Table 5.

Comparison of posterior means for pre-Covid and post-Covid yellow cards HA parameters from Model (4), ${\widehat{T}}_k$ and ${\widehat{T^{\prime }}}_k$, respectively

League	${\widehat{T}}_k$	${\widehat{T^{\prime }}}_k$	${\widehat{T^{\prime }}}_k$ - ${\widehat{T}}_k$	% Change	$P(T_k^{\prime }>T_k)$
Russian Premier Liga	− 0.404	0.037	0.441	109.1	0.997
German Bundesliga	− 0.340	0.039	0.379	111.4	0.986
Portuguese Liga	− 0.415	− 0.008	0.406	98.0	0.984
German 2. Bundesliga	− 0.392	0.090	0.482	123.0	0.982
Spanish La Liga 2	− 0.359	− 0.169	0.190	52.9	0.917
Danish Superliga	− 0.331	− 0.010	0.321	96.9	0.878
Austrian Bundesliga	− 0.251	0.063	0.314	125.1	0.863
Greek Super League	− 0.429	− 0.261	0.168	39.2	0.829
Italy Serie B	− 0.397	− 0.223	0.174	43.8	0.799
Spanish La Liga	− 0.269	− 0.094	0.176	65.3	0.719
Swedish Allsvenskan	− 0.196	− 0.063	0.132	67.6	0.682
English League Championship	− 0.478	− 0.393	0.085	17.7	0.675
Norwegian Eliteserien	− 0.323	− 0.266	0.057	17.8	0.615
Turkish Super Lig	− 0.199	− 0.122	0.077	38.8	0.599
Swiss Super League	− 0.327	− 0.282	0.045	13.7	0.581
English Premier League	− 0.293	− 0.366	− 0.073	− 24.9	0.376
Italy Serie A	− 0.344	− 0.489	− 0.145	− 42.1	0.240

In the context of yellow cards, smaller (i.e., more negative) 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 5 of 17 leagues, and to exceed 0.5 in 15 of 17 leagues