The Cost of Coming Out††thanks:  We especially would like to thank Michael Lechner and Franco Peracchi for feedback and suggestions. We are also grateful to Jaime Arellano-Bover, Nora Bearth, Jonathan Chassot, Caroline Coly, Daniel Goller, Eric Guan, Gior (2024)

1.1 Contribution to literature

Our paper contributes to four distinct strands of the literature. First, it relates to a growing literature studying the economics of LGBTQ+ individuals \parencite[see, e.g.,][]badgett2021lgbtq, badgett2023review. The current body of research primarily focuses on measuring discrimination against LGB individuals by comparing their labor market outcomes with those of non-minority individuals with similar observable characteristics, mostly documenting wage penalties for gay and bisexual men and wage premiums for lesbian women \parencite[see, e.g.,][]badgett1995wage, martell2021labor, carpenter2017does, carpenter2023orient.²²2The only study finding a wage premium for gay men is that of \textcitecarpenter2017does. \textcitetampellini2024pride does not find a wage penalty but finds a lower probability of being full-time employed and a higher probability of being a victim of work-related violence for gay men. There is also evidence that transgender workers face earning and employment penalties \parencitegeijtenbeek2018penalty, carpenter2022economic. However, despite their valuable contributions, these studies suffer from the endogeneity and selection issues discussed above that hinder the ability to draw causal inferences from their findings.³³3A related literature studies whether changes in laws and norms affect labor market outcomes and attitudes towards LGB individuals \parencite[see, e.g.,][]burn2018not, sansone2019pink, ofosu2019same, burn2020relationship, delhommer2020effect, deal2022bound, deal2023heterogeneity. \textcitebroockman2016 show that a randomized intervention that encourages actively taking the perspective of others can reduce transphobia. To tilt towards a more causal interpretation, other studies use correspondence designs to probe into hiring discrimination against LGB individuals, consistently revealing that LGB job candidates are less likely to be invited for interviews or offered job opportunities \parenciteweichselbaumer2003sexual, drydakis2009sexual, Tilcsik2011, ahmed2013gay, drydakis2014sexual. Nevertheless, a significant challenge lies in communicating that an individual belongs to a sexual orientation minority group, since such information is not typically included in job applications. This raises whether the observed results are affected by the choice and nature of the used signal \parencitebertrand2017field.

We make several contributions to this literature. First, our use of data from an online video game allows us to overcome the endogeneity issues of previous studies and to identify preferences toward LGB status. Second, to the best of our knowledge, our study is the first to investigate the immediate reactions to coming out. Due to the substantial anecdotal and scientific evidence that individuals often hide their sexual orientation status \parencite[see, e.g.,][]badgett2020economic and the prevalent evidence of the associated costs \parencitemeyer2003prejudice, pachankis2020sexual, several studies have explicitly focused on investigating the determinants and incentives of coming-out decisions. \textciteseror2021legalized investigate the impact of same-sex marriage legalization on coming-out decisions using a revealed preference mechanism inferred from data on Catholic priests’ vow of celibacy, finding reduced demand for priestly studies after the adoption of same-sex legalization. \textcitegromadzki2022iamlgbt explore spillover effects of coming-out decisions using Twitter data, discovering positive externalities, as exposure to peers coming out is associated with a higher probability of individuals coming out themselves. \textciteaksoy2023sexual conduct a lab experiment demonstrating that individuals strategically hide their sexual orientation in anticipation of discrimination in prosocial behavior, a result consistent with that of \textcitekudashvili2022minorities. Our study complements these studies by focusing on responses to revealing sexual minority status, potentially providing a rationale for the observed underrepresentation of individuals with sexual minority status in many areas.

Second, our contribution extends to the literature exploring the intersection of identity and decision-making, as discussed by \textciteakerlof2000economics. Empirical investigations encounter a challenge where causality is likely bidirectional - meaning that identity can be a cause or a consequence. Furthermore, identity is a multifaceted concept, thus isolating a particular component of identity is empirically challenging \parenciteshayo2020. Previous research overcomes these challenges and documents in-group and out-group behavior using either individuals’ inherent identities \parencite[see, e.g.,][]giuliano2009manager, price2010racial, oh2023does or by experimentally introducing identities \parencite[see, e.g.,][]chen2009, chen2011.⁴⁴4For recent reviews of the literature, see \textcitecharness2020social, shayo2020, kalin2018re. Results highlight the importance of an individual’s identity in shaping their behaviors, revealing a tendency for preferential treatment or bias towards those who share similar characteristics (in-group bias). To the best of our knowledge, our study is among the first studies to causally show the influence of sexual orientation status on preferences. Because sexual orientation is a key but non-salient facet of social identity, our paper makes an important contribution to this literature.

Third, our findings relate to the broader literature on discrimination. Early work by \textcitebecker1957economics paved the way for an extensive literature investigating discrimination instances, mostly based on gender and ethnicity, across diverse economic domains \parencite[see, e.g.,][]arnold2022measuring, kuhn2013gender. A substantial portion of the empirical evidence stems from field experiments, in which researchers use audit and correspondence studies to isolate the causal impact of identity on behavior \parencite[see, e.g.,][]ayres1995race, oreopoulos2011.⁵⁵5For recent surveys, see \textcitebertrand2017field and \textciteneumark2018experimental. \textciteonuchic2022recent provides a detailed review of traditional statistical and taste-based discrimination models, along with a discussion of recent theories that expand on these models. Our study contributes by exploring sentiments against sexual orientation minorities. The concealable nature of sexual orientation allows individuals to anticipate discrimination and strategically choose to hide their identity \parenciteaksoy2023sexual. This complicates the use of traditional methods to investigate discrimination against individuals based on their sexual orientation and necessitates innovative strategies for understanding sentiments against groups with stigmatized identities, particularly in environments prone to discrimination.

