Galaxy clusters constitute powerful cosmological probes thanks to comparisons between observed and simulated clusters. As such Virgo constitutes a formidable source for detailed observations facilitated by its proximity. However, the diversity of clusters complicates the comparisons on a one-to-one basis. Simulated clusters must be carefully selected, a daunting task since most properties are unknown. Alternatively, lookalikes produced in the proper large-scale environment can be used. Additionally, their statistical study give access to the mean properties of the observed cluster including its most probable history as well as its deviation from an average cluster. This paper presents such a statistical study with 200 Virgo-like and 400+ cluster-size random dark matter haloes. Only 18 per cent (0.5 per cent) of these random haloes comply within 3(2)σ with the mean values (radius, velocity dispersion, number of substructures, spin, velocity, concentration, centre of mass offset with respect to the spherical centre) of Virgo haloes at z = 0 and abide by a similar merging history up to redshift 4. None are within 1σ because of environmentally induced properties (number of substructures and velocity). For further comparisons, random haloes are selected to reproduce the mass distribution of the lookalikes to cancel mass bias effects. Redshift 1 appears then as a turning point: random to Virgo-like property ratios are alternatively smaller/larger than 1. This highlights the importance of studying clusters within their proper large-scale environment: simulated galaxy population, grandly affected by the cluster history, can then be compared with the observed one in details. Direct lookalikes simplify grandly the challenge.