Ironically, it is Arteta who is the bookies’ favourite to be the next Premier League manager to lose his job, and not Allardyce, whose team were relegated on Sunday night thanks to this 19th defeat of a dismal season.
Arteta’s team kept their slim hopes of playing European football next year just about alive with a result which left them five points off the Europa League places with three games left to go, four points off a Europa Conference League place. Don’t hold your breath.
Meanwhile, Allardyce, never before relegated from the Premier League as a manager, finally succumbed to the drop with his eighth top flight club, hard though they had fought after he took over in December.
The former England manager had said he would think about his position if the worst happened – and is due to meet the Albion board for talks this week.
Arteta, meanwhile, is the man apparently set to stay until next season despite this deeply unimpressive campaign.
Significantly he made six changes from the side which slumped out of the Europa League with barely a whimper on Thursday.
Mind you, this one was hardly a glorious triumph for the Gunners, who once again had their youngsters to thank, as Emile Smith-Rowe gave them the lead after superb work from Bukayo Saka.
Nicolas Pepe added a second before a brilliant strike from Matheus Pereira caused nerves to flutter. Willian’s late free-kick gave a mediocre performance an undeserved touch of gloss.
There was a strong police presence outside the Emirates as fans gathered for another protest against Stan Kroenke’s ownership. But it was a subdued affair.
Albion, to their credit, fought all the way. Pereira almost gave them the lead when he curled a lovely drive an inch over the angle, and then Callum Robinson hit the bar, but was ruled offside.
Six minutes later Pepe, until then anonymous, picked up the ball from Callum Chambers, stepped inside, and curled a glorious shot into the far corner.
If only this sort of thing had happened on Thursday. Pepe saw his shot saved by Sam Johnstone as Arsenal threatened a third goal.
But this is Arsenal – and it was Pereira who stunned them, when the Brazilian picked the ball up inside his own half, raced through the middle as Arsenal’s defence retreated – and stroked home a quite brilliant goal. Suddenly, hopes were raised.
From Matt Phillips’ cross Albion thought they had saved themselves – at least temporarily – but Darnell Furlong’s header was an inch wide.
Then a minute from time Willian stepped up to curl his free-kick past Johnstone for his first Gunners goal. Big Sam was down. Mikel? Anyone’s guess on this evidence.