Table 2.

Mean absolute bias (MAB) and mean bias (MB) in 1800 estimates of the home advantage in a single season of soccer games between 20 teams, 100 for each combination of data generating process, team strength correlation ($\rho \ast$) and home advantage ($T\ast$)

Model	$\rho \ast =-0.8$		$\rho \ast =-0.4$		$\rho \ast =0$
	MAB	MB	MAB	MB	MAB	MB
$\mathit{T}\mathbf{\ast }=0$
Data generating process: bivariate Poisson
Bivariate Poisson	0.058	− 0.005	0.051	− 0.005	0.053	− 0.003
Paired comparisons	0.065	− 0.005	0.058	− 0.005	0.059	− 0.003
Linear regression	0.399	0.020	0.403	− 0.090	0.382	− 0.029
Data generating process: bivariate normal
Bivariate Poisson	0.058	0.006	0.060	− 0.010	0.061	0.007
Paired comparisons	0.059	0.006	0.061	− 0.010	0.062	0.008
Linear regression	0.460	0.036	0.480	− 0.070	0.446	0.032
$\mathit{T}\mathbf{\ast }=0.25$
Data generating process: bivariate Poisson
Bivariate Poisson	0.061	0.001	0.061	0.000	0.064	0.015
Paired comparisons	0.075	0.034	0.075	0.034	0.082	0.049
Linear regression	0.424	0.100	0.474	0.036	0.425	− 0.054
Data generating process: bivariate normal
Bivariate Poisson	0.073	− 0.019	0.068	− 0.017	0.084	− 0.015
Paired comparisons	0.074	− 0.015	0.068	− 0.013	0.085	− 0.010
Linear regression	0.485	− 0.070	0.454	0.070	0.427	− 0.006
$\mathit{T}\mathbf{\ast }=0.5$
Data generating process: bivariate Poisson
Bivariate Poisson	0.065	0.001	0.072	− 0.012	0.071	− 0.004
Paired comparisons	0.094	0.069	0.091	0.047	0.089	0.056
Linear regression	0.453	0.138	0.485	0.036	0.529	0.083
Data generating process: bivariate normal
Bivariate Poisson	0.070	− 0.021	0.067	0.007	0.063	− 0.004
Paired comparisons	0.070	− 0.015	0.069	0.013	0.063	0.002
Linear regression	0.549	0.060	0.450	− 0.021	0.549	− 0.042

Estimates produced using linear regression, paired comparison, and bivariate Poisson regression models. The mean absolute bias for bivariate Poisson regression compares favorably; when the data generating process of goal outcomes is bivariate Poisson, bivariate Poisson models most accurately estimate the home advantage. Furthermore, when the data generating process of goal outcomes is bivariate normal, bivariate Poisson and paired comparison models perform similarly, with the bivariate Poisson model slightly more accurate