International Journal of Engineering and Management Research

Note that numerous studies have already identified various factors such as internal (e.g., psychological factor of spectators), external (e.g., weather or geographical distance between the cities where the teams are located), and economic factors (the income per capita of the home team’s and the visiting team’s region). Unlike prior studies, we intend to estimate and visualize both the direction and the magnitude of substitution effect caused by competing sport events on the attendance of MLB games. This substitution effect on the attendance demand of MLB games is often explained in terms of opportunity cost caused by the fact that spectators can physically attend only a sport event among available sport games due to schedule conflicts.

To this end, we consider games of two other professional sports leagues, NBA and the National Hockey League (NHL), as substitutes to MBL games. NFL games are not considered mainly because NFL season schedule is not overlapped with MBL season schedule. In contrast, NBA and NHL games can be accidently scheduled on the same day at near location when and where MLB games are scheduled. Under such circumstances, we speculate that the attendance demand of MLB games is somewhat impacted as the opportunity cost of attending to MLB games varies due to alternatively available NBA and NHL games.

In this study, we plan to measure the direction and magnitude of substitution effects across three dimensions. The first dimension we consider is a temporal dimension (e.g., the day of the week or play time of the game), which is most likely to affect the direction and substitution of substitution effects. The substitution effects on this temporal dimension will reflect the aggregated effects over the entire MLB franchises by the definition. On the second dimension, the substitution effects are aggregated over each MLB team based on team specific quality (e.g., fans’ relative loyalty toward MLB games over NBA and NHL games). Main insights from this dimension will be garnered by comparing substitution effects between MLB teams with and without high loyalty toward MLB games. Finally, the last dimension to assess substitution effects is to measure substitution effects based on teams’ current ranks in the league or performance in recent games (e.g., winning or losing streak).

attendance prediction models predict better than a generalized model (Strnad et al., 2017). Other studies identified scheduling (Forrest & Simmons, 2006), geographical distance between the cities where the teams are located (Buraimo & Simmons, 2008), or the population of hometown and league membership period of a team (Dobson & Goddard, 2011) as effective determinants of the attendance.

In terms of methodologies, many studies have adopted various tools from classical linear regression models to latest artificial intelligence and machine learning methods in sports economics and sports analytics fields. For example, the classical types of artificial neural networks (ANNs) and decision trees (DTs) have been widely adopted for various model tasks in sport literature (Maszczyk et al., 2011; McCullagh, 2010; Sahin & Erol, 2017).

Other studies combined multiple models into a collective prediction model called as ensemble as their analytics tools. Note that popular ensemble models such as Bagging (Breiman, 1996), AdaBoost (Freund & Schapire, 1995) or Random Forest (Breiman, 2001) have been known to significantly outperform the performance of single machine learning model in terms of its accuracy by reducing variance and bias components of errors from single prediction model. For example, King et. al. (2018) compared a set of machine learning algorithms to predict NHL average home game attendance with game- and team-level data. Interestingly, they included the number of Twitter followers as a surrogate for team popularity and recent team performance (e.g., win-loss streak). Similarly, Pand and Wang (2024) examined the attendance of NFL games over 5000 regular season games using various algorithms and reported that ensemble models like Random Forest outperformed other models using stadium related variables (e.g., name and age) and personal income as key predictive variables.

The most relevant set of previous studies to this paper, however, focuses on the economic factors of the attendance demand. For example, several studies tried to estimate the demand function based on ticket pricing (Garcia & Rodriguez, 2002; Madalozzo & Villar, 2009), the purchasing power of spectators measured by the income per capita of the home team’s and the visiting team’s region (Garcia & Rodriguez, 2002; Pand & Wang, 2024), or market size (Buraimo et al., 2009). In a recent study (Park et al., 2024), a macroeconomic variable,

Note, however, that thesubstitution effect considered in this study is different from the substitution effect in consumer choice theory, which relates a change in the relative price of a good to the amount of that good demanded by a consumer (Varian,2014).

On the second dimension, the substitution effects are aggregated based on team’s qualitative measure (e.g., fans’ relative loyalty toward MLB games over NBA and NHL games). The direction and magnitude of substitution effects on this dimension is difficult to be speculated in advance because fans’ relative loyalty is strongly dependent on state-, teams-specific, and other economic and demographic factors. Therefore, the analysis on this dimension will be mainly explorative.  

