What makes a coin or medal rare? Is it the total population, the graded population, or the avalible population?

This is a question that is always on my mind. I tend to believe it is the avalible population. Since regardless of the mintage the surviving population is the true degree of rarity. I know the graded population and the grade play a role in this as well. The problem I have is that since I primarily collect historical medals sometime finding the total mintage is extremely hard at time impossible. So I am forced to rely on what has come across the action block to make a determination of how rare a piece is.

By the way here is a picture of my latest addition. Betts 21 Holland Rivals Spain for the New World, 1602 desribed in the ford catalogue as follows Obverse: Dutch warships outmaneuver the Spanish galleon San Iago off St. Helena in 1601. The legend celebrates Dutch ability to do whatever can be done when needed. Reverse: Philip II of Spain's horse leaping into the New World closely pursued by the lion of Dutch Zeeland. The legend on this side may be translated as ''The world is not so big that where you go I cannot follow,'' alluding to Dutch rivalry with Spain for the towns of the West Indies and Brazilian coast. An important medal with the clearest connection to the larger history of the western hemisphere than any seen in Betts to this point. The rivalry between the two nations lasted the better part of the century to come. Non Sufficit Orbis is the Family motto of the Scottish Bond Family and was used as the title of the James Bond novel The World is Not Enough. This medal is quite rare.