Calculate cumulative item-drop odds, dry-streak probability, expected drops, and attempts needed from a percent or 1-in-X drop rate.

Predictive modes assume independent attempts, constant probability and at most one success per attempt. Pity systems or changing rates need a different model. Observed frequency is an estimate, not a guarantee.

Drop Chance Formula

The following formula estimates an observed drop frequency from successful attempts in a video game.

DC = DI / A × 100

Formula source: Principles of Epidemiology | Lesson 3 – Section 1: Proportion (CDC)

  • Where DC is the observed drop frequency (%)
  • DI is the number of attempts with at least one drop (count each successful attempt once)
  • A is the number of attempts to get that item (i.e. number of times killing a monster)

To estimate an observed drop frequency, divide successful attempts by total attempts, then multiply by 100. For independent attempts with a known constant probability p, the chance of at least one drop in n attempts is 1 − (1 − p)n. Exactly k successes follow the binomial distribution (NIST). These predictions do not apply unchanged to pity systems or changing rates.

What is drop chance?

Definition:

A drop chance is a term used in video games to describe the rate at which a player will receive an item on average per number of attempts.

The word “drop” comes from the saying that the items you get from killing a monster/unit are “dropped” by that unit.

How to calculate a drop chance?

Example:

The following example problem outlines the steps and information needed to calculate a drop chance.

First, set up an experiment where you kill a unit a certain number of times. In this example, the number of attempts will be 500.

Next, count the attempts with a drop. In this example, 3 of the 500 attempts were successful.

Finally, calculate the observed drop frequency using the formula above:

DC = #DI / A *100

DC = 3 / 500 *100

DC = .6% observed drop frequency; this sample estimate does not guarantee future drops.