Finally, the last dimension we consider to assess substitution effects includes teams’ current ranks in the league or performance in recent games (e.g., winning or losing streak). We first speculate that MLB teams with lower standings will suffer from more severe negative substitutions effects than teams with higher standings. We attribute this reasoning to the fact that spectators are more likely to attend to sports events when the chance of their home team winning the game is high (Lemke et al., 2010; Pawlowski & Anders, 2015). In addition, we posit that MLB teams in a long winning or losing streak suffer from more severely than other MLB teams. This is mainly because spectators are more likely to attend to sports events when the game between teams with rivalry relationships or similar ranks in the division is expected to be fun and exciting (Buraimo & Simmons, 2008; Neale, 1964).

In addition, we speculate that the substitution effect is affected by measures that reflect teams’ current ranks in the league or performance in recent games.

4. Data Sets and Data Engineering

We downloaded several data sets through a data scraping program created with Python from multiple sources. First, the attendance data sets were scrapped from www.baseball-reference.com for each MLB game between 2008 and 2018. These data sets result in a total of 53,452 records with several variables such as game date, game day of the week, home and away team names, result, day/night game indicator, scores of home and away teams, and so on.

team (denoted as t) and each day of the week (denoted as wd). Then we use Attd_{Avg(t, wd)} values to estimate the direction (i.e., positive or negative) and magnitude (i.e., large or small) of substitution effects due to conflicted NHL or NBA games bring. To estimate the substitution effect of either NHL or MBA game scheduled on the same day with a MLB game, we compute the attendance deviance for a chosen game g (denoted as Attd_Dev_g) by subtracting Attd_{Avg(t, wd)} from the attendance of a MLB game (denoted as Attd_g) as shown in Equation (1).

Attd_Dev_g = Attd_g – Attd_{Avg(t, wd)}  (1)

Note that a positive (a negative) value of Attd_Dev_g represents an increase (decrease) of attendance to a specific MLB game that has a schedule conflict. Then, we compute the proportion of attendance deviance out of the average attendance (denoted as P(Attd_Dev_g) as follows:

P(Attd_Dev_g) = Attd_Dev_g / Attd_{Avg(t, wd)} (2)

While we may use Equation (2) to estimate substitution effect of a specific MLB game, we do not intend to estimate the substitution effect for each MLB game with schedule conflict because such an estimate is not reliable. Instead, we intend to estimate substitution effects over multiple MLB games by aggregating factors (denoted as F) such as each day of the week, each year, or each team. So, the substitution effect (denoted as Sub) over an aggregating factor F due to a schedule conflict league (denoted as L ϵ {NHL, MBA, or Both}) is computed as follows:

Sub(F)^L = || Attd_Dev^L_g ⊆ F ||^- / || D(F) ||^L (3)

where || Attd_Dev^L_g ⊆ F ||^- represents the total number of MLB games that have schedule conflicts with L league games, are a subset of MLB games aggregated over a factor F, and have a negative value of Attd_Dev_g. Similarly, || D(F) ||^L represents the total number of MLB games that have schedule conflicts with L league games and are a subset of MLB games aggregated over a factor F. In essence, Sub(F)^L in Equation (3) simply presents the proportion of MLB games with decreased attendance when they have schedule conflicts with attendance, when they have schedule conflicts with NHL or NBA games. For example, the substitution effect of NHL

According to Figure 1, the negative substitution effects by conflicted NHL games were more prominent on weekdays in order of Thursday (68%, indicating that 68% MLB games on Thursday with conflicted schedules with NHL games resulted in the decrease in attendance) followed by Wednesday (65%) and Friday (62%) than on weekends (Saturday (52%) and Sunday (57%)). The negative substitution effects by conflicted NBA games followed a similar pattern, more prominent on weekdays (Wednesday (69%), Tuesday and Thursday (65%)) than on weekends (Saturday (59%) and Sunday (51%)).

These make sense from the spectators’ perspective of opportunity costs. For example, most spectators have more free times during weekends than weekdays, making the opportunity cost of watching MLB games during weekdays is more expensive if all other things being equal. Therefore, it is very likely that spectators prefer watching NHL or NBA games during weekdays to watching MLB games during weekdays, which makes negative substitution effects during weekdays from NHL or NBA games on the attendance demand on MLB games much greater than those during weekends. We also find that Friday suffered less from the negative substitution effect by either conflicted NHL or NBA games than other weekdays. We attribute this finding to the fact that the opportunity cost of Friday is lower than those of other weekdays because it is the beginning of the weekends.