Fourth, our study contributes to the literature on video games as social interaction platforms. The recognition of video game data’s potential for research is increasing among economists, who are already capitalizing on the abundance and quality of the available data.⁶⁶6For example, \textciteparshakov2018diversity explore the impact of diversity on team performance using data from an online video game, and \textcitedell2023super investigate the effects of artificial intelligence on collaborative production dynamics in controlled laboratory settings using a team-based video game. \textcitecorrell2002police utilize a self-designed video game to study racial discrimination. However, despite its industry size and the significant fraction of time spent on playing video games, the scientific literature on these social platforms is only slowly increasing.⁷⁷7\textciteaguiar2012recent highlight that, according to the American Time Use Survey, almost 10 % of leisure time is spent on playing games and computer use. Global revenues of the video game industry were around $180 billion in $2020$. \textciteparshakov2023lgbtq investigate consumer behavior in the video game industry. They examine the impact of marking products with a gay label on consumers’ demand, finding a significant, albeit short-lived, decrease in demand following the introduction of the gay label. \textcitegandhi2024beliefs study entertainment preferences in the context of video games and test economic theories of belief-based utility using data from League of Legends. Our study complements this line of research by expanding the understanding of individuals’ behavior within these virtual environments.

The rest of the paper unfolds as follows. Section 2 describes the key elements of League of Legends that are relevant to our study and outlines the natural experiment we leverage to identify the effects of coming out. Section 3 introduces the data and explains the methodology we use to isolate the effects of coming out. Section 4 presents our main results. Section 5 examines the underlying mechanisms driving the estimated effects. Section 6 concludes.

2.1 League of Legends

League of Legends is a prominent multiplayer online game developed and published by Riot Games. Originally launched on October $27^{th}$, $2009$, the game attracted an impressive player base, averaging $180$ million monthly active players as of $2022$ and reaching a peak of $14$ million players in one day. League of Legends has also achieved significant financial success, generating $\$1.8$ billion in revenue in $2022$.⁸⁸8See, e.g., https://prioridata.com/data/league-of-legends.

In League of Legends, players are divided into two teams of five players each to compete in matches with the aim of destroying the opposing team’s base. Players in each team sort themselves into one of five roles. These roles represent crucial strategic positions, each requiring specific playstyles and contributing differently to the team’s final objective.

Before a match begins, players must select a playable character to control during the match from a pool of $165$ available characters. In our analysis, we measure players’ revealed preferences for a specific character by quantifying how frequently they select that character for their matches. Our objective is to investigate whether these preferences undergo any shifts following the disclosure of the character’s sexual orientation. Thus, we devote the rest of this section to exploring the design of characters in League of Legends and the process through which players select their characters for matches.

Each character has a unique set of skills and abilities and is specifically designed to excel in one or two of the distinct roles that players can assume within the team. Additionally, characters are crafted with a rich background that adds a narrative dimension to the game but does not have any impact on the game’s mechanics. This is achieved through the creation of detailed biographies and short stories that provide players with a deeper understanding of the character’s history and motivations, thus offering players the opportunity to connect with their chosen characters on a more personal level.⁹⁹9The list of all characters along with details about their abilities and histories is available at https://www.leagueoflegends.com/en-gb/champions/.

The character selection process occurs in a virtual lobby where players can communicate with their teammates through a chat function. In a random order that alternates between teams, players take turns selecting their characters for the match. Once a player chooses a character, their selection becomes visible to all players participating in the match, including the opposing team. Each character can be chosen by only one player, making it unavailable for selection by others. Once all players have selected their characters, the match begins.

When making their character selection, players consider various factors. First, they consider the role they are assigned to fulfill in the game. Each role has its own set of responsibilities and playstyle requirements, and players aim to choose a character that aligns with their designated role. Second, players take into account their personal mastery of specific characters, opting for those they are most skilled and comfortable with. Third, players may also consider their personal preferences, such as the playstyle and background story of the character, adding a subjective element to the selection process.

2.2 Coming-Out Event

Every year in June, LGBT Pride Month, a dedicated time to honor and celebrate the LGBT community, takes place. Since $2018$, Riot Games has actively participated in this month-long celebration by integrating new content into League of Legends during the month of June. This includes the introduction of in-game cosmetics, such as character skins, as well as emotes that allow players to express themselves in the game. It is important to note that while these additions enhance the visual and expressive elements of the game, they do not alter the game’s mechanics or the characteristics and abilities of the League of Legends characters.¹⁰¹⁰10We check this in Section 5.1, where we demonstrate that characters’ strength was unaffected by LGBT Pride Month.

Riot has also supported the representation of the LGBT community in the game by unveiling the sexual minority status of specific characters.¹¹¹¹11For instance, in $2018$, the character Neeko was confirmed as lesbian, marking her as the first openly LGBT character in the game. Furthermore, in $2021$, the characters Diana and Leona were revealed to be lesbians, while the character Nami was declared to be lesbian and polyamorous. In our paper, we primarily focus on the character Graves, chosen due to the existence of a well-defined announcement regarding his sexual orientation.

At the beginning of the $2022$ LGBT Pride Month, Riot Games released a short story featuring Graves and Twisted Fate. This story officially unveils Graves’ sexual orientation, establishing him as a gay character.¹²¹²12The story unveiling Graves’ sexual orientation also subtly hints at Twisted Fate’s pansexuality, although this is not explicitly stated. We investigate whether this implied revelation has captured the players’ attention in Appendix D. We highlight the relatively low attention directed towards Twisted Fate from players, who were primarily focused on Graves and the explicit establishment of his sexual orientation. As a result, we concentrate our analysis on Graves and his disclosure for a more credible identification of the effects of coming out. The following quotes provide two pivotal passages of the narrative:¹³¹³13The whole story is available at https://universe.leagueoflegends.com/en_SG/story/the-boys-and-bombolini/.

