Diablo 3 - item sets

Modern item games like Diablo 3 (D3) use a mechanic called sets: when used together, certain items unlock particular bonuses. For example in D3, Litany of the Undaunted increases attack speed, The Wailing Host increases crit chance, and used together they give 15% extra gold from monsters. Item sets is an old mechanic - the Diablo 2 expansion already had some in 2001.

Sets in D3 are a great mechanic for at least two reasons. First, sets let developers encourage the use of certain skills. Since the bonuses from set items nearly always provide more damage than regular non-set items, players use them. For example, the Marauder set for Demon Hunters requires the use of sentries, a skill that would not be used otherwise because its AI for picking a target is unpredictable. Second, set items are a great mechanic also because they give players a goal. When I dropped my first set item and saw the set bonuses, I immediately wanted other items in the set.

Sudden increase in power

End-game starts after reaching level 70. Reaching level 70 by yourself takes roughly 15 hours. Difficulty from then on can be measured by the Greater Rift (GR) level your character can reach. Set bonuses are so powerful that they make your character jump multiple GR levels at once. For example, going from 5 set items to 6 can double your character's effective damage or toughness, and make you reach 5 or 6 GR levels higher. This explains why the Ring of Royal Grandeur, which reduces the number of items needed for set bonuses by 1, pretty much a wild-card for all your sets, is such a game-changer. These sudden increases in power sometimes surprise players, but I think each bump makes them suddenly feel very powerful. Interestingly, back in 2013, sets used to be as good as non-set legendary items.

Vague descriptions or hidden mechanics?

The descriptions of D3 set bonuses are often vague, and require the player to check the forums and Youtube videos for details. Here are two examples.

Marauder set

This is a Demon Hunter set. The 2-piece bonus is straightforward: it gives 500 dexterity (on top of the approximately 500 dexterity already contributed by each set piece).

The 4-piece bonus makes the Companion skill call all possible companions (instead of only one). Do passive effects from the Companion skill (e.g. the boar increases life regeneration) apply as well? And do all active effects trigger when I use the skill? The answers are not written in the description, but people figure it out quickly by trying.

The 6-piece bonus reads: Sentries cast your equipped Hatred spenders. After trying it out, I realized that sentries have a different rate of fire for each spender: Cluster Arrow (massive area damage) seems to happen only every 5 shots, whereas Elemental Arrow (small multi-target damage) the rest of the time. Looking at high-level Demon Hunters, most wear Tasker and Theo, which increases the attack speed of your pets by 40-50%. Are sentries pets? (Yes!) And how can I make my sentries use Cluster Arrow more often? (You can't!) Theorycrafters figured it all out by analyzing game frames one by one and sharing their findings. But is the average player supposed to read the forum to improve their character?

Zunimassa set

This is a Witch Doctor set. The 2-piece bonus gives 250 intelligence and grants 30 Mana per Kill. Is it only when my character performs the killing blow on a monster? Does it also work when it's one of my pets? Does it also work when it's another player?

The 4-piece bonus reads: Your Fetish Army (FA) lasts until they die. This is straightforward, and it made me think about the passive skill Fetish Sycophants (FS). FS seems to combo well with FA: When you hit enemies with your spells, you have up to a 10% chance to summon a dagger-wielding Fetish to fight by your side for 60 seconds. There are several problems with this apparent FA-FS synergy.

First, why the up to? What makes the rate be less than 10%? That is where theorycraft comes to the rescue. The community found out that one can have at most 15 active FS at the same time. So the rate of FS trigger is 10% until 15, at which point it becomes 0%. The description of FS should also mention this cap of 15.

A second problem is the easy confusion between the two types of fetishes. 1) Witch Doctors can have many pets: a Gargantuan, zombie dogs, FA fetishes, FS fetishes, and mimics. FA and FS are both fetishes, so intuitively, they must benefit from the same bonuses. 2) Why excluding FS from the 4-piece bonus when the effect from the Carnevil helm applies to both FA and FS? 3) The distinction between FA and FS is not for game balance: in practice, it's very easy to maintain 15 FS active all the time by speeding through monsters.

Why so vague?

I can see several reasons:

• Practicality: the developers want to be able to modify the bonus (through hotfix or patch) without modifying the description.
• Brevity: a precise description may require too much space in the item tooltip.
• Practice: figuring it out by trial is more visceral than by just reading the description.
• Theorycraft: explaining everything spoils the fun of theorycrafters.

Uselessness, sub-optimality, and combinatorics

Some sets are clearly underpowered compared to others. The Witch Doctor Invoker set and the Demon Hunter Shadow set are only useful when your character gets hit. Sadly, in D3, the best defense is offense: the goal is to kill monsters quickly enough that they don't kill you. Therefore these sets end up never being used (except the 2-piece Shadow set in hardcore mode, maybe?).

