Steve Tandy's side were a whisker away from playing in last season's Final at the Kingspan Stadium but they have not the hit the ground running this time around.
Indeed only the Ospreys, Benetton Treviso and Zebre are yet to record a win and the Welsh region - who last won the title after a thrilling 2012 Final with Leinster at the RDS - are lying at the wrong end of the table.
This season's Final will be in Scotland, with BT Murrayfield playing host to the clash - click here to secure your seats.
Their next opportunity to arrest a slow start to the season comes on Friday night when they visit an in-form Edinburgh, who have not kicked off a PRO12 campaign with three straight wins since 2009.
But the omens suggest Ospreys could struggle - they have tasted victory just once in Scotland since September of that same year, while the last six encounters between these sides have been won by the hosts.
Should Edinburgh win, the table-topping Scarlets will have to match that feat on Sunday if they have designs of staying at the summit.
The Welsh region welcome Zebre - currently on an eight-match losing run in the GUINNESS PRO12 and having never toppled the Scarlets.
The closest they have ever come to that is a 16-16 draw in October 2013 and Wayne Pivac's troops, having won six on the bounce going back to last season, will be confident of ensuring that is still the case come Monday.
Newport Gwent Dragons will be hoping for a repeat of last season's trip to the RDS, where they beat Leinster 16-14 as part of a GUINNESS PRO12 double.
That result also represents the only time the Leinstermen have lost at home in all competitions since this weekend last year.
Glasgow Warriors have the opportunity to extend their GUINNESS PRO12 winning streak against Irish provinces to six when they travel to Munster.
Elsewhere, Benetton Treviso go in search of their first win outside of Italy since May 2013 when they visit the Kingspan Stadium, where Ulster are unbeaten in all competitions since Toulon came to town in October 2013.
And on Saturday, Cardiff Blues visit Connacht seeking to end a run of seven consecutive defeats on the road.
But Connacht also have an unwanted record to improve, having won just one of the last 11 meetings between these two sides.
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