This coming-out event closely approximates an ideal experiment where individuals randomly disclose their sexual minority status, thus providing a unique setting to identify the effects of coming out on players’ preferences for Graves.¹⁴¹⁴14It is crucial to distinguish between the coming-out event and the disclosure of Graves’ sexual orientation. The coming-out event encompasses both Graves’ disclosure and the start of LGBT Pride Month. While this is not a concern for identification, it requires careful interpretation of the findings. To maintain clarity, we generally refer to the effects of the coming-out event in our analysis. Further discussion on this topic is deferred to Section 5.5 and Appendix E.

To ensure the credibility of our identification, it is crucial that the disclosure was not anticipated by players. The top panel of Figure 1 displays the Google search interest for the query “Graves gay”. We observe minimal interest in this search term throughout the year $2022$, with a remarkable spike occurring during the week of the coming-out event. This pattern supports our assumption of no anticipation and strengthens the credibility of our identification strategy.

Furthermore, the lower panel of Figure 1 displays the Google search interest for the query “LoL Graves”.¹⁵¹⁵15LoL is the common short-hand for League of Legends. Similarly to the previous search term, we observe a remarkable spike in interest during the week of the treatment. What is particularly interesting is that this surge in interest surpasses the level observed during the $2022$ League of Legends World Championship (held from September $29^{th}$ to November $5^{th}$), despite Graves being among the top-eight most played characters during the tournament. This finding emphasizes the substantial impact and attention that the coming-out event received from players.

3.1 Data

We obtain our data by accessing the Riot Games API, which provides us with valuable information about League of Legends matches. The game operates on multiple servers located worldwide, and we focus on specific servers for our analysis. These servers include Brazil, North and East Europe, West Europe, Korea, North Latin America, South Latin America, and North America.

Within these servers, we target the top tier of the League of Legends ranked system, which comprises the top 200 or 300 players (approximately the top 0.01% of players) on each server. By targeting this specific group of players, we aim to minimize the noise that may arise from players who are not fully engaged in the game, thus reducing the risk of attenuation bias. Furthermore, this focus increases the chances that players in our data set are aware of the coming-out event, thereby strengthening the credibility of our identification strategy.¹⁶¹⁶16We acknowledge that some of these players may have followers or engage in streaming activities, which could reduce the level of anonymity within our sample. Essentially, our focus trades off a degree of anonymity for reduced attenuation bias and strengthened credibility of identification.

Specifically, we identified the players within the top tier of each server as of July 2022. For each of these players, we gathered data on all the matches they engaged in the ranked mode during the period January-July $2022$.¹⁷¹⁷17Players can choose between draft or ranked matches. Both game modes share the same mechanics and objectives. However, while draft matches are more casual and do not have consequences for players’ rankings or ratings, in ranked matches players earn or lose points based on the outcome of the match to determine their position within the ranked system. By focusing on ranked matches we aim to further reduce the risk of attenuation bias. This approach inherently includes players who were not in the top tier as of July $2022$ but have been matched with our focal players during the time span we consider.

From these data, we construct a balanced daily panel data set that tracks the usage of each character over time. We then exclude characters that have been released after the coming-out event. This results in a final data set composed of $161,756$ players, engaging in a total of $142,856$ matches played over $193$ days, encompassing a total of $159$ characters.

To gauge players’ revealed preferences for characters, we construct a metric called pick rate, which measures the frequency with which players choose a specific character in their games each day. Our primary objective is to investigate whether the disclosure of Graves’ sexual orientation influences the pick rate of this character.

Figure A.I in Appendix A displays the distribution of average pick rates across characters before and after the coming-out event. The distribution remains stable before and after the event. Graves ranks among the most played characters before the treatment but loses positions afterward. Table A.I in Appendix A provides additional details by presenting the most popular characters before and after the treatment. Conditional on the role for which Graves is predominantly designed, the character ranks as the second most played before the disclosure. However, after the treatment, it drops to fourth place, with a decline in its average pick rate of more than 30%.

3.2 Methodology

A simple comparison of Graves’ pick rates before and after the disclosure may not accurately reflect the impact of the coming-out event on players’ preferences for that character, as other factors could have changed during that period. To address this issue, we construct a synthetic control unit \parencite[see, e.g.,][]abadie2003economic, abadie2010synthetic, abadie2015comparative, abadie2021using, abadie2022synthetic by weighting other characters to approximate the pick rates of Graves before the disclosure. This method allows us to isolate the effects of the coming-out event on players’ revealed preferences for Graves and gain insight into how these preferences would have behaved in the absence of the disclosure.

Formally, our data set comprises $n=159$ characters ($i=1,\dots,n$) observed over $T=191$ days ($t=1,\dots,T$). $T^{pre}$ is the length of the period (150 days) before the coming-out event, which occurs at time $T^{pre}+1$ (i.e., June $1^{st}$, $2022$). For each unit $i$ and time $t$, we denote the observed pick rate as $Y_{i,t}$. We represent the coming out as a binary variable $C_{i}\in\left\{0,1\right\}$ equal to one if character $i$ discloses his sexual orientation at time $T^{pre}+1$. We then posit the existence of two potential pick rates $Y_{i,t}^{c}$, where one denotes the pick rate in the absence of disclosure ($Y_{i,t}^{0}$) and the other denotes the pick rate in the presence of disclosure ($Y_{i,t}^{1}$).¹⁸¹⁸18These potential outcomes are based on Rubin’s model for causal inference \parenciterubin1974estimating.

Without loss of generality, we let the first unit $i=1$ be Graves. This implies that $C_{1}=1$ and $C_{i}=0$ for all $i\neq 1$. Then, for each period $t>T^{pre}$, we define the effect of the coming-out event on players’ preferences for Graves as the difference in Graves’s potential pick rates at time $t$:

Note that we allow the effects to change over time.

