# Popularity of Video Games and Collective Memory

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^{†}

## Abstract

**:**

## 1. Introduction

- The number of video games and of players are growing either linearly or exponentially over time;
- The relative popularity among games is described by a distribution that resembles the lognormal one, a hypothesis which was driven by the fact that this distribution has been employed and studied in the context of econophysics [30], quantitative linguistics [31], and in the popularity analysis of other cultural products, such as patent citation, scientific citation, Wikipedia entries, and memes in social networks [32,33,34,35];
- The distributions are stable over time;
- The popularity distributions for the major categories will be similar to each other and to the global one;
- The number of categories will grow more slowly compared to the number of games and players.

## 2. Materials and Methods

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Number of players in and of games released on Steam. (

**A**) The average number of players by hour in each month (discs) and a linear adjustment (straight line) along 111 months, where the first one is July 2012 and the last one is December 2020. (

**B**) During these same months, growth of the number of games (discs) released and an exponential fit (straight line).

**Figure 2.**Mean and standard deviation of the trimester groups. (

**A**) Mean of the average number of players per hour in each month (${x}_{i}$) of all games of each trimester group along the months after release. (

**B**) For these groups, the time evolution of their standard deviations. By using the logarithmic variable (${y}_{i}=log{x}_{i}$), the time dependence of the corresponding means (

**C**) and standard deviations (

**D**). Each one of the thirty-four trimester groups has its own color.

**Figure 3.**Box–Cox analysis of the $01/2015$ trimester group. (

**A**) Probability distribution function of the normalized logarithmic variable ${z}_{i}=({y}_{i}-\langle {y}_{i}\rangle )/{\sigma}_{y}$ with ${y}_{i}=log{x}_{i}$ for the $01/2015$ trimester group, where ${x}_{i}$ is the average number of users per hour in each month of the i-th game. (

**B**) The same as (

**A**) but employing the optimal $\lambda $ value (${\lambda}_{opt}=-0.07$) of the Box–Cox transformation, Equation (3). The dashed lines refer to a normal distribution with the mean zero and unity standard deviation. (

**C**) Time evolution of the optimal parameter $\lambda $, ${\lambda}_{opt}$, of the trimester group along the twenty-four quarters. The discs represent the ${\lambda}_{opt}$’s along the time evolution of the $01/2015$ trimester group and the straight line of the mean of all quarters, $\langle {\lambda}_{opt}\rangle =-0.08$, which is close to the value obtained with the ${\lambda}_{opt}$ obtained via the maximum-likelihood method in (

**B**). The error bars refer to the $95\%$ confidence interval of the ${\lambda}_{opt}$’s estimated via the maximum-likelihood method.

**Figure 4.**Box–Cox analysis for all trimester groups. (

**A**) Optimal $\lambda $, ${\lambda}_{opt}$, for each trimester group (disc) and the mean value, $\overline{{\lambda}_{opt}}=-0.04$, represented by the red straight line. The error bars indicate $95\%$ confidence intervals. (

**B**) For the normalized global data, the PDF of the logarithmic variable, ${z}^{\left(0\right)}$. (

**C**) The same as in (

**B**) but employing ${\lambda}_{opt}=-0.05$ in the Box–Cox transformation. The dashed lines correspond to the normal distribution with mean zero and unity standard deviation.

**Figure 5.**Number of players in and of games released on Steam for the Indie category. (

**A**) The average number of players per hour in each month for the Indie category (purple discs) and a linear adjustment (straight line, red), where month one is July 2012 and the last month is December 2020. (

**B**) During these same months, growth of the number of games released in this category (green discs) and an exponential fit (straight line, red).

