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There are many measures of prediction skill and "reliability" is only one of them.  At this point there is no evidence that we're aware of that says that La Nina is more predictable than El Nino.  However, in this *one model* the reliability score does seem to suggest probabilities assigned during La Nina are better than that of El Nino. Sample size could play a role as well.  And in any case, this result doesn't necessarily translate to other models.

You're other idea is interesting and not one that we've ever looked at.  Agreed it would make an interesting figure, possibly something we'll look at in the future.