Since Graves’ sexual orientation has been disclosed after period $T^{pre}$, under a standard SUTVA assumption \parencite[see, e.g.,][]imbens2015causal we observe $Y_{1,t}=Y_{1,t}^{1}$ for all $t>T^{pre}$. Thus, as shown in equation (1), the challenge in estimating our causal effects of interest is to estimate $Y_{1,t}^{0}$ for $t>T^{pre}$, i.e., how Graves’ pick rates would have evolved in the absence of the disclosure. To this end, we can construct a synthetic control unit that approximates the pick rates of Graves before the coming out. The idea is that if the synthetic control and Graves behave similarly before the disclosure, then the synthetic control can serve as a valid counterfactual.

The synthetic control unit is characterized by a set of weights, denoted as $\omega:=\left(\omega_{2},\dots,\omega_{n}\right)$, chosen to align the pre-treatment pick rates of the synthetic unit with those of Graves. This is achieved by solving the following optimization problem \parencitearkhangelsky2021synthetic:

where the weights are restricted to be non-negative and to sum up to one and a ridge penalty is employed to ensure the uniqueness of the weights. In our main specification, we set the regularization parameter to zero, thus employing a standard synthetic control estimator. As a robustness check, we follow \textcitearkhangelsky2021synthetic and set $\zeta=\left(T-T^{pre}\right)^{1/4}\hat{\sigma}$, with $\hat{\sigma}$ denoting the standard deviation of first differences of $Y_{i,t}$ for control units over the pre-treatment period.

We estimate the counterfactual outcome of Graves as a weighted average of the outcome of the control units:

Finally, to estimate the causal effects of interest, we compute the differences between Graves’ observed pick rates and the synthetic counterfactual for all $t>T^{pre}$:

We summarize the estimated effects by reporting the average treatment effect on players’ preferences for Graves, with the averaging carried out over the post-treatment periods:

We employ the “placebo approach” of \textcitearkhangelsky2021synthetic to estimate the variance of $\hat{\tau}$. We then use the estimated variance to construct asymptotically valid conventional confidence intervals.¹⁹¹⁹19The validity of this placebo approach hinges on a hom*oskedasticity assumption which requires that treated and control units have the same noise distribution. In general, with only one treated unit, nonparametric variance estimation for treatment effect estimators is typically impossible without a hom*oskedasticity assumption \parencitearkhangelsky2021synthetic.

4.1 Main Results

We apply the synthetic control estimator of Section 3.2 to estimate the effects of the coming-out event on players’ revealed preferences for Graves. To mitigate the potential for spillover effects, we exclude Twisted Fate and other four characters (Diana, Leona, Nami, and Neeko) that were already members of the LGB community prior to the coming-out event from the donor pool.²⁰²⁰20Nevertheless, even if included in the donor pool, the estimator assigns these characters zero weight.

Figure 2 displays Graves’ actual and synthetic pick rate series, while the first column of Table 1 displays the point estimate and $95\%$ confidence interval for the average treatment effect.²¹²¹21Figure B.I in Appendix B displays the identities and the contributions of the characters in the donor pool with non-zero estimated weights. Overall, our analysis suggests a substantial negative impact of the coming-out event on players’ preferences for Graves. Before the disclosure, the synthetic control estimator closely approximates the trajectory of Graves’ pick rates, providing support for the estimator’s ability to predict the counterfactual series. However, starting from June $1^{st}$, $2022$, the two series diverge substantially, with Graves’ pick rates consistently dropping below those of the synthetic control. This gap persists over time, extending even beyond the conclusion of LGBT Pride Month. The average effect is estimated to be around $-7$ percentage points and is statistically different from zero at the $5\%$ significance level.²²²²22To provide further evidence that our main estimate is not driven by chance, we reassigned the treatment to all control characters in our data set. This allowed us to generate a distribution of “placebo” effects, which serves as a basis for comparing the impact on Graves \parencite[see, e.g.,][]abadie2010synthetic, abadie2015comparative. We report the ratios of post- to pre-treatment root mean squared error (RMSE) in Figure C.I in Appendix C, where Graves ranks second in terms of RMSE ratio. This implies that the impact on Graves is unusually large compared to the distribution of placebo effects, reinforcing the interpretation that our analysis provides significant evidence of a negative effect of the coming-out event. This implies a decline of $38.69\%$ of the pre-treatment average preferences for Graves.

We examine the robustness of our results to the choice of the estimator and the composition of units in the donor pool. In particular, we repeat our analysis employing a regularized synthetic control estimator (see Section 3.2) and we explore different donor pool configurations focusing on characters from distinct roles. Notably, Graves is predominantly designed for and played in three of the possible roles within a team. Consequently, there is a possibility of spillover effects on other characters mainly played in these positions, as players transitioning away from Graves are likely to switch to these alternatives.²³²³23The findings of Section 5.2 support this intuition. To mitigate this potential for spillover effects, we restrict our donor pool to characters that are “non-substitutes” of Graves, that is, those primarily designed for the remaining two roles.²⁴²⁴24Graves is predominantly designed for and played in the top lane, jungle, and mid lane positions. Therefore, we consider characters designed for and played in the bottom lane and support positions as “non-substitutes.”

The first panel of Table 1 displays the results. For any donor pool composition, the results are not sensitive to the choice of the regularization parameter. Point estimates are consistently negative and are statistically different from zero at the $5\%$ significance level across most of the considered specifications. The results are consistent also quantitatively across all specifications, with a decline ranging between $38.69\%$ and $37.49\%$ of the pre-treatment average preferences for Graves. Overall, these results support our main finding of a substantial negative impact of the coming-out event on players’ preferences for Graves.

We also assess the credibility of the synthetic control estimator by conducting a robustness check that artificially shifts the coming-out event ten days earlier. This backdating exercise allows us to evaluate the estimator’s predictive accuracy during a ten-day hold-out period \parencite[see e.g.,][]abadie2022synthetic. The upper panel of Figure C.II in Appendix C presents the results of this analysis. We observe three key findings. First, the estimated effects remain qualitatively and quantitatively consistent, confirming a negative and persistent impact of the coming-out event on players’ revealed preferences for Graves. Second, the synthetic control estimator demonstrates a good fit during the hold-out period, indicating its ability to accurately capture Graves’ behavior prior to the disclosure. Third, the actual and the synthetic series begin to diverge on the true day of disclosure, even when the estimator has no knowledge of the actual disclosure date. The absence of estimated effects before the coming-out event also lends support to the plausibility of a no-anticipation assumption \parencite[see e.g.,][]abadie2021using.