The Natalya set is not useless, but rather suboptimal. Both the 2-piece and 3-piece bonuses increase damage slightly and enhance mobility (more discipline means more Vaulting). The 4-piece bonus reduces the cooldown of Rain of Vengeance by 2 seconds for each enemy you kill. RoV has a base cooldown of 30 seconds, and does 1000% area damage for 5 seconds, so the set seems very interesting. In practice however, it is difficult to keep monsters grouped in an area for 5 seconds. So while some players use the 2- and 3-piece bonus, nobody cares about the 4-piece bonus. I wonder if the set would be more used if the cooldown was reduced by 2 seconds for every enemy hit (instead of killed).

ArcheAge boasts 120 classes, but it's only because players can pick 3 skill trees among 10, ie C(10,3) = 120 different combinations of skill trees. I don't think that all combinations are efficient, but ArcheAge achieves such diversity simply by leveraging combinatorics on 10 coherent sets of skills. In D3, a player using a Demon Hunter can pick 6 active skills among 24, so that's a total of C(24,6) = 134k different builds. Add to this that each active skill has 4-5 runes, and that there are also another 4 passive skills (5 if we count the Hellfire Amulet) to pick among 18. That's billions of combinations! Yet the only sustainable Demon Hunter builds actually played are minor variations around the same 6 skills. That is because the Marauder set forces players to pick these skills. Moreover, I really liked combining multiple 3- and 4-piece sets together, but the 6-piece Marauder took all the spots. I wish D3 had 1) more 4-piece sets and fewer 6-piece sets, and 2) combinations between sets, not just between sets and legendary items (e.g. Marauder and Tasker and Theo)

Diablo 3 - the item game

In item games, the main goal of players is to continuously upgrade their gear. Diablo 3 (D3) is the perfect example: kill monsters in order to drop better gear in order to kill monsters faster. Bungie just released Destiny, an item-game FPS budgeted with half a billion dollars. Yet Destiny could learn from Diablo 3. So here are some thoughts about the item game in D3.

Prevent farming ...

In D3, like in D2, the drops are completely random: with a few exceptions, nearly any item can drop from any monster or wreckable object (e.g. jars). The odds are just higher for harder monsters, and way lower for wreckable objects. The exact drop rates are secret (except the 10% legendary drop rate from Kadala). This secrecy has led to various rumors and tinfoil hat theories about how loot can be influenced.

D3 has, or used to have, farming spots such as the Decaying Crypt, but they were mostly for XP, not for drops. In D3, farming boss monsters actually brings fewer drops than farming normal or elite monsters. This contrasts with Diablo 2, where players were grinding bosses like Baal or Diablo for XP and loot. So in a way, the grind in D3 is less boring than in D2.

... Yet allow farming

As of October 2014, there are 2 exceptions to what I just wrote: 1) bounty rewards like RoRG or Helltrapper, and 2) Hellfire Amulet.

The RoRG was introduced in February 2014. It is a mandatory item to reach the game's highest difficulty levels. Players have to camp Act-1 bounties to get one with good rolls. To farm as quickly as possible, players join co-op games to split farm: instead of spending 15-20 minutes completing the 5 bounties together, they each complete a bounty in 5 minutes. I am surprised that the developers did not see it coming: split farming is very clearly not how we want players to play the game. Yet nearly a year later, they still have not changed the bounty system.

The Hellfire Amulet is not as mandatory compared to the RoRG. But its bonus is so useful that all of the top players have it. Farming it is somewhat more fun than farming for RoRG, since it is a quest in itself: a) hunt for the 4 Keywardens on the game's largest maps to obtain 4 keys, b) combine the 4 different keys into a portal, c) kill 2 super bosses at once, a somewhat more difficult task than the Keywarden hunt, and d) combine 4 super bosses' loots to obtain a Hellfire Amulet.

The Reaper of Souls expansion

From launch in May 2012 until the retirement of the Auction House (AH) in February 2014, players were mostly buying their gear from the AH, and sometimes grind-crafting it. They nearly never dropped it themselves. Legendary weapons had 7-8 affixes. After the AH retired, Loot 2.0 arrived, and the expansion Reaper of Souls (RoS) shortly after that. Legendary weapons now have 4 primary and 2 secondary affixes. Secondary affixes do not matter much (e.g. more XP when killing a monster), so RoS drastically reduced the item entropy.

The expansion also reminded me of Blizzard's somewhat elegant solution to a common MMO problem. Most MMOs in the early 2000s had the same problem: players who have been playing for a year have too much of a head start compared to players who have been playing for 3 months. New players are hopeless, especially in PvP situations. World of Warcraft solved this problem with what I call expansion gating: WoW vanilla capped the character level at 60 and item level at 92. Until the first expansion came out to increase these two caps, players were gated there. The advantage of expansion gating is that it gives the same chance to old and new players. The main drawback (if any) is mudflation. Diablo 3 is no different: level-70 items have twice more DPS than level-60 items. Thus when the expansion launched, players threw away all the gear they had acquired before.

