During the group stages, against Shakhtar Donetsk and Real Sociedad, United showed minimal ambition, happy enough to leave with a draw. The game against Bayer Leverkusen feels like an anomaly in United's season so far as, operating ahead of Ryan Giggs and Phil Jones, Shinji Kagawa orchestrated a devastating attacking performance.
The away fixtures during the Champions League knockout stages are a markedly different proposition from the group stages. Given the importance of away goals, a non-scoring draw has less value than it would in the group stages, and a score draw more.
With this in mind, it will be interesting to see whether Moyes varies from the extremely defensively minded approach he took against Shakhtar in the Ukraine, and more recently against Arsenal in the Premier League.
Given the need for an away goal, and the threats posed by Olympiakos, Moyes will need to strike a difficult balance.
Manchester United's Defensive Shape
Should Moyes opt for a safety-first approach, the midfield may look a little something like the image below, when in possession.
Robin van Persie operated as a lone striker in that game, with Danny Welbeck acting as an inside forward from the left and Valencia patrolling the right flank. In this image, Michael Carrick is off-screen, even deeper than Marouane Fellaini. Ashley Young would fulfil Welbeck's role should he play on Tuesday night.
This was the most straightforward 4-5-1 formation Moyes has played all season, with Tom Cleverley, Carrick and Fellaini packing midfield. Against Olympiakos, it seems more likely that Moyes will choose his preferred 4-4-1-1 with Young on the left, Antonio Valencia on the right and Wayne Rooney behind van Persie.
If he does, United's defensive shape may more closely resemble this still from the Arsenal game.
Whilst Rooney is seen in this image providing cover for Patrice Evra at left-back, that position would be, presumably, filled by Young, with Rooney himself dropping into a more central area, occupied by the cup-tied Juan Mata against Arsenal.
If Moyes does favour a 4-4-1-1 which morphs into something akin to a 4-5-1 when Olympiakos are in possession and Rooney drops deep, there is a selection dilemma in the heart of midfield.
With Fellani having returned against Crystal Palace, and he and Carrick having played reasonably well together, there is likely to be no place in the side for Cleverley, who, against Arsenal, had probably his best game of the season so far.
It is perhaps worth noting that were Sir Alex Ferguson still in charge, there is every chance that all three would play, with Rooney operating from the left wing.
The Arsenal image provides a template for how that could work. That has not been typical of the Moyes era so far, but it will be interesting to see how often Rooney is used in this way now that Mata is in the picture.
United's midfielders will be up against tremendous power and energy, in the form of Giannis Maniatis and Delvin N'Dinga. Against a more lightweight midfield, Ryan Giggs may have been more likely to be considered for selection for his experience, but more physical options will be preferred.
It would not, however, be a surprise to see Giggs return for the home leg.
In Javier Saviola, United's defenders and midfielders will also have to be extremely aware of the threat posed by the Argentine's intelligent movement.
Counter-Attacking Down the Flanks
Moyes' version of Manchester United are not shy about using the wings to attack. Much as the "get it out wide and get it in" approach has become something of a stick to beat Moyes with, there is no doubting that United can be a threat from the flanks on the counter-attack.
In these two stills from the game against Real Sociedad (with apologies for the slightly poor quality), it can be seen just how quickly intelligent wide play can be used to create a problem for opposing defenses.
In the first image, Kagawa is poised to release a through ball to the overlapping Evra, with Rooney, Fellaini and Javier Hernandez making their way into the box.
In the second, Rooney has received the ball from a cut back from Evra and is about to lay off the ball to Kagawa. Fellaini and Hernandez offer options, distracting defenders, and are potentially able to chase any rebounded ball.
The key to this is the number of players joining in United's attack and their movement. It also shows that Fellaini offers something neither Carrick nor Cleverley are likely to, both in his desire to get into the box, and how much he occupies defenders once he does. He lacks some speed to be truly vital in counter-attacking, but he does offer other contributions to that mode of attack.
With Hernan Perez likely to be a significant attacking threat, United's wingers will have to be wary of their own defensive duties, but they may be able to take some advantage of Perez's own preference for attack.
Counter-Attacking Through the Middle—Particularly Late On
In this image from the Arsenal game, Mata can be seen poised to release a through ball to van Persie, as Rooney occupies the attention of two Arsenal defenders.
Mata is, of course, cup-tied, but depending on the course of the match, and assuming he does not start, Adnan Januzaj may operate in a similar position should he come on as a substitute.
The key to this approach is that United's forward players are capable of remarkable things. In the moments that followed this still, van Persie received the ball from Mata and was able to make an opportunity from an extremely tight angle.
The Arsenal game was something of an off-day for van Persie. Should he be on his game, there is every possibility of an away goal or two.
Moyes will be hoping the balancing act comes off and United can head to Old Trafford with the advantage in the tie. Given United's performance this season, there is a great deal at stake for Moyes.