Drop Rate & Pity Calculator

How pity changes the real drop rate

The rate on the banner is not the rate players experience. Pity cuts off the long tail of bad luck, so the long-run share of top-rarity drops is higher than the base rate. That long-run number is the consolidated rate, and it is the honest figure to design your economy around.

For each pull k since the last drop the calculator takes the rate r(k): the base rate, plus the soft pity step for every pull past the soft pity start, and 100% at hard pity. The chance that the drop lands exactly on pull k is:

With a 0.6% base rate, soft pity from pull 74 at +6% per pull and hard pity at 90, E[T] is about 62.3 pulls, so the consolidated rate is about 1.6%, close to three times the advertised base.

Soft pity vs hard pity

Hard pity is the promise: nobody goes past pull 90. Soft pity is the shape: it moves most drops into a narrow window before the cap. Players feel soft pity as "it always comes around 75", which makes spend more predictable for them and for your forecast.

50/50 and guarantees

A featured share splits each top-rarity drop between the featured item and the standard pool. With a guarantee after a loss, a featured copy costs on average 1.5× the pulls of a top-rarity drop, and the worst case is twice the hard pity. Without the guarantee the average doubles and there is no worst case.

Design notes from LiveOps practice

• Price the P90, not the average. Your most engaged spenders sit in the unlucky tail more often than you think, because they pull the most. If the P90 cost of a featured copy is above your top pack, expect complaints.
• Decide if pity carries over. Carrying the counter between banners makes saving rational and smooths revenue. Resetting it pushes spend into the current banner but feels punishing.
• Copies multiply the tail. Duplicates for upgrades turn a fair single-copy system into a long grind. Check the 5- and 7-copy numbers before you ship a dupe-based progression.
• Publish the consolidated rate. Players will work it out anyway. Showing it builds trust, and some markets expect it.

FAQ

What is the consolidated drop rate?

It is the long-run share of pulls that give a top-rarity item once pity is included: one divided by the expected number of pulls per item. A 0.6% base rate with soft pity from pull 74 and hard pity at 90 consolidates to about 1.6%.

What is the difference between soft pity and hard pity?

Hard pity guarantees the item on a fixed pull, for example pull 90. Soft pity raises the per-pull rate step by step before that point, so most players get the item a few pulls before the hard cap and rarely reach it.

How does a 50/50 guarantee change the expected number of pulls?

With a 50% featured share and a guarantee after a loss, the expected pulls per featured item are 1.5 times the pulls per top-rarity item. Without the guarantee they double.

Do I have to disclose loot box odds?

Apple's App Store guidelines and Google Play's policy require apps that sell randomized items to disclose the odds before purchase, and several countries add their own rules. The calculator drafts a disclosure text, but check the current rules for each market with your legal team.

Is the calculation exact or a simulation?

It is exact. The calculator tracks the probability of every pity state pull by pull, so the percentiles do not change between runs.

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