As of this writing (2015), it has been almost thirty years since David Akers published his ground-breaking "United States Gold Coins, An Analysis of Auction Records Volume IV Half Eagles 1795-1929." His observations on the 1872 Half Eagle can be seen in his excerpt below. In re-assessing this date, it is clear that several changes have taken place not only with this date but in the context of the other dates, as well.
Akers noted in 1976 that the 1872 was the only date among the half eagles struck at the Philadelphia Mint from 1862-1872 known in Uncirculated condition. However, in the intervening years, all of the 1862-1871 dates have been found in Mint State with the exception of 1865 and 1869. The 1872 Half Eagle remains a rare date. In terms of overall populations, only the 1865 beats the 1872 among the Philadelphia Mint issues from 1862 to 1872. Akers remains correct that the 1872 is the most populous coin in Mint State, though not by much. The most common grade for an 1872 Half Eagle, as determined by the PCGS Population Report, is AU53, which is a shift upward from Akers' EF. His statement that "...a few relatively choice examples exist" remains correct, and none have appeared in Gem condition. Today, the finest examples top out at MS64.
David Akers (1975/88)
The 1872 has one of the lowest mintages in the entire $5 series and so it is not surprising to find that it is very rare in all grades. Most specimens are in the EF range but a few VF's and AU's are also known. Unlike the earlier Philadelphia Mint Half Eagles from 1862-1871, the 1872 is known in uncirculated condition and a few relatively choice examples exist. All the business strikes I have seen have proof-like surfaces.