Due to errors in complex coupled feedbacks that compensate differently in different global climate models, as well as nonlinear nature of El Niño-Southern Oscillation (ENSO), there remain difficulties in detecting and evaluating the reason for the past and future changes in the ENSO amplitude,σniño. Here we use physics parameter ensembles, in which error compensation was eliminated by perturbing model parameters, to explore relationships between mean climate and variability. With four such ensembles we find a strong relationship between σniño and the mean precipitation over the eastern equatorial Pacific ( ). This involves a two-way interaction, in which the wetter mean state with greater acts to increase the ENSO amplitude by strengthening positive coupled feedbacks. Such a relationship is also identified in 11 single-model historical climate simulations in the Coupled Model Intercomparison Project phase 5 despite mean precipitation biases apparently masking the relationship in the multi-model ensemble (MME). Taking changes inσniño and between pre-industrial and recent periods eliminates the bias, and therefore results in a robustσniño– connection in MME, which suggests a 10–15% increase in the ENSO amplitude since pre-industrial era mainly due to changing mean state. However, theσniño– connection is less clear for their future changes, which are still greatly uncertain.