Biocontrol potential index of pseudomonads, instead of their direct-growth promotion traits, is a predictor of seed inoculation effect on crop productivity under field conditions

•Seed inoculation with several Pseudomonas isolates improved wheat and maize yields.•Inoculation effect was assessed along 3 consecutive seasons in 3 different sites.•Isolates’ biocontrol potential index correlates positively with relative yields.•Isolates’ direct growth potential index correlates negatively with relative yields.•In vitro biocontrol potential of pseudomonads could predict their field performance.