Subject
[Math, Transparency] Lootbox unit pricing explained - Update Gems & HotM added
Inquiry
An Australian inquiry into lootbox in game ( see Notes ) discussed several tactics loot boxes use the hide the cost of acquiring a virtual item.
Currency
There are many reasons virtual premium currencies are used, but one unintended consequence is to hide the real world price. Instead of $3.74 USD per Epic summons lootbox, it is 300 gems.
Grouping items
There are many reasons to simplify listed odds. But one unintended consequence is to hide the odds for acquiring a desired virtual item like Boldtusk or Vivica.
Probability
Most users do not have a good grasp on probability, even the users that do, can have trouble understanding the cost of a desired virtual item like Boldtusk or Vivica.
Lootbox unit pricing
One proposal in the inquiry was a cash value assigned to each virtual item using the 99% threshold. If 100 users spend $ X USD, each, then 99 of them will acquire the desired virtual item. So Boldtusk would be $1,616+ USD and Vivica would be $22,967+ USD.
This is similar to items at the food store having $ X USD per pound, or $ Y USD per quart, or $ Z USD per 100 count. This lets you compare lootbox pricing by generating a single simplified cost.
When displaying a possible prize, displaying the lootbox unit pricing would allow users to make a more informed decision. This would also allow users to shop around between different games with micro transactions.
Epic summons
Lootbox unit pricing for Epic summons
| USD | Gems | Hero | Hero | Hero |
|—|—|—|—|—|—|
| $467+ | 37,500+ | Hawkmoon ( red 3* ) | Gan Ju ( yellow 3* ) |
| $587+ | 47,100+ | Tyrum ( purple 3* ) | Valen ( blue 3* ) |
| $707+ | 56,700+ | Belith ( green 3* ) |
| $1,291+ | 103,500+ | Wu Kong ( yellow 4* ) | Rigard ( purple 4* ) | Kiril ( blue 4* ) |
| $1,312+ | 105,300+ | 5* HotM |
| $1,616+ | 129,600+ | Boldtusk ( red 4* ) | Melendor ( green 4* ) |
| $22,967+ | 1,841,100+ | Vivica ( any color 5* ) |
Leveling
In Empires, lootbox rewards are unleveled.
Another unit cost would be the leveling cost per hero using only Epic Summons.
Example
$ X USD using Epic Summons to level a 5* 1.1 hero to 5* 4.80 .
Tavern of Legends
Edit:
Tavern of Legends is an example of how Merciless RNG can conceal costs to players, even when odds are posted, as more past HotM are added each time.
Tavern of legends v2.0
Notes
Click for notes
Math
300 gems per Epic summons / 400 gems * $4.99 USD = $3.74 USD
From a bug with red troops, and from long term tracking of red heroes, we know rarity is determined first, then color, then specific hero.
4x 3* heroes= Red, Yellow
5x 3* heroes= Blue, Purple
6x 3* heroes= Green
4x 4* heroes= Blue, Purple, Yellow
5x 4* heroes= Red, Green
4x 5* heroes= all colors
Posted summons odds
3*= 0.72
4*= 0.265
5*= 0.015
3* heroes= 0.72 / 5 colors = 0.144
0.144 / 4= 0.036
1- 0.036 = 0.964
log ( 0.01 ) / log ( 0.964 ) = 125
Check 0.964^125= 0.01
125 * $3.74 = $467
0.144 / 5= 0.0288
1- 0.0288 = 0.9712
log ( 0.01 ) / log ( 0.9712 )= 157
Check 0.9712^157= 0.01
157 * $3.74 = $587
0.144 / 6= 0.024
1- 0.024= 0.976
log ( 0.01 ) / log ( 0.976 )= 189
Check 0.976^189= 0.01
189 * $3.74= $707
4* heroes= 0.265 / 5 colors= 0.053
0.053 / 4 = 0.01325
1- 0.01325= 0.98675
log ( 0.01 )/ log (0.98675 )= 345
Check 0.98675^345= 0.01
345 * $3.74= $1,291
0.053 / 5 = 0.0106
1- 0.0106 = 0.9894
log ( 0.01 ) / log ( 0.9894 )= 432
Check 0.9894^432= 0.01
432 * $3.74 = $1,616
5* heroes= 0.015 / 5 colors = 0.003
0.003 / 4 = 0.00075
1- 0.00075 = 0.99925
log ( 0.01 ) / log ( 0.99925 )= 6,137
Check 0.99925^6,137= 0.01
6,137 * $3.74 = $22,967
Edit:
Hotm
0.013 odds
351 summons
351 * $3.74= $1,312
FIN
