In the Champions League they have three wins from five, and will guarantee their status as group winners if they beat Benfica.
The two sides of Schalke
As it prepares for the 20th anniversary of its formation, in 2012, the Champions League will not look back with huge pride on the group stage of the current competition.
Sure, it has had its moments, its glamour ties, such as AC Milan against Real Madrid, but, looked at through the lense of greater diversity, wider opportunities for the upwardly mobile, the values Michel Platini, the Uefa president, wants injected into the event, the picture is cloudy. This has so far been a polarised edition of club football's greatest tournament.
Ask MSK Zilina, the Slovakian champions. They have conceded 17 goals in five matches on their debut among the 32 elite teams of the European continent.
Their points yield is zero, their impact appreciated mostly by Bursapor, the Turkish league title-holders, whose record of conceding, on average, three goals in each of their group games was set to make theirs the worst defensive record on display, until Zilina let in seven against Marseille.
Bursapor played 429 minutes of Champions League group-stage football before scoring their only goal. Partizan Belgrade, meanwhile, actually scored an equaliser at home to Arsenal, whom they meet again in London tomorrow, back in September. But they lost, and have not scored since. Like Bursaspor and Zilina, they are without points or prospects.
If Arsenal have made life strangely difficult for themselves, the Champions League seems a far easier environment than the Premier League for Tottenham Hotspur, Chelsea and Manchester United, who all top their groups. Real Madrid and Barcelona secured first place in their mini-leagues ahead of deadline, while, of the Italians, Roma need only a point to join AC Milan and Inter Milan in the next phase.
As for Germany's finest, only Werder Bremen are gasping for air. Their struggles in the Bundesliga have been matched in Europe. But Bayern Munich and Schalke - both through to the last 16 - must wish they could play Champions League opposition, rather than compatriot teams, every weekend.
Especially Schalke, Europe's most Jekyll-and-Hyde club. Having made their big splashes in the summer transfer window, hiring the Champions League legend Raul from Real Madrid, the prolific Klaas-Jan Huntelaar from Milan and the playmaker Jose Manuel Jurado from Atletico Madrid, they promptly plummeted in the domestic table, losing their first four Bundesliga fixtures.
They suffered defeat on Matchday One in Group B of the Champions League, too, against Lyon, but in Europe, their fortunes would alter much sooner than in the Bundesliga, where they remain 15th, one place above the relegation play-off position, with just four wins from 15 games.
In the Champions League they have three wins from five, and will guarantee their status as group winners if they beat Benfica, who are competing only for Europa League status, in Lisbon tonight.
Now compare Schalke's form against Champions League opposition with their record against non-Champions League teams, and their dual personality is even more pronounced.
Their two most recent wins against German teams have been at the expense of Bremen, who they thrashed 4-0, and Bayern, who they beat 2-0 at the weekend: Bayern and Bremen are both in the Champions League; Kaiserslautern, who walloped Schalke 5-0 nine days ago, are not.
One theory offered to explain this sort of inconsistency is that the newcomers, such as Raul and Huntelaar, need more adapting to the Bundesliga than to competitions in which they have been involved, with other clubs, for several years.
Raul, after a slow start domestically, is now finding the net regularly, though he must at times have wondered what he let himself in for at Schalke.
Felix Magath, the coach, suspended three players, Jermain Jones, Hans Sarpei and Alex Baumjohann after the Kaserslauten debacle. "I don't like their attitude," he said. He also threatened the rest of the squad with a shorter than anticipated holiday over the winter break.
11.45pm, Aljazeera Sport +6