# Complexity of Popularity and Dynamics of Within-Game Achievements in Computer Games

## ๐ Abstract

The article investigates the relationship between the difficulty of tasks and the persistence needed to accomplish them, using data from the online gaming platform Steam. The key findings are:

- The distribution of the number of achievements in games follows a log-normal distribution.
- The distribution of the number of players per game also follows a log-normal distribution.
- Most games require an intermediate level of persistence from players, rather than very high or very low persistence.
- Players also prefer games that demand a certain intermediate level of persistence.
- The proportion of players who complete achievements in a game declines approximately exponentially.

## ๐ Q&A

### [01] Complexity of Popularity and Dynamics of Within-Game Achievements in Computer Games

**1. What is the main objective of the study?**
The main objective of the study is to mathematically describe the proportion of players who unlocked game achievements in the Steam gaming platform.

**2. What data was used in the study?**
The study used data from the Steam gaming platform, including the name of the games, the total number of players, and the fraction of players that completed each achievement.

**3. How did the researchers associate persistence with unlocking achievements?**
The researchers associated persistence as the main factor for unlocking achievements, as the feeling of motivation among players increases as they approach the achievement.

**4. What are the five major findings of the study?**
The five major findings are:

- The probability distribution for the number of achievements is log-normal.
- The distribution of game players also follows a log-normal.
- Most games require neither a very high degree of persistence nor a very low one.
- Players also prefer games that demand a certain intermediate persistence.
- The proportion of players as a function of the number of achievements declines approximately exponentially.

**5. Why are the log-normal and exponential functions considered mathematical forms that describe random effects?**
The log-normal and exponential functions are considered mathematical forms that describe random effects because they are memoryless, meaning they do not depend on the history of the system.

### [02] Methods

**1. What is the Steam platform and how was it used in the study?**
Steam is an online platform that sells and manages a large quantity of video games. The study used data from Steam, including the name of the games, the total number of players, and the fraction of players that completed each achievement.

**2. How did the researchers define persistence and engaging factor in the context of the study?**
The researchers defined persistence as the main factor for unlocking achievements, as the feeling of motivation among players increases as they approach the achievement. The engaging factor was defined as the proportion of players who unlocked achievements, as an indicator associated with the engaging factor of the game.

**3. What were the two groups of games analyzed in the study?**
The first group consisted of games in which at least one player completed all available achievements, and the second group consisted of games in which no player completed all achievements.

**4. How did the researchers quantify the engaging factor for the two groups of games?**
For the first group of games, the engaging factor was defined as the fraction of completists, or the fraction of players that unlocked all the achievements of the game. For the second group, the engaging factor was defined as the completed fraction, or the fraction of achievements that the best player reached with success.

### [03] Results

**1. What were the key findings regarding the distributions of the number of achievements and the number of players per game?**
The distribution of the number of achievements per game follows a log-normal distribution, and the distribution of the number of players per game also follows a log-normal distribution.

**2. What were the findings regarding the fraction of completists and the completed fraction?**
The majority of games have a low fraction of completists, and the majority of games without any completists have a low completed fraction.

**3. How did the researchers analyze the fraction of players along the achievements of each game?**
The researchers found that the fraction of players along the achievements of each game decays approximately exponentially, and they identified an average exponential behavior that depends on the engaging factor of the game.

**4. What are the implications of the exponential decay in the fraction of players along the achievements?**
The exponential decay suggests that players are dropping out at a fixed rate, where the rate depends on the engaging factor of the game.

### [04] Discussion

**1. How did the researchers interpret the log-normal distributions observed in the data?**
The researchers interpreted the log-normal distributions as indicating random processes of fragmenting achievements and players, similar to other social systems that exhibit log-normal distributions.

**2. How did the researchers connect the findings to theories of human motivation and persistence?**
The researchers connected the findings to theories that suggest motivation grows with increasing task difficulty, while success is possible and justified. They also discussed how the findings relate to the concept of "flow" in psychology.

**3. What are some of the limitations of the study and potential future research directions?**
Limitations include not differentiating between specific game conditions (e.g., Ironman mode) or player types (e.g., casual vs. "achievement hunters"). Future research could connect the findings to scales for measuring human persistence and explore the dynamics of player motivation over time.

**4. How could the findings from this study be applied in practical contexts?**
The findings could be useful for the gaming industry in understanding player engagement and persistence, as well as for educational contexts in developing techniques to maximize learning based on task difficulty and persistence.