Finally, we conduct an additional robustness test by performing a leave-one-out exercise, where we repeatedly estimate the synthetic control series by excluding one character with non-zero estimated weights at a time from the donor pool \parencite[see e.g.,][]abadie2021using. The lower panel of Figure C.II in Appendix C presents the results of this analysis. Overall, our finding of a negative and persistent impact of the coming-out event on players’ preferences for Graves is robust to the exclusion of any particular character. Most of the leave-one-out synthetic series closely align with the main estimate, thus reinforcing the robustness of the main conclusion of our study. One leave-one-out series falls beneath the other synthetic series, suggesting a somewhat reduced, although still negative, impact. However, this series diverges from the actual series in the weeks prior to the treatment, which undermines the reliability of its results.²⁵²⁵25This series is obtained by excluding the character Ezreal from the donor pool. Figure B.I shows that this character receives the largest weight in our main specification. Therefore, the divergence of this leave-one-out series from the actual series is unsurprising.

4.2 Regional Heterogeneity

Previous research has demonstrated that attitudes toward LGB people can substantially vary between countries, causing also a large variation in the number of individuals openly identifying with the LGB community \parencite[see, e.g.,][]badgett2020economic, badgett2021lgbtq.²⁶²⁶26An OECD report shows that even within a set of relatively comparable OECD countries, the size of the LBG communities differs by a factor of four \parenciteoecd2019. To explore regional differences in players’ attitudes towards this community, we exploit the regional information of the matches. We divide our sample based on the server on which the matches were hosted. For comparability and data availability reasons, the matches are classified into four regional categories: European matches (North and East Europe and West Europe servers), Korean matches, Latin American matches (Brasil, North Latin America, and South Latin America servers), and North American matches. We then apply the synthetic control estimator of Section 3.2 to each of these categories separately.

Figure 3 and Table 1 display the results.²⁷²⁷27Figure B.II in Appendix B displays the identities and the contributions of the characters in the donor pool with non-zero estimated weights. The synthetic control estimator closely approximates the trajectory of Graves’ pick rates for matches in Europe and Latin America before the disclosure, exhibiting pre-treatment root mean squared errors comparable to those of the pooled specifications. However, discrepancies arise in Korean and North American matches, where the pre-treatment root mean squared error is two to three times higher than that achieved with European and Latin American matches. In Europe, Korea, and Latin America, we estimate negative and persistent effects of the coming-out event on players’ preferences for Graves. Point estimates for the average treatment effect in these regions are consistently negative and are statistically significant at the 5% level across most of the considered specifications. In North America, where the pre-treatment root mean squared is relatively large, we are unable to determine the sign of the impact, as the confidence intervals for the estimated average effect consistently encompass zero.

The estimated average effect varies substantially across regions, with the largest effect observed in Europe (-$61.30\%$ relative to the pre-treatment average preferences) and the smallest effect observed in Korea ($-32.39\%$) in our main specification, indicating heterogeneous responses to the coming-out event. However, it is important to consider that the different magnitudes of the estimated effects do not necessarily reflect differential attitudes towards the LBG community, as various other factors may differ across servers. One such factor could be the differential levels of competitiveness on different servers, which may affect the character selection process by introducing different levels of subjectivity. We therefore carefully interpret our results in this section as evidence for anti-LGB sentiments in various regions, rather than interpreting the differences in the effect sizes.

5.1 Graves’ Strength

Crucial to the plausibility of social stigma attached to playing an LGB character as the primary explanation for the players’ observed behavior is the fact that Graves’ strength remained unaffected by the coming-out event, as any change in character relative strengths could explain why players’ preferences shift away from Graves.

To address this concern, we employ the synthetic control estimator described in Section 3.2 to examine the potential impact of the coming-out event on Graves’ strength. We measure characters’ strength using daily win rates, which indicate the percentage of matches won by a character out of the total matches they participated in each day.

Figure 4 displays the results. Overall, our analysis reveals that the coming-out event had no impact on Graves’ strength. Despite the actual series exhibiting daily fluctuations around the $50\%$ mark, the synthetic control estimator effectively captures its pre-treatment trend, showcasing its ability to predict the counterfactual trend. After the treatment date, the synthetic control estimator continues to align with Graves’ win rate trend, confirming that the character’s strength was unaffected by the disclosure. The average effect is estimated to be $-1.446$ percentage points (standard error: $3.506$), and the conventional $95\%$ confidence interval encompasses zero, indicating a failure to reject the null hypothesis of no effect. These findings demonstrate that Graves’ strength remained unchanged during the coming-out event, dismissing the possibility of a shift in his strength as an explanation for the results of Section 4.1.

Moreover, we note that players have real-time access to detailed information regarding characters’ strengths, weaknesses, and overall performance, as numerous websites continuously provide updated data on characters’ in-game statistics.²⁸²⁸28Examples of such websites include https://lolalytics.com/lol/graves/build/ and https://www.leagueofgraphs.com/champions/stats/graves. Therefore, players were well-informed that no game-relevant skills or attributes were altered during the treatment period, and they could observe that Graves’s strength remained consistent. These factors suggest that the negative impact of the coming-out event estimated in Section 4.1 is unlikely to be driven by actual or presumed changes in character relative strengths.

5.2 Players’ Skills

If highly skilled players exhibit distinct preferences for Graves or are less influenced by the character’s sexual orientation, the decision to switch from Graves might be driven by gameplay factors rather than social preferences for sexual orientation, thus challenging our social stigma narrative.

