### Introduction

### Attendance Determinants in Sporting Events

### Attractiveness factors

### Economic factors

### Demographic factors

### Residual preference factors

### Location Modeling in Sports

### Methodology

*Att*: average attendance of team

_{ij}*j*in season

*i*

*P*_{1ij}: population size of nearest county

*I*_{1ij}: median household income of nearest county

*D*_{1ij}: distance between stadium and population center of nearest county

*i*: season *i* (*i*=1,…,12)

*j* : team *j* (*j*=1,…,29)

*x*) values, the effect of the distance (

*x*) between the stadium and the county on MLB attendance could be determined. Based on the results of this model, a demand-weighted location model was constructed using the effect of the distance (

*x*) with data of not only the nearest county to an MLB team, but also other counties near the stadium. The demand-weighted location model of a stadium was constructed thus:

*n*: county of

*n*

^{th}nearest from stadium (

*n*=1, …, 5)

*n*is decided via this demand-weighted location model and the model fit tests (i.e., -2 log likelihood, AIC, and BIC).

*x*) of (

*n*) counties on attendance, the location variable of MLB stadium was decided. Also, it was possible to construct the full model of seasonal average attendance demand with other attendance determinants that were eliminated for reducing biases at the initial location models. Hierarchical linear modeling (HLM), also known as multilevel modeling (MLM) was also employed to provide an efficient explanation of the differences between seasons and between teams. Table 1 shows the variables that are employed in the model.

##### Table 1.

### Results

*σ*

^{*2}) and II (

*τ*

_{0}

^{*2}) were 17,422,451 and 49,450,062. Based on these values, the intraclass correlation (ICC) of season was calculated at 26.1%, indicating that nearly 26% of the total variance in MLB teams’ average attendance could be attributed to the seasonal differences of each team. Also, the remainder (73.9%) was from the differences between teams. This variance structure of data shows the average attendance of MLB depended on team characteristic more than seasonal changes.

^{-3}) because of high standard deviation by multiplying two variables.

##### Table 2.

*x*) of distance (Figure 1),

*x*was changed from 0.1 to 10. The model fit statistics, such as -2 log likelihood, AIC, and BIC, indicate that the model fits become better by increasing the power of distance. However, the model fit results were converged, and their difference was gradually reduced after the square of distance (

*x*=2). Also, the location variable was a significant predictor of average attendance from the original value of distance (

*x*=1.0;

*α*

_{1}=.0232,

*t*=2.03,

*p*<.05) to the 10

^{th}power (

*x*=10;

*α*

_{1}=.0309,

*t*=2.08,

*p*<.05). Based on these results of the model fit comparisons and simplification of the equation, the optimal power (

*x*) of distance was determined as two (

*x*=2) for the analysis of the distance effect between the stadium and the city on MLB attendance, and the location model of an MLB stadium was determined as follows:

*n*) of counties to influence MLB attendance. Figure 2 shows that the model fits (i.e., -2 Log Likelihood when

*x*=1,2,and3) are stable when the number of counties is increased. Therefore, the optimal number of counties for the location variable was one (

*x*=2,

*n*=1;

*β*

_{1}=.0247,

*t*=2.11,

*p*<.05). This result showed the MLB attendance was principally influenced by the demographic and geographic factors of the county that stadium is located.

*τ*

_{o}

^{2}=42,122,476) while the variance by seasonal differences wasn’t changed (

*σ*

^{2}=17,445,840) because most MLB teams had not changed the location of their home stadium during 2006-17 seasons. Even though six MLB teams (i.e., Atlanta Braves, Miami Marlins, Minnesota Twins, New York Yankees, New York Mets, and Washington Nationals) relocated to another stadium during this period, only the Braves and the Marlins moved to a new stadium in the different county.

##### Table 3.

##### Table 4.

*Location, FinalRank, Playoff, TeamAge, Champs, STD_Age, ProTeams*, and

*Season*) were excluded at the full model of MLB attendance model. Per these results, the final model of MLB attendance model was suggested as follows:

^{2}*γ*

_{10}=20210,

*t*=7.07,

*p*<.001), payroll (

*γ*

_{20}=.0023,

*t*=11.87,

*p*<.001), and number of star player (

*γ*

_{30}=284.4,

*t*=2.05,

*p*<.05) of teams positively affected the seasonal MLB attendance. Furthermore, the effects of stadium capacity (

*γ*

_{40}=0.55,

*t*=7.57,

*p*<.001) and ticket price (

*γ*

_{50}=79.68,

*t*=2.02,

*p*<.05) on attendance were significant. However, the recent season’s attendance had been gradually decreased by years (

*γ*

_{60}=-570.8,

*t*=-9.89,

*p*<.001).

*R*

^{2}measures were adopted in this study. Based on the variance between seasons, and between teams,

*R*

_{1}

^{2}and

*R*

_{2}

^{2}were measured, and

*R*

_{1}

^{2}indicates that the proportional reduction of prediction error by the final model six independent variables is 68.3%. Also,

*R*

_{2}

^{2}shows that the prediction error of MLB attendance would be reduced to 72.6% if season

*i*is fixed and team

*j*is randomly chosen, while

*R*

_{1}

^{2}and

*R*

_{2}

^{2}of the location model are 10.9% and 14.4%.

### Discussion

*Season*, and

*Season*) and the location variable, formulated by population, median income and distance, for an analysis of MLB attendance. However, some limitations remain. As previously mentioned, the unit of location data should be small and consistent because there was a variation in the size of the counties examined in this study. Furthermore, the location modeling in this study did not reflect the specific accessibility conditions of each team (e.g., public transportations, parking availability and price, traffic and road conditions). Because these conditions vary with cities, investigating the stadium location of each team or city is something that would be of value in future studies. Moreover, the detailed and precise data related to population, income level and population center would contribute to an even more robust description of the relationship between attendance and stadium location.

^{2}