**Figure 6.**Video game categories. (

**A**) PDF for the Indie category obtained via the Box–Cox transformation (${\lambda}_{opt}=-0.049$), analogous to Figure 4C (all quarters of all trimester groups together). (

**B**) The Box–Cox parameter for Indie games in each trimester of our dataset, analogous to Figure 4A. The bars refer to $95\%$ confidence intervals. The straight line refers to the mean of all trimestral Box–Cox parameters, $\langle {\lambda}_{opt}\rangle =-0.06$. (

**C**) Optimal Box–Cox parameter, ${\lambda}_{opt}$, for the twelve largest game categories, calculated via the same procedure of (

**A**). The ${\lambda}_{opt}$’s are sorted in descending order of their number of games by category. The straight line represents the average of these ${\lambda}_{opt}$’s, $\langle \lambda \rangle =-0.028$ for the twelve major categories.

**Figure 7.**Distribution of video game categories. (

**A**) Time evolution of the number of categories along the months from July 2012 to December 2020. The straight red line represents a linear adjustment from month 10 to the last one. (

**B**) PDF for categories obtained via the Box–Cox transformation (${\lambda}_{opt}=-0.12$) as a function of the number of video games in each category in December 2020. The dashed line refers to a Gaussian distribution of mean zero and unity standard deviation. (

**C**) Time evolution from 2012 to 2020 of the ${\lambda}_{opt}$, where each disc represents a semester. The bars indicate $95\%$ confidence intervals of ${\lambda}_{opt}$ parameters. The straight red line exhibits the mean behavior of the last two years.

Total of games: 21,752 | Number of tags: 1044 | |

$\Delta t$: $8.5$ years | ${t}_{i}$: July 2012 | ${t}_{f}$: December 2020 |

${\rho}_{global}$: $1.78\times {10}^{8}$ | ${\rho}_{Indie}$: $2.46\times {10}^{7}$ |

**Table 2.**Statistical parameters for the transformed data. The parameters of the Box–Cox transformed data (first column): Box–Cox parameter ($\lambda $), mean ($\mu $), standard deviation ($\sigma $), skewness ($\gamma $), and kurtosis ($\kappa $). Values for these parameters are shown for log-transformed (second column), Box–Cox all data transformed (third column), Box–Cox transformation for the Indie category (tag) (fourth column), and Box–Cox transformation for the distribution of the number of video games by category (fifth column). After the ± symbol, the $95\%$ confidence interval of each parameter are exhibited.

Lognormal (All Data) | Box–Cox (All Data) | Box–Cox (Indie Tag) | Box–Cox (Games by Tags) | |
---|---|---|---|---|

$\lambda $ | $\phantom{-}0.00$ | $-0.053\pm 0.001$ | $-0.049\pm 0.002$ | $-0.12\pm 0.05$ |

$\mu $ | $\phantom{-}0.27\pm 0.01$ | $\phantom{-}0.43\pm 0.02$ | $\phantom{-}1.60\pm 0.02$ | $\phantom{-}3.72\pm 0.25$ |

$\sigma $ | $\phantom{-}1.2\pm 0.1$ | $\phantom{-}2.6\pm 0.2$ | $\phantom{-}2.6\pm 0.2$ | $\phantom{-}0.74\pm 0.15$ |

$\gamma $ | $\phantom{-}0.41\pm 0.02$ | $\phantom{-}0.01\pm 0.01$ | $\phantom{-}0.01\pm 0.01$ | $\phantom{-}0.03\pm 0.05$ |

$\kappa $ | $\phantom{-}0.15\pm 0.07$ | $-0.28\pm 0.02$ | $-0.34\pm 0.03$ | $-0.5\pm 0.6$ |

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**MDPI and ACS Style**

Mendes, L.O.; Cunha, L.R.; Mendes, R.S.
Popularity of Video Games and Collective Memory. *Entropy* **2022**, *24*, 860.
https://doi.org/10.3390/e24070860

**AMA Style**

Mendes LO, Cunha LR, Mendes RS.
Popularity of Video Games and Collective Memory. *Entropy*. 2022; 24(7):860.
https://doi.org/10.3390/e24070860

**Chicago/Turabian Style**

Mendes, Leonardo O., Leonardo R. Cunha, and Renio S. Mendes.
2022. "Popularity of Video Games and Collective Memory" *Entropy* 24, no. 7: 860.
https://doi.org/10.3390/e24070860