Frequency, probability, and miracles

A stock objection to miracles is that, "by definition," miracles are improbable. That depends, in part, on how you define improbability.

Many people who object to miracles treat improbability as a synonym for infrequency. Suppose we grant that definition for the sake of argument.

Can something be both frequent and improbable? That would seem to be a contradiction in terms, but is it?

Take chess. It's unlikely that a chess player will win all the time or even most of the time. In fact, it becomes more unlikely as he moves up the ladder because he is pitting himself against ever more talented opponents. The competition becomes increasingly tougher. 

Yet some chess players dominate the game. In their prime they are nearly invincible. 

Although a chess genius is improbable or infrequent, once you have a chess genius, he may win games with great frequency. The same holds true in other sports, viz. golf, tennis. 

Or we might take music. It's improbable that music of Mozartean quality would be a frequent occurrence. Yet Mozart was a very prolific composer, despite dying at a young age.

A musical genius is improbable or infrequent, but once you have a musical genius, he may compose top quality music with great frequency.

So we should perhaps distinguish between the frequency of the source and the frequency of the product given the source. Even if the existence of the producer is highly improbable, assuming the producer exists, the product may then be highly probable.