Using a linear stochastic dynamical system, we further develop a recently proposed criteria of measuring variations in the predictability of ENSO. It is found that model predictability is intrinsically related to how the initial signal variance (ISV) projects on to its eigenmode space. When the ISV is large, the corresponding prediction is found to be reliable, whereas when the ISV is small, the prediction is likely to be less reliable. This finding was validated by results from a more realistic model prediction system for the period 1964--1998. A comparison of model skill and ISV for prediction made with and without data assimilation reveals that the role of data assimilation in improving model predictability may be mainly due to a further increase of ISV. Furthermore, model skill may result mainly from a few successful predictions associated with large ISV.