For the optimistic Rangers supporters who stayed up into the early hours of Friday morning, mathematical possibilities provided fleeting hope. With their first point finally secured and three group matches remaining, Danny Rohl's team could theoretically accumulate 10 points in the Europa League.
European Prospects Hanging by a Thread
The precedent exists - Fenerbahce progressed to the knockout stages with exactly that total and a negative goal difference last season. While the possibility remains technically alive, the reality facing Rangers is considerably more sobering.
The notion that Rohl's side could defeat Ferencvaros, Ludogorets and Porto to qualify seems increasingly fanciful. This current Rangers team lacks both the quality and character of previous squads that excelled on the European stage.
This European campaign has proven deeply forgettable. Believing that a team struggling so consistently domestically can suddenly transform itself for Thursday night European fixtures appears irrational. The supporters recognise this reality, evident in the peculiar atmosphere at Ibrox before the Braga encounter.
Squad Deficiencies Laid Bare
With Kevin Thelwell and Patrick Stewart now departed, the stands lacked their previous animosity. Yet there was equally no sense of a new beginning dawning. Instead, a profound lack of faith in this squad permeates the support, coupled with a long-overdue realism about what Rohl can realistically achieve.
The German manager has made a respectable start since taking charge. Supporters have clearly warmed to his charm and positive approach. However, the standard of player at his disposal remains modest and the ceiling for improvement appears worryingly low.
Rohl's immediate challenge involves making the most of his available resources until he can implement changes. While victory in Budapest in two weeks would keep their European hopes faintly flickering, the more pressing concern involves ensuring Rangers remain in Premiership title contention come the New Year.
Daunting Festive Schedule Ahead
Beginning with Falkirk's visit and extending through to the Parkhead trip on January 3, Rangers face eight crucial Premiership matches. This demanding schedule includes challenging away fixtures at Tannadice, Rugby Park and Tynecastle, while Hibs, Motherwell and St Mirren all travel to Ibrox.
Such a run would test even an in-form team. If Rohl can navigate this period unscathed with his current mediocre squad, it would represent an exceptional achievement. Although he has extracted slight improvement since his appointment, he began with the bar set remarkably low.
The impression remains that a season-defining winning streak across the festive period seems unlikely. Overcoming challenges like those ahead requires both ability and mentality - this Rangers squad demonstrates deficiencies in both areas.
These shortcomings became evident even during Thursday's draw that lifted them from the group's basement. Leading at half-time and seemingly coasting toward victory, Rangers faced a Braga side reduced to ten men around the hour mark.
Rather than pressing their advantage, Rangers became hesitant and erratic. Although Nasser Djiga's weak header that led to Braga's equaliser proved the costliest error, it wasn't the only mistake.
As the midfield trio of Mohamed Diomande, Connor Barron and Nico Raskin began malfunctioning, Rohl's team lost control of the match, ultimately clinging on desperately for a point during the closing minutes.
Despite encouraging passages of play either side of half-time, the German manager will have been troubled watching so many players retreat into their shells and display such limited composure during critical moments.
While Thelwell cannot be blamed for untimely injuries to John Souttar and Derek Cornelius, the signing of Djiga occurred under his watch. The on-loan Wolves defender possesses the physical attributes required of a centre-half, but his concentration remains suspect.
Having been culpable for Livingston's goal last weekend, he repeated the error against Braga. The moment Souttar returns to fitness, Djiga will likely be displaced, with a January return to Molineux probable if all parties agree.
Rohl's problems extend throughout the team, particularly in attack. The combined contribution of Youssef Chermiti and Danilo against Braga proved wholly inadequate, while Bojan Miovski appeared off the pace after coming off the bench.
No Rangers striker has scored in their previous five matches, nor does any appear likely to break that drought soon. The £8 million spent on Chermiti at Thelwell's recommendation must be causing chairman Andrew Cavenagh sleepless nights.
The data justifying such significant expenditure remains mystifying. The player hadn't scored a league goal for Everton in two years since arriving from Sporting Lisbon. Against his compatriots, he appeared as blunt as ever, managing just one goal in fourteen appearances despite his four-year contract.
The decision to move 29-goal Cyriel Dessers on to accommodate him seems increasingly questionable. Danilo continues to flatter to deceive. The Brazilian, contracted until 2028, has experienced injury problems since his £4.5 million arrival from Feyenoord.
However, he has been fit this season yet still failed to deliver. Three goals in nineteen matches represents a paltry return unlikely to attract potential suitors.
Miovski arrived with proven pedigree, having excelled at Aberdeen where his form earned the Dons a £6.8 million fee from Girona. Rangers paid an initial £2.6 million and offered a four-year deal.
Thus far, he has resembled a shadow of the player who first arrived in Scottish football from MTK Budapest. Two goals in sixteen appearances tells its own story. Has he regressed as a player or is he simply weighed down by the mediocrity surrounding him?
Rohl appeared unfazed this week about assuming greater recruitment responsibilities until Thelwell's successor is appointed. Given the scale of the mess the sporting director left behind, one transfer window probably won't suffice to resolve it.
The German manager faces numerous immediate challenges before that process begins. He must instil confidence and a winning mentality throughout the squad. Only when Rangers consistently demonstrate these qualities domestically will European campaigns become worth losing sleep over.