To address this concern, we examine the correlation between players’ skills and their decision to abandon Graves. We classify players into two groups based on their preferences for Graves before his disclosure: the first group comprises those who chose Graves in at least $5\%$ of their matches before the coming-out event (henceforth labeled as prior users), while the second group comprises the remaining players (henceforth labeled as non-prior users). We then examine performance differences both within and between these groups before and after the treatment. To mitigate potential noise from players with limited match appearances, we restrict our analysis to players who engaged in a minimum of $50$ matches before the disclosure. This yields a sample of $6157$ players, with $5317$ being non-prior users.

The top panel of Figure 5 displays the average pick rate for Graves among prior and non-prior users before and after the treatment. We observe a sharp decline in pick rates among prior users following the coming-out event, similar in size to the decrease shown in Figure 2. Conversely, non-prior users exhibit a marginal increase in average pick rates post-treatment, although this increase is practically negligible.

In the remaining panels of Figure 5, we investigate whether prior and non-prior users exhibit differences in their characteristics. First, the bottom left panel displays the average number of daily matches played by players. We observe similar numbers between groups both before and after the treatment, indicating that prior and non-prior users tend to engage in a comparable number of matches each day. We also note no differences in matches played post-treatment within both groups. This suggests that players are not leaving the game after the coming-out event. Instead, they are shifting their focus to other characters. Furthermore, Figure B.III in Appendix B reveals that neither prior nor non-prior users exhibit a change in their revealed preferences for roles in the game following Graves’ disclosure. This observation aligns with the intuition that players have sufficient alternatives, allowing them to easily switch to other characters and express their preferences at a low cost.

Second, the bottom right panel displays the players’ average win rates, a metric capturing players’ skills by measuring the percentage of matches won out of their total engagements. We observe no substantial disparities within and between groups, indicating that the preference for Graves and the decision to abandon this character are unrelated to players’ skill levels. Overall, these findings dismiss the possibility that game-play factors are the driving force behind the estimated effects of Section 4.1, lending additional support to the social stigma attached to playing an LGB character as the mechanism underlying the players’ observed behavior.

5.3 Players’ Performance

To ensure the accuracy of our measurement of players’ genuine attitudes toward the LGB community, it is crucial to assess whether shifting away from Graves to other characters impacts players’ performance. If there are performance costs, our estimates could be biased toward zero, as players might continue using Graves for strategic considerations. Moreover, if players switch characters primarily for convenience, our analysis might unintentionally capture a different phenomenon instead of the intended social stigma.

We employ difference-in-differences identification and estimation strategies to assess the impact of players abandoning Graves on their performance. We gauge players’ performance by their daily win rate, which measures the percentage of matches won out of their total engagements. Our analysis focuses on the $840$ prior-users of Section 5.2, who are classified into treated or control groups based on their responses to Graves’ disclosure. We consider two different definitions of the treatment, sorted by their intensity. In the first version, labeled moderate reduction, we classify as treated those players who decreased their average pick rate for Graves following his disclosure by at most $75\%$ of their pre-treatment average pick rate (the number of treated units is $244$). In the second version, labeled substantial reduction, we classify as treated those players who reduced their average pick rate for Graves by $75\%$ to $100\%$ post-disclosure (the number of treated units is $451$).²⁹²⁹29Figure B.IV in Appendix B shows the distribution of percentage reduction in average pick rates for Graves from pre-treatment to post-treatment among prior users. In both scenarios, the control group remains the same and consists of the $145$ prior users who did not reduce their average pick rate for Graves following his disclosure.

Under the standard assumptions of parallel trends and no anticipation \parencite[see, e.g.,][]roth2023s, we can identify the average treatment effect on the treated (ATT) using observable data. The parallel trend assumption posits that the performance of treated and untreated players would have evolved similarly if Graves’ disclosure had not occurred. While we cannot formally test this assumption, the findings of Section 5.1 and Section 5.2 provide substantial support for its plausibility.³⁰³⁰30Moreover, we demonstrate below the absence of pre-treatment differences in trends by reporting placebo estimates of the ATT that are not statistically different from zero. This is often viewed as a natural plausibility check, although even if pre-trends are perfectly parallel, this does not necessarily guarantee the satisfaction of the post-treatment parallel trends assumption \parencite[see, e.g.,][]roth2023s. As for the no anticipation assumption, it stipulates that in the weeks preceding the disclosure, players’ performance did not change due to the incoming Graves’ disclosure. The plausibility of this assumption was thoroughly discussed in Section 2.2 and Section 4.1.

We implement the approach of \textcitecallaway2021difference to target the ATT at a particular day $t>T^{pre}$:³¹³¹31The framework outlined in \textcitecallaway2021difference is broader as it accommodates multiple groups defined by the timing of treatment reception. This enables the identification and estimation of the group-time ATTs, defined as $ATT\left(g,t\right):=\operatorname{\mathbb{E}}\left[Y_{i,t}\left(g\right)-Y_{i$, where $G_{g}$ is a binary variable indicating treatment reception in period $g$. However, our data set features a single group, given that all treated players receive the treatment simultaneously (i.e., at Graves’ disclosure date). This allows us to simplify notation and focus on the time ATTs in equation (6) for the single group we observe.

where potential outcomes are defined as in Section 3.2, and $D_{i}$ is a binary variable indicating whether a player is treated or not. Under the assumptions of parallel trends and no anticipation, \textcitecallaway2021difference show that $ATT\left(t\right)$ can be identified by comparing the change in outcomes between the latest period before the coming-out event and day $t$ experienced by treated players to the change in outcomes experienced by control players.³²³²32Formally, \textcitecallaway2021difference show that $ATT\left(t\right)=\operatorname{\mathbb{E}}\left[Y_{i,t}-Y_{i,T^{pre}}|D_{i}=1$. Estimation is carried out by replacing expectations with their sample analogs.

