Ron Guth:
The 1913-S Quarter is one of the great rarities in the Barber Quarter series. It is second rarest to the 1901-S Quarter and about on par with the 1896-S, though the 1896-S is less rare in circulated grades. Fortunately, collectors of long ago preserved some very nice examples of the 1913-S Quarter, including approximately 50-75 Mint State examples. Amazingly, the 1913-S is one of the few dates in the series that is represented by an MS68 example (a phenomenal condition-rarity). MS64 and MS65 seem to be the most plentiful Mint State grades, but even those are very rare and valuable. Above MS66, the 1913-S is extremely rare.
Some 1913-S Quarters feature a die crack connecting the lower right loop of the 3 with the bust just left of the tip. On the latest die states, the crack continues from the bottom of the 3 downward to the left until it hits the rim. Given the small mintage of this date, the crack may have been the reason for the early retirement of the dies.