Few links to other end-game activities

Item games have a great loop, but it is not enough in itself. D3 launched in May 2012. The Auction House (AH) launched in May 2012 too, so players could play two games in one: the action RPG and the auction game. Note that you did not need to play the aRPG to play the auction game, but you did need to buy gear off the AH to play the aRPG well. Had it been the opposite, I think the game would have been much better.

In July 2012, the developers realized that the item hunt is just not enough for a long-term sustainable end-game. Since launch, the game also allowed players to hunt for achievements and start new characters (in softcore or hardcore). In August 2012, the developers added the leveling up grind through 100 Paragon levels. Every Paragon level increased the chance to drop an item and the amount of gold dropped by 3%. In February 2014, Paragon levels became infinite, and the 3% bonus was removed. Clans and communities were also added in February 2014. Since August 2014, players can compete on the greater rift leaderboards, and start new seasonal characters (in softcore or hardcore). Interestingly, the item game is completely independent of all other end-game activities (except the AH and the original 100 Paragon levels increasing magic find and gold find). In other words, the item game of Reaper of Souls could be directly copied into another game without having to also copy the other activities.

[Literature] Game Balance ch2 - Numerical Relationships

My notes from course 2 of the Game Balance class of Summer 2010, by Ian Schreiber.

Numbers only have meaning in relation to each other. A few kinds of numerical relationships:

• identical (1:2:3:4)
• linear (2:4:6:8)
• exponential (2:4:8:16)
• triangular (1:3:6:10)

It is much easier to balance a system when you can put everything in terms of a single central resource. For example in CRPG such as Final Fantasy, everything can be put in terms of HP (gold is used to buy stuff to reduce dmg, hence increasing HP). In 2D platformers, the loss condition is lives (sometimes, it is score), and everything is tied to it.

Various loops in CRPG

XP - encounters: more encounters gets you more XP. Your level increases, and so do your stats, which in turn lets you face more encounters. The feedback loop here is not exactly positive, because as the level increases, the number of encounters needed to level up increases (non-linearly).

Equipment - encounters: Fight monsters, get gold, use it to buy better equipment, which lets you fight better monsters for even more gold and so on. This stops being a positive feedback loop at some point because there’s a limited set of equipment you can buy, and the best stuff requires you to travel to distant towns which can’t be reached from the start.

Gold - encounters: get more gold, which lets you buy keys, which lets you progress to new areas, which gets you to more dangerous and advanced encounters for more gold. Truly positive.

In RPG, the XP system serves as a negative feedback loop: higher-level players need to kill more monsters than low-level players. The designer can know quite precisely the level of the player, which makes it easy to design adequately challenging enemies. A fast leveling at the start is useful: it hooks up the player.

Drop systems

Traditional

In MMORPGs, monsters have a list of items they can drop when they are killed. A player can get 0, 1 or more items from the same monster, but a dice is rolled for EACH of the dropable items.

WoW: To get Zod's Repeating Longbow, one knows Lady Deathwhisper is the only one monster to be killed. The game rolls a 1000-sided dice, and if 136 or below comes out, the bow is dropped. However, one can also drop the Nibelung from Lady Deathwhisper at 15.6%. Hence, approximately 2.1% of the time, the dragon will drop both the Longbow and the Nibelung, and maybe other things as well.

RO: To get an Ice Pick, one has to kill Eremes, LoD or RSX, but they drop it at respectively 15%, 0.1% and 0.05%. But Eremes also drops Glittering Jacket at 90% or Exorciser at 35%. So 4.7% of the time, Eremes will drop at least these 3 items.

Procedural

Roguelikes generate a lot of their content procedurally. Unlike MMORPGs, roguelike drops are most of the time randomly-generated: monsters do not drop specific items at certain percentage, they drop classes of items.

Diablo (and Diablo II): the drop system consists of Treasure Classes (sets of items) and a drop process. When a player kills a monster, a first random number is used to determine which TC will be dropped. For Andariel, some of these TC are armo18 (1.02%), weap69 (0.017%) or nothing (28.35%). All monsters have the sum of their TC = 100%. In other words, 28.35% of the time Andariel will drop nothing, and the rest of the time, it will drop one item. Once the TC has been chosen, another random number comes out for "the odds". "The odds" is the chance a particular item is chosen from a TC. For the weap69 TC, the Eldritch Orb has 1/15 chance to be selected. In the end, a player has around 0.001% chance to drop exactly the Eldritch Orb from Andariel. But Baal also drops the weap69 TC at 0.54%, so Baal can drop Eldritch Orb at 0.54% * 1/15 = 0.036%. Finally, various elements such as the item property (fire, ice, ...), name prefixes/suffixes or durability are generated.

Scheduled

Team Fortress 2: the Item Drop System used to give (at 25% chance) a weapon to the player every 25 minutes of game. To avoid unlucky streaks that players complained about, Valve changed it: every time an item drops, the time of the next drop is determined.