Figure 6 displays the point estimates and simultaneous $95\%$ confidence bands for the $ATT\left(t\right)$.³³³³33Table B.I in Appendix B reports aggregated results by displaying the average time ATT. Overall, we find that shifting away from Graves to other characters has no impact on players’ performance. None of the estimated $ATT\left(t\right)$ is statistically different from zero, suggesting that transitioning to other characters does not result in any performance-related consequences. This finding highlights that the decision to move away from Graves is not influenced by performance considerations.

As a robustness check, we explore an alternative scenario where the parallel trends assumption is required to hold only conditional on pre-treatment covariates. In this context, we identify and estimate $ATT\left(t\right)$ using the doubly-robust approach of \textcitecallaway2021difference.³⁴³⁴34In essence, this approach entails estimating the change in outcomes for control players conditional on the pre-treatment covariates $X_{i}$ and averaging out $X_{i}$ over the distribution of covariates for treated players. For a more detailed understanding of this approach, readers are referred to \textcitecallaway2021difference. Our pre-treatment covariates encompass players’ skills information, such as average kills, deaths, assists, and gold earned prior to the treatment, as well as the average number of daily matches they engaged in before the treatment. Table B.I in Appendix B displays the results. The results are consistent with those obtained under the unconditional parallel trend assumption.

Finally, Figure 6 also displays placebo estimates of the time ATTs for the ten days before the treatment.³⁵³⁵35Figure B.V in Appendix B displays the remaining estimated placebo $ATT\left(t\right)$. As explained above, these estimates are valuable for “pre-testing” the credibility of the parallel trend assumption \parencitecallaway2021difference. Notably, all placebo time ATTs in the pre-treatment periods are statistically insignificant, supporting the validity of the parallel trends assumption.

5.4 New Substitute Character

On June $9^{th}$, $2022$, a new character (Bel’Veth) was released.³⁶³⁶36Figure B.VI in Appendix B displays Bel’Veth’s daily pick rates. Since the primary position the character is designed for is the same position as Graves is designed for, it can be considered a close substitute. Therefore, players’ decisions to switch away from Graves (after June $9^{th}$) might to some degree be driven by the desire to experiment with the new character and to explore potential competitive advantages, challenging social stigma as the primary explanation behind our main result.

If the release serves as the primary explanation for the observed drop in Graves pick rate we would expect a positive correlation between the size of the drop in players’ Graves usage and players preferences for the new character. In Figure 7 we show that this is not the case. Figure 7 shows the average pick rate for Bel’Veth for the prior users in Section 5.2, classified as in Section 5.3. We find that those players who feature a substantial reduction in their Graves’ pick rates following the coming-out event are less likely to pick Bel’Veth for their matches than players who feature a moderate reduction. Moreover, these players are even less likely to pick Bel’Veth for their matches than players who did not react at all to Graves’ disclosure. We therefore argue that the release is unlikely to serve as the primary explanation for the observed main result of the paper.

5.5 Coming Out versus LGBT Pride Month

As described in Section 2.2, the disclosure of Graves’ sexual orientation coincided with the start of LGBT Pride Month. This means that the coming-out event encompasses two “simultaneous treatments” \parencite[see, e.g.,][]roller2023differences, namely the announcement of Graves’ hom*osexuality and the introduction of visual and expressive elements in League of Legends that support the LGBT community. It is therefore plausible that the findings presented in Section 4.1 may, to some extent, be influenced by the presence of LGBT Pride Month, which might elicit negative reactions from certain players, leading them to shift their preferences away from LGB characters. While this alternative perspective does not undermine the validity of our identification strategy, it does raise questions about our interpretation of the estimated effects as solely stemming from Graves’ disclosure.

In Appendix E, we introduce a theoretical framework that formalizes the existence of two simultaneous treatments and discuss the implications for interpretation. Additionally, we outline sufficient assumptions that enable us to separate the impacts of coming out and LGBT Pride Month on players’ preferences for Graves. Here, we provide the main intuitions behind our approach, directing the reader to the appendix for technical details.

To examine the potential impact of LGBT Pride Month on players’ preferences for LGB characters, we leverage the existence in our data set of other four characters (Diana, Leona, Nami, and Neeko) already acknowledged as part of the LGB community before the coming-out event. These characters are subject only to a part of our treatment, specifically being part of the LGB community while LGBT Pride Month is ongoing, whereas Graves experiences both the disclosure of his sexual orientation and LGBT Pride Month.

We create a composite LGB unit by averaging the pick rates of Diana, Leona, Nami, and Neeko and employ the synthetic control estimator described in Section 3.2 to estimate the effect of LGBT Pride Month on players’ preferences for LGB characters. Then, under the assumption that the influence of LGBT Pride Month is uniform across all LGB characters, we can compare the results with those obtained for Graves to separate the impacts of coming out and LGBT Pride Month on players’ preferences for Graves. Intuitively, if the estimated impact of LGBT Pride Month on players’ preferences for LGB characters is small relative to the estimated impact of the coming-out event on players’ preferences for Graves, this suggests that the findings of Section 4.1 must be primarily attributed to Graves’ disclosure.

Figure 8 displays the actual and the synthetic pick rate series for the composite LGB unit. Overall, our analysis suggests that LGBT Pride Month had no impact on players’ preferences for LGB characters. Before the treatment, the synthetic control estimator closely aligns with the actual series, providing support for the estimator’s ability to predict the counterfactual series. After the treatment date, the synthetic control estimator continues to align with the actual series, confirming that the players’ preferences for LGB characters were unaffected by LGBT Pride Month. The average effect is estimated to be $-0.149$ percentage points (standard error: $2.832$), and the conventional $95\%$ confidence interval encompasses zero, indicating a failure to reject the null hypothesis of no effect. Under the hom*ogeneity assumption discussed above, these findings support the interpretation that the estimated effects presented in Section 4.1 are primarily driven by Graves’ disclosure rather than being influenced by the broader context of LGBT Pride Month.

