The Gunners have beaten Chelsea and Brighton & Hove Albion in their last two games to move into 13th position in the table, but West Brom remain in 19th, having collected just eight points from 16 matches.
West Brom entered Tuesday's clash with Leeds United off the back of an excellent point at Liverpool and would have been looking to record their first home victory since the end of November.
A record of one win, five draws and 10 defeats has brought the Baggies eight points, leaving them in 19th position, five points from the safety of 17th place, which is currently occupied by Brighton.
There is still plenty of time for things to change, but it remains to be seen whether Allardyce is given the funds required to improve a struggling squad during the January transfer window.
West Brom are actually unbeaten in their last three Premier League home games with Arsenal, though, recording two wins in the process, and they have performed impressively against Manchester City and Liverpool over the last couple of weeks.
Head coach Mikel Arteta had been under huge pressure earlier this month, but there have been signs of progress in their last two matches, with a number of youngsters taking their opportunities to impress.
Three of Arsenal's next four matches in all competitions are at home, and a win at the Hawthorns would certainly hand them confidence ahead of a run of potentially-winnable fixtures.
That said, there is no getting away from the fact that it has been a disappointing campaign for the club thus far, having picked up just 20 points from their 16 matches to sit down in 13th position.
The Gunners are actually only nine points off the top four at this stage, but it is very difficult to imagine them being in contention for a Champions League spot come the end of the campaign.
West Bromwich Albion Premier League form: LLDLDL
Arsenal Premier League form: LLDLWW
Arsenal form (all competitions): LDLLWW
Allardyce is expected to recall Matheus Pereira to his starting XI on Saturday, while Branislav Ivanovic and Filip Krovinovic are also in contention. The experienced manager is likely to resist the temptation to make wholesale changes, though, despite the disappointing showing against Leeds.
Bukayo Saka is expected to be fit despite picking up a slight issue against Brighton, meaning that the Gunners could be unchanged from Tuesday's clash. Alexandre Lacazette for Gabriel Martinelli is a possibility, but the former has been excellent since his return from injury and could therefore keep his spot.
West Bromwich Albion possible starting lineup:
Johnstone; Furlong, Ajayi, O'Shea, Peltier; Robinson, Pereira, Sawyers, Gallagher, Diangana; Grant
Arsenal possible starting lineup:
Leno; Bellerin, Holding, Mari, Tierney; Elneny, Xhaka; Saka, Smith Rowe, Martinelli; Aubameyang
We say: West Bromwich Albion 1-2 Arsenal
West Brom will be determined to bounce back from their heavy defeat to Leeds, but it is difficult to back the Baggies on Saturday night. Arsenal have shown improvement in their last two matches, and we fancy the Gunners to claim all three points courtesy of a narrow success.
Top betting tip
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