Figure 2: Substitution Effect of NHL and NBA Leagues over Years

Similarly, we aggregate the substitution effects of conflicted NHL or NBA games over another temporal aggregation factor, year, and summarize them in Figure 2.

Figure 3: Substitution Effect across Teams

In terms of the proportion of conflicted MLB games with negative substitution effect, most of teams that had more than 60 conflicted games experienced negative substitution effect (= decrease in the attendance) from 42% (BOS) to 78% (CHW) of conflicted MLB games. This great deviance of substitution effect indirectly insinuates that there are other MLB-team-specific factors to determine the magnitude of substitution effect. From limited data sets shown in Figure 3, among MLB teams with more than 60 conflicted games, MLB teams in the west division (e.g., LAA and LAD) suffered a relatively lighter substitution effect (50% to 51%), while several MLB teams in the central (e.g., CHC and CHW) and in the east division (e.g., NYM, NYY) experienced severe substitution effects (greater than 65%). However, it warrants follow-up studies to support the finding.

While substitution effects reported in Figure 3 present the aggregated substitution effects from both NHL and NBA league across MLB teams, substitution effects in Figure 4 show substitution effects for each league across MLB teams. Note that there are many MLB teams located in the cities that do not host NHL or NBA teams, which make them free from substitution effects by these alternative leagues. According to Figure 4, while several MLB teams (ATL, PIT, STL, and TBR) experienced substitution effect from only NHL league, several MLB teams (FLA, HOU, MIL, OAK, and SEA) experienced substitution effect from only NBA league.

Pawlowski & Anders, 2015) that audiences are more likely to attend to sports events when the chance of their home team winning the game increases.

We present a chart in Figure 5 that shows substitution effects of NHL or NBA leagues depending on MLB teams’ standings in the division. According to Figure 5, the proportion of MLB games that have conflicted schedules with NHL games and lower attendance than average attendance is steadily increasing (i.e., from 57% to 59%, 61%, 61%, and 62%) as the standing of MLB teams in the division is worse (i.e., from 1st rank to 5th rank). Similarly, the proportion of MLB games that have conflicted schedules with NBA games and lower attendance than average attendance also shows an increasing trend (i.e., from 58% to 57%, 62%, 61%, and 63%) as the standing of MLB teams in the division is worse (i.e., from 1st rank to 5th rank).

When we consider conflicted games of both NHL and NBA with MLB games, we observe that MLB teams in high standings suffered less from negative substitution effects than MLB teams in low standings in the division. While MLB teams ranked at 6th suffered most from conflicted NBA games (i.e., 69% of MLB games with conflicted schedules lead to less attendance than average), they suffered least from conflicted NBA games (i.e., only 40% of MLB games lead to lower attendance than average).

Figure 5: Substitution Effect with Team Places in Division

Another aggregation factor team performance we consider is the team’s winning or losing streak. We anticipate that spectators are more likely to attend to sports events when the game between teams with rivalry relationships or similar ranks in the division is expected to be fun and exciting.

As they are in more games of winning streaks, the proportion of MLB games with lower attendance starts to increase, peaks at a four-game losing streak, and decreases at a five or more games of winning streak.

6. Conclusion

In this study, we estimate the direction and magnitude of substitution effects due to NHL or NBA games with schedule conflicts on the attendance demand of MLB games. In particular, we aggregate such substitution effects over three different factors such as temporal factors, team qualitative factor, and team performance factor.

Overall, we observe that substitution effects NHL and NBA games more significantly negatively impact the attendance on MLB games during the weekdays (in particular, Thursday and Wednesday) than during the weekend. We also observe that MLB teams in high standings suffer less from negative substitution effects than MLB teams in low standings in the division. In particular, when MLB teams are in a losing streak, spectators show their deepest disappointments in their teams and avoid to attend MLB games in stadium.

While our analysis in this paper provides general insights on the direction and magnitude of substitution effects in MLB franchises, its empirical implication on each MLB team is somewhat limited. Therefore, in future work, we intend to focus our analysis on the subjectively chosen MLB team so that the stakeholders of the MLB develop tailored marketing and promotion strategies to minimize the negative impact of competing sports on the attendance demand on MLB games.

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