Having Arteta and Flamini as a two-man shield at the base of midfield was a sound tactic against Napoli. The Gunners already had ample experience of what the Serie A outfit could do on the break.
During the Emirates Cup, Napoli came to North London and stunned Arsenal with a pair of quick counter-attacking strikes. Both goals were created by runs and passes through the middle.
But Flamini and Arteta created a buffer against Marek Hamsik supplying passes for the likes of Lorenzo Insigne drifting off the flank and sprinting through the middle.
Perhaps buoyed by the solidity the Gunners showed in their 2-0 triumph over Napoli, manager Arsene Wenger retained the deep-lying partnership in midfield.
But this was a tactical misstep that was exposed against West Brom. With a pair of deep midfielders, Arsenal were simply too defensive and lacked their usual style and fluency.
With one less attack-minded player in midfield, the Gunners often had one fewer forward player supporting attacks. This suited West Brom perfectly.
Baggies manager Steve Clarke set his team up in a way that should have made Wenger realise he didn't need two holding players. After all, it was West Brom who positioned two enforcers, Youssouf Mulumbu and Claudio Yacob, in front of their back four.
So Wenger would have lost nothing defensively if he had stuck with relying on one holding player at the base of his midfield. That has worked wonders in the league this season and allowed Aaron Ramsey to flourish as an attacking force.
Playing both Flamini and Arteta ruined the balance of Arsenal's forward line. It meant moving Mesut Ozil, who was a delight on the left against Napoli, into the middle.
The German schemer went missing for large periods against West Brom. He needs to replicate his form in Europe in the EPL.
Granted, Ozil's struggles were partly due to having few options to provide scoring chances for. That is because moving him back into the middle put Jack Wilshere on the left.
But perhaps more importantly, it put Ramsey on the right. Neither player has the quickness to run behind a defensive line and it showed at the Hawthornes.
The result was Arsenal's attacks becoming too narrow and being funnelled straight into West Brom's own two-man, midfield barrier. The Gunners would have been better served with Ozil staying on one flank with either fleet-footed youngster Serge Gnabry or veteran Tomas Rosicky on the other.
They would have bracketed striker Olivier Giroud. Behind that forward line, Flamini could have shielded the back four, while Wilshere and Ramsey rotated positions and broke to support the attacking trio.
That would have retained Arsenal's forward-thinking quintet. Breaking in numbers has been the key to the Gunners' success so far this season.
Combination play formed by different triangles of players from quick-countering units has produced a number of goals. But that whole approach relies on committing more people in attack.
So what does that mean for the idea of playing Flamini and Arteta together? Perhaps its true value lies in deploying it for home games where Arsenal can expect teams to invite pressure and counter with pace.
Maybe the Champions League remains the best stage for it. In Europe's premier club competition, the pace of attacking and defensive exchanges is less intense than the frenetic, buccaneering environment of the EPL.
In most domestic games, Arsenal are gambling more if they take away one of their forward-breaking players. It was perhaps an experiment worth trying after the solidity Flamini and Arteta displayed against Napoli.
That would have appealed to Wenger, particularly since Arsenal had kept just one clean sheet in six prior league matches. It's not as if the ploy cost the Gunners too dearly. They still battled back against the Baggies to earn a creditable and valued away point.
But for Arsenal to regain their fluid ingenuity as an attacking force, Wenger has a tough choice to make between Flamini or Arteta to shield his defence and solidify the midfield.