Pedestal and global plasma parameters are compared in conventional ELMy H-modes and improved confinement discharges from ASDEX Upgrade (AUG), DIII-D, JET and JT-60U with varying net input power. Both electron and ion pedestal pressures are studied. The pedestal top pressure pPED increases moderately with power in all tokamaks, in broad agreement with the power dependence of the IPB98(y,2) scaling. Higher pedestal pressures are observed in AUG improved H-modes and in JT-60U high βpol discharges at q95 ~ 6.5 and high triangularity. For all machines and all scenarios a robust correlation between total and pedestal thermal stored energy is observed, with the ratio of the two varying between ~0.3 and 0.5. However the relative importance of pedestal and core confinement varies from regime to regime. In AUG the confinement improvement with respect to the IPB98(y,2) scaling is due to improved pedestal confinement in improved Hmodes with early heating and to both improved pedestal and core confinement in improved H-modes with late heating. In DIII-D hybrid discharges the increase in confinement factor compared to conventional H-modes is due to improved confinement in the plasma core. JT-60U reversed shear H-modes have strong internal transport barriers and thus improved core performance. In all four tokamaks improved edge stability is correlated to increasing total bpol and H98(y,2) increases with pedestal βpol. The analysed multimachine data set supports a scaling expression for the pedestal stored energy derived under the assumption that the dominant loss term for the pedestal is by thermal conduction in the edge transport barrier region.