damage every time you attack with it, and you can only attack every second 100 damage / 1 second = 100 DPS Another weapon deals 250 damage, and you can attack every 3.2 seconds. Is it better? 250 damage / 3.2 seconds = 78.125 DPS Simple Start Special case: What if you can make an attack at the very start (meaning the swing timer only kicks in after the first attack), and what if the enemy had 200 life? This scenario usually doesn't matter to theorycrafters unless it happens frequently or it's part of a bigger scenario But yes, the second weapon results in a quicker kill Introduction of Chance Weapon deals 80-120 damage every 1 second Formula must now take variance into account Solution: Always consider the average! Average damage = (80 + 120) / 2 = 100 100 damage / 1 second = 100 DPS Introduction of Chance 50-200 damage every 1.25 seconds Average damage = (50 + 200) / 2 = 125 125 damage / 1.25 seconds = 100 DPS Gamblers might prefer this one because of its potential for “burst” damage in the form of consecutive high-damage attacks More Chance Land a critical hit = do double damage (damage x2) 100-400 damage, 3.0 seconds per swing, and chance for a critical hit is 10% Solve for actual average damage per swing first, then divide by the swing timer More Chance AvgDmgPerAtk = (AvgBaseDmg * 90%) + (AvgBaseDmg * 2 * 10%) DPS = AvgDmgPerAtk / timer = [([(100+400) / 2] * 0.9) + ([(100+400) / 2] * 2 * 0.1)] / 3.0 = [(250 * 0.9) + (500 * 0.1)] / 3.0 = 91.6667 DPS (rounded) Even More Chance Base damage = 300-500 Chance to hit = 90% Chance for the hit to be a critical = 10% Swing timer = 2.8 seconds AvgBaseDmg (ABD) = (300+500) / 2 = 400 90% = chance to hit, which means 10% = chance to miss Even More Chance Each hit has a 10% chance to be a critical Therefore, chance to critically hit is 90% * 10% = 9% and chance for a regular hit is 81% Check “table”: Miss% + Hit% + Crit% = 10%+81%+9% = 100% AvgDmgPerAtk (ADPA) = (0 * 0.1) + (ABD * 0.81) + (ABD * 2 * 0.09) = 0 + 324 + 72 = 396 DPS = ADPA / timer = 396 / 2.8 = 141.428571 (rounded) Uh… Haste affects weapon speed New swing timer (SWT) = Old swing timer / (1 + Haste%) From previous example, now with 10% haste SWT = 2.8 / (1 + 10%) = 2.55 (rounded) DPS = AvgDmgPerAtk / SWT = 396 / 2.55 = 155~ Uh… If haste is multiplicative, then: If you had personal 10% haste, and then you were given another 10% haste aura, your total haste would be (1 + PersonalHaste%) * (1 + AuraHaste%) = 1.21 SWT = 2.8 / 1.21 = 2.31 (rounded) DPS = AvgDmgPerAtk / SWT = 396 / 2.31 = 171~ But I Hate Division It is recommended that you convert the swing timer to attacks per second before doing anything BaseAPS = 1 / SWT = 1 / 2.8 = 0.357~ NewAPS = BaseAPS * 1.1 * 1.1 = BaseAPS * 1.21 = 0.432~ DPS = AvgDmgPerAtk * NewAPS = 396 * 0.432~ = 171~ NO I'VE HAD ENOUGH Base Damage = 650-950, Hit = 95%, Crit = 25%, Personal Haste = 20%, Aura Haste = 5%, Base Swing Timer = 1.7 seconds Average base damage? 800 Average damage per attack? 950 Actual swing timer after haste? 1.349~ DPS? 704.11~ SOMEONE SAVE ME We didn't include (not a complete list): Abilities other than regular attacks Consistent but temporary buffs/debuffs Abilities with cooldowns Enemy defenses However, you now have an idea of what both designers and players do when the need for math arises HUHUHU What if you had to compute HPS (healing-per-second)? What if you had to compute HPM (healing-per-mana)? You have one heal spell: costs 50 mana, cast time is 2 seconds, base heal amount is 100 to 150, never misses Add 10% chance to crit to heal for double the amount Add 10% haste HUHUHU What if you had to compute EHP (effective health pool)? You have 1000 hit points Add armor that reduces damage taken by 10% Add 10% chance to dodge to avoid all damage of a dodged attack Add 40% chance to block to reduce damage by another 25% (multiplicative) MAMI What if you want to tune a particular boss fight so that a group of 4 players must have at least a total DPS of X to win in 5 minutes, otherwise the boss' triple-all-my-damage-kill-everything ability triggers? Note that the above “enrage timer” can serve as an effective time limit for players, but it isn't as strict as instant death No Rule is an Island A lot of thought (usually) goes into designing games If mechanics are dots, then dynamics is connecting the dots and aesthetics is the resulting fun Which brings us to our game design document deliverable Up next: Outcomes and Uncertainty