Drop rate

Drop rate is a common but unofficial term used by players to denote the expected average amount of an item in relation to all items granted by a random game mechanism in the long run, expressed in percent. Examples for random game mechanisms in Asphalt 8 are Pro Kit Boxes or daily ad rewards.

The games themselves do not use the expression. For example, when an Asphalt 8 player taps on the box info icon of a Pro Kit Box, the displayed screen only shows percentages without further information on their meaning. This often leads to misunderstandings as players can be tempted to understand the values as probabilities or even guarantees, thinking that a percentage of 25 % for a desired card in a 4-item box should grant 1 card in every box. This is not the case.

Drop rates change frequently. While they are usually stable between two game updates, they will almost surely change when a new update comes out. Pro Kit Boxes on have a "last checked" tag that indicates when the official box data, including drop rates, was checked. Example:

Definition
Drop rates are closely related to expected values. Let then the drop rate $$\operatorname{D}[X]$$ is defined as
 * $$\operatorname{E}[X]$$ be the expected value of a random variable $$X$$, and
 * $$S$$ the sum of all random variables of the experiment,


 * $$\operatorname{D}[X] = \frac{\operatorname{E}[X]}S$$.

Drop rate and expected value
In other words: The drop rate of an item is the ratio of its expected value to all items.
 * The expected value is a number and denotes the expected average amount of an item per box.
 * The drop rate is a percentage and denotes the expected average amount of an item in relation to the sum of all items.

Examples:
 * A box contains 10 cards and has an expected value of 0.8 legendary cards per box. The drop rate of legendary cards is $$0.8 : 10 = 0.08 = 8 %$$.
 * A box contains 10 cards and has a drop rate of 8 % legendary cards. The expected value of legendary cards per box is $$8 % \cdot 10 = 0.8$$.


 * A drop rate is not an expected value. It is the ratio of the expected value to all items, expressed in percent.

General
Drop rates do not guarantee a ratio for a single opened box. The definition of the drop rate is built on that of the expected value, and the expected value is an average number that is only obtained in the long run, when a large number of boxes is opened (see law of large numbers). Values for a single box can differ significantly.

This is also the reason why WikiProject Statistics has set the "acceptable" sample size for a box to a minimum of 200 cards. Experience has shown that this sample size allows making first predictions and reduces the risk of false conclusions to an acceptable amount.


 * A drop rate is not a guarantee. It is a random-based average that predicts the outcome of eperiments in the long run with a big sample size.

Boxes with guarantees
Although a drop rate is not a guarantee in itself, it can be more important than guarantees provided in the box description. The, for example, officially contains 1 guaranteed V8 Engine, while an Engine Box doesn't have this guarantee.


 * Players who need only 1 V8 Engine will open the Champion Kit Box first because they can be sure to get the desired engine.
 * However, if many V8 Engines are needed, it is recommended to open Engine Boxes first, because in the long run, their drop rate of V8 Engines is higher than that of Champion Kit Boxes.

Note: The game does not provide drop rates for single cards. The values in the table to the right are unofficial results of statistical analyses by WikiProject Statistics.
 * In the long run, drop rates are more important than guarantees.

Drop rate and probability
The probability of getting a desired card can usually be inferred from its drop rate. In certain cases, drop rate and probability are equal.

The reason for this difference is that the drop rate predicts the result for many repetitions of an experiment (e. g. opening a large number of boxes), whereas the probability predicts the result of one repetition (opening a single box).

Random experiments
An experiment is random if there are no guarantees for certain events. In this case, the drop rate of an event equals the probability that it will occur.

The, for example, does not guarantee any cards, so its content is completely random. As of the 2019 Spring Update, its drop rate of legendary cards is 2.61 %. This means that in the long run, the amount of legendary cards a player obtains from this box will converge to 2.61 % of all obtained cards. If 10,000 boxes are opened, the number of legendary cards among them will likely be 261, so picking a random card from these 10,000 cards will deliver a legendary card with a probability of $$\frac{261}{10,000} = \frac{2.61}{100} = 2.61 %$$. This is the same result as if the player opened only one box.


 * The drop rate of an item equals the probability of obtaining it when the outcome of the experiment is completely random.

Experiments with guarantees
Many boxes in Asphalt 8 have official or undocumented guarantees.

The, for example, has the official guarantee that at least 1 of its 4 cards will be rare:0:0. As of the 2019 Spring Update, its drop rate of rare cards is 38.79 %, but the probability of getting a rare card from one box is 100 %.


 * Drop rate and probability are not the same if an experiment includes guaranteed events.

Nevertheless, it is possible to deduce further probabilities from experiments with guarantees if the guaranteed events are excluded: Taking out the guaranteed rare card from the content of an Extra Box makes the experiment completely random again, creating a 3-card box with no guarantees.
 * The guaranteed rare:0:0 card makes up $$\frac14 = 25 %$$ of all cards. Taking it out will leave the remaining $$\frac34 = 75 %$$ cards. $$38.79 % - 25 % = 13.79 %$$ of these 75 % will be rare. $$\tfrac{13.79}{75} \approx \tfrac{18.39}{100}$$, so the probability of getting a second rare card is 18.39 %.
 * The drop rate of 59.25 % cards out of 4 delivers $$\tfrac{59.25}{75} = \tfrac{79}{100}$$ out of 3, so the real probability of obtaining a common card from an Extra Box is 79 %
 * Analogously, the probability of getting a card from an Extra Box (drop rate 1.96 %) is $$\tfrac{1.96}{75} \approx \tfrac{2.61}{100} = 2.61 %$$.