<p>The inherent asymmetry and diversity of the El Niño-Southern Oscillation (ENSO) pose substantial challenges to its prediction. Potential predictability measures the upper limit of predictability for a certain event. Assessing the potential predictability of ENSO across varying phases and intensities with sophisticated climate models is crucial for understanding the upper limits of forecasting capabilities and identifying room for future enhancement. Based on the hindcast dataset with a recently developed ensemble forecasting system (the community earth system model, CESM), this study comprehensively investigates potential predictability for ENSO across different phases and intensities. The findings reveal that La Niña events possess higher potential predictability relative to their El Niño counterparts. Strong events exhibit significantly higher potential predictability than weak events within the same phase. The potential predictability of distinct ENSO types is primarily influenced by the seasonal variation inherent to their predictability. Regardless of the event classification, the potential predictability is characterized by a rapid decline from spring onwards, with the apex of this decline occurring in summer. The intensity of the seasonal predictability barrier inversely correlates with the upper limit of potential predictability. Specifically, a weaker (stronger) seasonal barrier is associated with a higher (lower) potential predictability. In addition, there is significant interdecadal variability both in the predictability of warm and cold ENSO events. The potential predictability for La Niña events decreases more slowly with increasing lead months, particularly in recent decades, resulting in an overall higher upper limit of potential predictability for La Niña events than for El Niño events over the past century. Nevertheless, El Niño events have also maintained a high potential predictability. This suggests substantial potential for improvement in future prediction for both.</p>