[Math, Transparency] Loot box unit pricing explained - Update Gems & HotM added

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 .

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

8 Likes

It is great that when the world has real problems to deal with, governments everywhere are taking the time to learn how video games generate revenue. Obviously regulating loot boxes is the most pressing issue Australia faces at present. It is not as if it is literally on fire.

$23k hahahahahahaha that’s awesome

I get the idea, but it just doesnt work. The concept is so inaccurate thats absolutely useless. Nobody is chasing a 3 certain hero. Every summon (unless the common) guarantee you at least a rare hero. Using a “math based” system that sets the avarege price of a rare hero to more than 400 dollars is just ridiculous

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