David Akers (1975/88): The 1883-S is a relatively common date that can be obtained in any grade up to and including average uncirculated without much difficulty. In choice mint state, the 1883-S is certainly scarce but not rare. True gems, of course, are quite rare but I have seen a number of coins in that category. Overall, the 1883-S is similar in rarity to the 1875-S, 1877-S, 1884-S, and 1902-S although it is much more difficult to locate in choice or gem Unc. than the 1884-S.
The Saddle Ridge Hoard of gold coins, discovered in northern California in 2013, contained forty-six 1883-S Double Eagles, the bulk of which were circulated. Of the ten Mint State examples in the hoard, the best examples were three PCGS MS63s.