They were probably produced each December for use as New Year's gifts, continuing the earlier imperial tradition of producing both bronze medallions and ordinary copper
asses at the same time of year for the same purpose. See the Purpose of Medallions
thread in Classical
Numismatics.
Ordinary 1st-3rd cent. bronze coins with hammered-up edges were apparently also used as New Year's gifts, perhaps especially in the late third century and the first half of the fourth century, when the mints were producing very few bronze medallions and no larger bronze coins for circulation.
This custom influenced the design of the
contorniates in two ways: their raised
rim and incised groove imitated the hammered-up edges of those bronzes, and their
types frequently copied old bronze coins, e.g. obverses of
Augustus,
Nero,
Vespasian,
Trajan, and corresponding reverses too, sometimes even taking over the letters S C of the prototypes.
The
countermarks on
contorniates, and many of the
types too, apart from those copied from old coins,
had to do with
chariot races and other entertainments in the
Circus. I proposed a possible reason for this
Circus connection in my unpublished paper presented at the 1986 International Numismatic Congress in
London: the New Year's medallions and
asses, and later the
contorniates, may have been distributed at
circus games held in
honor of
Sol on 25
Dec. each year.