Ticket consumption forecast for Brazilian championship games

For the efficiency of sales and marketing management of athletic clubs, it is crucial to find a way to appropriately estimate the level of demand for sporting events. More precise estimates allow for an appropriate financial and operational plan and a higher quality of service delivered to the fans. The focus of this study is to analyze and forecast the ticket consumption for soccer games in Brazilian stadiums. We compare the results of the regression model with normally distributed errors (benchmark), the TOBIT model and the Gamma generalized linear model. The models include explanatory variables related to the economic environment, product quality, as well as monetary and non-monetary incentives that people are given to attend sporting events at stadiums. We show that most of these variables are statistically significant to explain the amount of fans that go to stadiums. We used different measures of accuracy to evaluate the performance of demand forecasts and concluded that Gamma generalized linear model presented better results to forecast the ticket consumption for Brazilian championship games, when compared to a benchmark.

Keywords
Sports management; GLM; Ticket consumption; Soccer

Variable	Description	Expected effect
Economic enviroment variables
PCI	Annual per capita income in the city where the game takes place (in R$)	-
POP	City population where the game occurs	+
Variables related to product quality (soccer specific variables)
CLH	Classification of the home team	-
CLV	Classification of the visiting team	-
PGH	Points won by the home team in the past 3 games	+
PGV	Points won by the visiting team in the past 3 games	+
GLH	Goals scored by the home team in the past 3 games	+
GLV	Goals scored by the visiting team in the past 3 games	+
PT2	Value 1 if the match occurs on the 2nd stage of the championship	+
PT3	Value 1 if the match occurs on the 3rd stage of the championship	+
PT4	Value 1 if the match occurs on the 4th stage of the championship	+
CLS	Value 1 if the match is considered a classic	+
BIG	Value 1 if the game has a major league team from SP or RJ	+
Incentive variables
PRC	Average ticket price	-
WND	Value 1 if the match occurred on the weekend	+
NGT	Value 1 if the match occurred after 9:00 PM	+
RAN	Rainfall (in mm)	-

Variable	n	Average	Standard deviation	Minimum	Maximum	Skewness
PUB	3659	13,939	11,033	147	87,895	1.89
LOT	3660	42,259	22,525	9500	95,000	0.78
PCI	3660	2262	584	364	3835	-0.17
POP	3639	3,608,558	3,771,287	15,051	11,253,503	1.10
CLH	3660	10.57	6.14	0	24	0.07
CLV	3660	10.55	6.13	0	24	0.07
PGH	3602	3.83	2.31	0	10	0.25
PGV	3602	4.16	2.34	0	12	0.15
GLH	3601	3.89	2.14	0	13	0.45
GLV	3597	4.10	2.20	0	14	0.44
PRC	3583	20.36	12.27	1.00	39,099	10.08
RAN	3660	3.43	9.47	0	110	4.37

Variable	Categories	Frequencies	Relative frequencies (%)
CLS	Yes	292	8.0
CLS	No	3368	92.0
BIG	Yes	1683	46.0
BIG	No	1976	54.0
WND	Yes	2609	71.3
WND	No	1051	28.7
NGT	Yes	413	11.3
NGT	No	3247	88.7
PT	1	847	23.1
	2	971	26.5
	3	955	26.1
	4	887	24.2

	PUB	LOT	PCI	POP	CLH	CLV	PGH	PGV	GLH	GLV	PRC	RAN
PUB	1.000	0.382	-0.002	0.217	-0.241	-0.098	0.247	0.069	0.184	0.076	-0.347	-0.037
LOT		1.000	0.119	0.297	-0.111	-0.013	0.064	0.008	0.058	0.046	0.006	-0.022
PCI			1.000	0.086	-0.124	0.001	0.094	-0.016	0.151	0.073	-0.139	-0.019
POP				1.000	-0.176	0.007	0.080	-0.019	0.044	0.000	0.230	-0.045
CLH					1.000	-0.016	-0.348	0.056	-0.285	-0.019	-0.151	0.028
CLV						1.000	-0.034	-0.407	-0.029	-0.256	-0.043	0.003
PGH							1.000	0.148	0.541	0.028	0.079	-0.006
PGV								1.000	0.052	0.536	0.023	-0.013
GLH									1.000	0.120	0.028	0.002
GLV										1.000	-0.021	-0.014
PRC											1.000	-0.038
RAN												1.000

Variable	LRM		TOBIT		Gamma-GLM
	Coefficient	Std. error	Coefficient	Std. error	Coefficient	Std. error
Log PCI	-0.207^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.064	-0.262^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.062	-0.237^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.054
Log POP	0.166^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.012	0.164^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.011	0.151^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.010
CLH	-0.019^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.002	-0.020^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.002	-0.017^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.002
CLV	-0.012^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.002	-0.013^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.002	-0.009^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.002
PGH	0.048^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.006	0.049^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.007	0.043^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.006
PGV	-0.005	0.006	-0.004	0.007	-0.008	0.006
GLH	0.025^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.007	0.027^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.007	0.022^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.006
GLV	0.014^* * Significant at 5%.	0.007	0.013^* * Significant at 5%.	0.007	0.017^* * Significant at 5%.	0.006
PT2	0.148^* * Significant at 5%.	0.035	0.156^* * Significant at 5%.	0.038	0.135^* * Significant at 5%.	0.033
PT3	0.129^* * Significant at 5%.	0.035	0.133	0.038	0.116	0.033
PT4	0.221^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.038	0.242^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.038	0.272^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.036
CLS	0.289^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.043	0.301^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.048	0.276^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.040
BIG	0.226^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.027	0.236^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.028	0.200^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.025
Log PRC	-0.172^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.032	-0.177^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.030	-0.156^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.025
WND	0.198^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.032	0.201^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.032	0.177^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.029
NGT	-0.013	0.051	-0.014	0.052	-0.001	0.047
RAN	-0.002^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.001	-0.002^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.001	-0.002^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.001
Constant	8.236^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.496	8.725^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.491	8.875^ Significant at 1%. Heteroskedasticity-consistent standard errors (std. error).	0.428
Year dummies	Yes		Yes		Yes
n observations	3175		3175		3175
Log-likelihood	-3385		-3251		-32,593

Model	LRM	TOBIT	Gamma-GLM
RMSE
In sample	9866	9548	9429
		(3.22)	(4.43)
Out sample	42,349	38,026	30,064
		(10.21)	(29.01)
MAE
In sample	6707	6641	6382
		(0.99)	(4.85)
Out sample	10,938	9165	7238
		(16.21)	(33.83)
MAPE
In sample	73.34	72.56	61.65
		(1.06)	(15.94)
Out sample	59.32	58.03	50.62
		(2.17)	(14.66)

Departamento de Administração da Faculdade de Economia, Administração e Contabilidade da Universidade de São Paulo Avenida Professor Luciano Gualberto, 908, sala F184, 05508-900 São Paulo / SP Brasil, Tel./Fax 55 11 3818-4002 - São Paulo - SP - Brazil
E-mail: rausp@usp.br

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[1] * Corresponding author at: Rua Quatá 300, 04546042 São Paulo, SP, Brazil. E-mail:adrianab@insper.edu.br (A.B. Bortoluzzo).