Hello math side of FR!
The game database gives us broad categories for coliseum drop rates, but I'm a numbers person, so I've done some grinding to determine-- what does "scarce" mean anyway?
The Numbers
On average, when you face any monster, the odds for the different loot categories are:
What're the Odds?
Let's say you want a particular item. To have a very certain (99%) chance of getting that item, you will need to face a monster that drops it:
That's an awful lot of grinding. To have a high certainty (95%) chance of getting that item, you will need to face a monster that drops it:
Relaxing down to a decent (75%) chance of getting that item, you will need to face a monster that drops it:
Even a 50% chance of getting an item can be a bit of a grind:
This is why the advice is often to buy a familiar rather than grind for it. Most familiars are rare, so it's not unusual to face it hundreds of times before finally getting that drop.
Of note: monsters typically have many possible "very rarely" loot items. Because there are so many, the odds of collecting any "very rarely" item (as opposed to a specific one) is about 1%. The math for all "very rarely" items lumped together would look like that for "rare" items.
Method
I emptied my hoard, and then went of to the Coliseum. I fought about 300 monsters in each stage, over an arbitrary number of battles and refreshes. Then I tallied the results in my hoard. As a result, I do not link drops to specific monsters. This was to make the data-gathering manageable.
When a particular item is dropped with different frequencies by monsters in the same stage, I assumed it was dropped by the monster with the higher drop rate.
Assumptions
I don't actually think all of these assumptions are true. I would guess, for example, that each category represents a range of drop rates.
These assumptions are here just to make the problem tractable. I think they are close enough to provide a useful sense of the drop odds.
Data
(Apologies for the poor formatting)
For each stage, here is a tally of {Monsters Fought} {Common Drops} {Uncommon Drops}{Scarce Drops} {Rare Drops} {Very Rare Drops}
Training Fields 301 279 70 14 0 4
Woodland Path 300 221 68 17 6 6
Scorched Forrest 302 242 87 9 0 2
Sandswept Delta 301 213 89 15 1 4
Blooming Grove 302 214 128 4 0 3
Forgotten Cave 301 239 102 9 3 3
Bamboo Falls 300 273 37 14 2 5
Thunderhead Savanna 300 132 105 0 6 0
Redrock Cove 301 224 112 8 5 2
Waterway 301 188 122 6 0 5
Arena 300 236 78 19 2 3
Volcanic Vents 301 225 111 7 2 2
Rainsong Jungle 301 277 90 7 1 5
Boreal Wood 300 237 87 15 2 5
Crystal Pools 300 207 79 5 0 2
Harpy's Roost 300 257 79 17 3 4
Ghostlight Ruins 300 214 113 7 2 2
Mire 301 208 103 12 1 4
Kelp Beds 301 225 102 7 1 6
Golem Workshop 300 187 62 4 4 2
Forbidden Portal 302 226 102 3 3 1
The game database gives us broad categories for coliseum drop rates, but I'm a numbers person, so I've done some grinding to determine-- what does "scarce" mean anyway?
The Numbers
On average, when you face any monster, the odds for the different loot categories are:
- COMMON : 75%
- UNCOMMON : 30%
- SCARCE : 3%
- RARE : 1%
- VERY RARELY : 0.03%
What're the Odds?
Let's say you want a particular item. To have a very certain (99%) chance of getting that item, you will need to face a monster that drops it:
- COMMON : 4 times
- UNCOMMON : 13 times
- SCARCE : 152 times
- RARE : 459 times
- VERY RARELY : 15349 times
That's an awful lot of grinding. To have a high certainty (95%) chance of getting that item, you will need to face a monster that drops it:
- COMMON : 3 times
- UNCOMMON : 9 times
- SCARCE : 99 times
- RARE : 299 times
- VERY RARELY : 9985 times
Relaxing down to a decent (75%) chance of getting that item, you will need to face a monster that drops it:
- COMMON : 1 time
- UNCOMMON : 4 times
- SCARCE : 46 times
- RARE : 138 times
- VERY RARELY : 4621 times
Even a 50% chance of getting an item can be a bit of a grind:
- COMMON : 1 time
- UNCOMMON : 2 times
- SCARCE : 23 times
- RARE : 69 times
- VERY RARELY : 2311 times
This is why the advice is often to buy a familiar rather than grind for it. Most familiars are rare, so it's not unusual to face it hundreds of times before finally getting that drop.
Of note: monsters typically have many possible "very rarely" loot items. Because there are so many, the odds of collecting any "very rarely" item (as opposed to a specific one) is about 1%. The math for all "very rarely" items lumped together would look like that for "rare" items.
Method
I emptied my hoard, and then went of to the Coliseum. I fought about 300 monsters in each stage, over an arbitrary number of battles and refreshes. Then I tallied the results in my hoard. As a result, I do not link drops to specific monsters. This was to make the data-gathering manageable.
When a particular item is dropped with different frequencies by monsters in the same stage, I assumed it was dropped by the monster with the higher drop rate.
Assumptions
- Each monster has one loot item in each category, except Very Rarely
- Monsters have about 30 loot items in the Very Rarely category
- Each loot item drops independently of the other items
- Each loot item in a category drops at around the same rate
I don't actually think all of these assumptions are true. I would guess, for example, that each category represents a range of drop rates.
These assumptions are here just to make the problem tractable. I think they are close enough to provide a useful sense of the drop odds.
Data
(Apologies for the poor formatting)
For each stage, here is a tally of {Monsters Fought} {Common Drops} {Uncommon Drops}{Scarce Drops} {Rare Drops} {Very Rare Drops}
Training Fields 301 279 70 14 0 4
Woodland Path 300 221 68 17 6 6
Scorched Forrest 302 242 87 9 0 2
Sandswept Delta 301 213 89 15 1 4
Blooming Grove 302 214 128 4 0 3
Forgotten Cave 301 239 102 9 3 3
Bamboo Falls 300 273 37 14 2 5
Thunderhead Savanna 300 132 105 0 6 0
Redrock Cove 301 224 112 8 5 2
Waterway 301 188 122 6 0 5
Arena 300 236 78 19 2 3
Volcanic Vents 301 225 111 7 2 2
Rainsong Jungle 301 277 90 7 1 5
Boreal Wood 300 237 87 15 2 5
Crystal Pools 300 207 79 5 0 2
Harpy's Roost 300 257 79 17 3 4
Ghostlight Ruins 300 214 113 7 2 2
Mire 301 208 103 12 1 4
Kelp Beds 301 225 102 7 1 6
Golem Workshop 300 187 62 4 4 2
Forbidden Portal 302 226 102 3 3 1