E.1 Simultaneous Treatments

As described in Section 2.2, the disclosure of Graves’ sexual orientation coincided with the start of LGBT Pride Month. This means that the coming-out event encompasses two treatments occurring at the same time, namely the announcement of Graves’ hom*osexuality and the introduction of visual and expressive elements in League of Legends that support the LGBT community.³⁹³⁹39See, e.g., \textciteroller2023differences for a discussion on “simultaneous treatments” and methodologies for disentangling their effects under a Difference-in-Differences identification strategy.

We recognize the potential influence of LGBT Pride Month on players’ preferences for characters by introducing the binary variable $L_{i}\in\left\{0,1\right\}$ to represent character $i$’s inclusion in the LGB community no later than $T^{pre}+1$. Consequently, we observe three distinct groups of units: the first group includes only Graves, with $C_{i}=L_{i}=1$; the second group includes only Diana, Leona, Nami, and Neeko, with $C_{i}=0$ and $L_{i}=1$; and the third group includes all other characters, with $C_{i}=L_{i}=0$.⁴⁰⁴⁰40Neglecting the presence of two simultaneous treatments and treating them as a single treatment does not invalidate the results of Section 4.1. It primarily affects their interpretation, which, without further investigation, could only be attributed to the combined effects of simultaneously receiving both treatments $C_{i}$ and $L_{i}$ - referred to as the coming-out event in the main body of the paper.

To explicitly account for the influence of the two treatments $C_{i}$ and $L_{i}$, we define the potential pick rates as $Y_{i,t}^{c,l}$. Then, for each period $t>T^{pre}$, the effect of the coming-out event on players’ preferences for Graves in (1) corresponds to:

Equation (E.1) shows why we need to be cautious in interpreting the estimated effects of Section 4.1 as solely stemming from the disclosure of Graves’ sexual orientation. Under an extended version of the SUTVA assumption (see Section E.2), we observe $Y_{1,t}=Y_{1,t}^{1,1}$ for all $t>T^{pre}$, and the estimator in (3) effectively targets the counterfactual series $Y_{1,t}^{0,0}$. Consequently, the estimated effects presented in Section 4.1 encompass the combined impacts of both disclosing Graves’ sexual orientation and his affiliation with the LGB community during LGBT Pride Month. This can be formalized as follows:

with $\tau_{t}^{C}$ representing the effects of the disclosure on players’ preferences for Graves, and $\tau_{t}^{L}$ representing the effects of being part of the LGB community during LGBT Pride Month on players’ preferences for Graves.

E.2 Separating Simultaneous Treatment Effects

The decomposition in (E.2) offers a strategy to disentangle the effects of the two treatments $C_{i}$ and $L_{i}$ for Graves. If we can successfully estimate the two counterfactual series $Y_{1,t}^{0,1}$ and $Y_{1,t}^{0,0}$, then we would be able to construct estimates $\hat{\tau}_{t}^{C}=Y_{1,t}^{1,1}-\widehat{Y}_{1,t}^{0,1}$ and $\hat{\tau}_{t}^{L}=\widehat{Y}_{1,t}^{0,1}-\widehat{Y}_{1,t}^{0,0}$ of $\tau_{t}^{C}$ and $\tau_{t}^{L}$, respectively. This would allow us to quantify the extent to which LGBT Pride Month drives the main findings of Section 4.1.

To this end, we assume an extended version of the SUTVA that accommodates the existence of two different treatments.

Under Assumption 1, we can estimate the counterfactual series $Y_{1,t}^{0,0}$ by constructing a synthetic control unit that approximates the pick rates of Graves before the coming-out event as in Section 3.2. Thus, as shown in (E.2), the challenge in disentangling our causal effects of interest is to estimate $Y_{1,t}^{0,1}$ for $t>T^{pre}$, i.e., how Graves’ pick rates would have evolved if Graves were already part of the LGB community prior to the 2022 LGBT Pride Month.

Having a sufficient number of LGB characters other than Graves (that is, sufficient units such as $C_{i}=0$ and $L_{i}=1$) would enable us to estimate the counterfactual series $Y_{1,t}^{0,1}$ through standard synthetic control methods. However, since we only have four such characters in our data set, this approach is infeasible.

One way out is to estimate the impact of LGBT Pride Month on players’ preferences for LGB characters and compare the results with those obtained for Graves. If the influence of LGBT Pride Month is uniform across all LGB characters, this strategy provides insight into the role of LGBT Pride Month in driving the main findings of Section 4.1.

To achieve this, we create a composite LGB unit by averaging the pick rates of all characters such as $C_{i}=0$ and $L_{i}=1$ (namely, Diana, Leona, Nami, and Neeko), denoting this unit as character $j$ without loss of generality. Then, for each period $t>T^{pre}$, we define the effect of LGBT Pride Month on players’ preferences for LGB characters as the difference in character $j$’s potential pick rates at time $t$:

Under Assumption (1), we observe $Y_{j,t}=Y_{j,t}^{0,1}$ for all $t>T^{pre}$, and we can estimate the counterfactual series $Y_{j,t}^{0,0}$ by constructing a synthetic control unit that approximates the pick rates of character $j$ before the beginning of the 2022 LGBT Pride Month. We can then estimate $\gamma_{t}^{L}$ by computing the differences between character $j$’s observed pick rates and the synthetic counterfactual for all $t>T^{pre}$:

Finally, we introduce a hom*ogeneity assumption that leverages the estimates $\hat{\gamma}_{t}^{L}$ to provide an interpretation for the estimates $\hat{\tau}_{t}$ presented in Section 4.1:

Under Assumption 2, the relationship $\tau_{t}^{C}=\tau_{t}-\gamma_{t}^{L}$ holds. Thus, if the estimated effects of LGBT Pride Month on players’ preferences for LGB characters are small relative to the estimated effects of the coming-out event on players’ preferences for Graves, this suggests that the findings of Section 4.1 must be primarily attributed to Graves’ disclosure.