It all started so well for the Clarets when Scott Arfield gave them a 14th-minute lead over Chelsea on the opening weekend, but that remains their only goal of the campaign - a drought of 616 minutes without finding the back of the net.
They are, at least, a hard team to beat - as evidenced by three consecutive goalless draws against Manchester United, Crystal Palace and Sunderland respectively.
Only two teams in Premier League history have ever recorded four goalless draws in a row, however, while Burnley have not kept a clean sheet in their last 19 meetings with West Brom in all competitions.
The Clarets did record their first ever away clean sheet in the Premier League at Selhurst Park a fortnight ago, however, and Dyche will be confident of another this Sunday.
Both will be missing again this weekend, although the latter is expected to be back in action in time for next week. Matthew Taylor is also absent through injury, while David Jones, Kieran Trippier and Dean Marney are all slight doubts.
While Burnley are still going in search of that crucial first win, West Brom got that particular monkey off their back last weekend in surprising fashion.
The Baggies took all three points away from White Hart Lane to hand Alan Irvine his first Premier League victory as manager, and they followed that up with a 3-2 win over Hull City in the League Cup on Wednesday.
Despite their midweek treble, league goals have also been an issue for the hosts, who have found the net just three times themselves this season.
They too have injury problems up front, with Brown Ideye due to undergo a late fitness test having been forced off early during the win over Hull on Wednesday.
The Baggies are yet to pick up a home victory in the Premier League this season, but they will certainly fancy their chances of ending that duck this weekend.
West Brom: WWLLDD
Possible starting lineups
West Brom: Foster; Wisdom, Dawson, Lescott, Pocognoli; Dorrans, Gardner, Brunt, Morrison; Berahino, Ideye
Burnley: Heaton; Trippier, Duff, Shackell, Mee; Arfield, Marney, Jones, Boyd; Jutkiewicz, Sordell
Sports Mole says: 1-0