# Determining Drop Rates

Dropped items, experience points, and even gold pieces are Value entering the system. Your goal is to keep the value entering the system equal to the value leaving a system. Otherwise known as preventing Inflation.

This Value entering the market is like someone quickly turning on a faucet in a sink. Let's call the rate of money coming into the system: Vf. This Value spirals around inside the market (sink) to various people (or just stays with the player), and eventually drains out of the market removing Value from the economy. Let's call the total rate of Value coming out of the market as: Vd.

Thus, you want the following equation to hold true:

Vf = Vd

In God of War: Chains of Olympus, when I kill a monster it gives me Red Orbs (Vf). I accumulate Orbs over time, and then I open the menu and I spend these orbs to upgrade something (Vd). I have essentially traded on the Global MarketThe market defined by NPC Merchants. In most games NPC Merchants provide an infinite supply, they consume an infinite demand for any given item, and they are self contained so that trading within that market has no impact on either the player market or the NPC merchants., and in return I get to upgrade my Avatar CapitalThese are the abstract rewards we give the player, such as new skills and abilities. They have value, but they have no physical representation in the world. These are things that cannot be traded, but like Physical Capital, the impact on the player's production function will drive their importance.. This upgrade (my magic is more powerful) increases Kratos's ability to kill, and in turn increases the rate of Vf. See how it's all connected?

Let's take this example further with a fake MMO we are going to call: “World of Flarks” (COMING FALL 2023). The labor force is the number of people on a server, and due to the level of the mob I can guess the general level of Capital (Avatar and Physical) of the labor force. Assuming those values are fixed, then we are free to play with other variables in an effect to control our Vf. Things like the drop rate of the item, the spawn rate of the mob, the difficulty of the mob, and the Fixed Cost of the mob.

Let's define some values, and a sample mob.

# World of Flarks

  • Server Population: 2,000
  • Max Level: 20
  • Population at or above level 10: 500
  • Population between levels 9-12: 100

# Sword of the Flarkmaster

  • Value: 10g

# Flinkar the Weakling

  • Location: Forest of Losers (World Spawn)
  • Quantity in Zone: 1
  • Spawn Rate: 5 Minutes
  • Mob Level: 10
  • Difficulty: Low
  • Sword Drop Rate: 50%

Here we have Flinkar the Weakling, who has managed to acquire the Flarkmaster’s Sword. Oh Flinkar, you crafty little scamp you. He spawns in the world, so there are no fixed costs associated with killing him. He’s the only one of his kind in the game, and he spawns 12 times an hour. Since he is a low difficulty mob, player skill is less of an issue. Therefore, I will assume that all players at (or above) level 10 can use this resource.

Since there are 500 potential users that match this criteria I can assume that this resource is being Perfectly Consumed (he is killed and looted as soon as he spawns). Given this simple set up, I can determine the rate of value (Vf) entering the economy every hour.

Vf = (Kills Per Hours) x (Drop Rate) x (Sword Value)
60g = 12 x 0.5 x 10g

60g an hour is pretty high. Even given no information about our desired Vd, I think it’s safe to say that my economic goals are not being met. I have several options here. Since the value of the item and level of the mob are constant, I am left with changing the drop rate, adding fixed costs, or altering the mob spawn rate.

Let's try a different mob:

# Dinky the Diabolical Dinosaur

  • Location: Flarkmaster’s Grove (Instanced, 5 Man Dungeon)
  • Quantity in Zone: Optional Boss (1)
  • Summoning Materials Cost: 1g
  • Average Dungeon Length: 1 hour
  • Mob Level: 10
  • Difficulty: High
  • Sword Drop Rate: X

# Inflation Ceiling

  • 0.5g / hour

This is a more complicated scenario. The mob is now located in a dungeon, he has a cost for summoning him that must be paid, and he’s a difficult mob to boot. Also, this time we are going to start with a desired Vf (0.5g / hour), and solve for our drop rate.

The first new wrinkle is that I need to determine how quickly people are going to be killing this mob. From looking at the world statistics I see that the there are 100 players between the levels of 9 and 12, which feels like a good range for people that would be running this dungeon. However, Dinky is a pretty tough –it does say diabolical– Dino who requires more skill and better gear. Only 60 of those 100 players have the required Capital (H, K, and A) to effectively take down Dinky.

This is a 5 man dungeon, so those 60 players are grouped into 12 groups; additionally, it is an Instanced dungeon, which means that those 12 groups can all be running this dungeon at the same time. This assumes, however, that all 60 of those people are playing all the time, and they are always perfectly grouped with each other. From the article “Alone Together” it was shown that players only spend about 30-40% of their time in groups, so for the sake of this we can assume that only 3 to 4 groups are running concurrently at any given moment. Given that this is an optional boss we can reduce it to 3.

The last consideration is the Fixed Cost. Regardless of whether Dinky drops that sweet sword, every group must pay a fee of 1g in order to summon him. With this final bit I can finally draw up the new equation:

Vf = ((Kill Rate) x (Drop Rate) x (Sword Value)) — ((Kill Rate) x (Fixed Cost))
0.5g = (3 x DropRate x 10g) — 3g
3.5g = 30g x DropRate
0.117 = Drop Rate

Given this current mob, this current labor force, and this desired faucet value, the desired drop rate for this item is around 12%. A simple case, but you can see the power of thinking like an economist.