Table 4.

Comparison of posterior means for pre-Covid and post-Covid goals HA parameters from Model (3), ${\widehat{T}}_k$ and ${\widehat{T^{\prime }}}_k$, respectively

League	${\widehat{T}}_k$	${\widehat{T^{\prime }}}_k$	${\widehat{T^{\prime }}}_k$ - ${\widehat{T}}_k$	% Change	$P(T_k^{\prime }<T_k)$
Austrian Bundesliga	0.161	− 0.202	− 0.363	− 225.7	0.999
German Bundesliga	0.239	− 0.024	− 0.263	− 110.2	0.995
Greek Super League	0.409	0.167	− 0.243	− 59.3	0.972
Spanish La Liga	0.306	0.149	− 0.157	− 51.3	0.959
English League Championship	0.234	0.114	− 0.119	− 51.1	0.912
Swedish Allsvenskan	0.231	0.108	− 0.123	− 53.3	0.907
Spanish La Liga 2	0.346	0.232	− 0.114	− 32.9	0.903
Italy Serie B	0.315	0.232	− 0.083	− 26.4	0.825
Norwegian Eliteserien	0.356	0.295	− 0.061	− 17.1	0.745
Russian Premier Liga	0.254	0.204	− 0.050	− 19.6	0.655
Danish Superliga	0.236	0.206	− 0.030	− 12.9	0.610
Turkish Super Lig	0.271	0.290	0.019	7.0	0.419
English Premier League	0.246	0.264	0.018	7.2	0.416
German 2. Bundesliga	0.191	0.249	0.058	30.5	0.266
Portuguese Liga	0.256	0.338	0.082	32.2	0.194
Italy Serie A	0.204	0.292	0.088	43.4	0.125
Swiss Super League	0.180	0.362	0.182	101.1	0.043

Larger values of $T_k$ and $T_k^{\prime }$ indicate larger home advantages. Relative and absolute differences between ${\widehat{T^{\prime }}}_k$ and ${\widehat{T}}_k$ are also shown. Probabilities of decline in HA without fans, $P(T_k^{\prime }<T_k)$, are estimated from posterior draws. We estimate the probability of a decline in HA without fans to exceed 0.9 in 7 of 17 leagues, and to exceed 0.5 in 11 of 17 leagues