The 1913-S Half Dollar is a semi-scarce date. In Mint State, it is ever-so-slightly more common than the 1913-P, but it is much less common than the 1913-D. As with most Barber Half Dollars, the 1913-S is most apt to be seen in MS63 and MS64. Gems are rare, with the low end of the PCGS CoinFacts Condition Census starting at MS65 to MS65+ then terminating on the high side with a single PCGS MS67 (that being the remarkable Friend-Duckor-Greensboro Collection coin illustrated above).
The 1913-S usually shows softness of strike on Liberty's lips, the upper right corner of the shield, and the adjacent feathers. Fully struck examples may not exist, but, if they do, they should be worth a substantial premium.