In a World Cup where the boffins with their big brainy heads and their super computers are working overtime on who might play who in the last 32, there are other calculations worth conjuring with.

As Steve Clarke's squad prepare to head for Miami to face Brazil on Wednesday, potentially the biggest day in the history of Scotland's national team, they travel having had no shot on target in their last game and a half in America and only two overall.

Che Adams, the principal striker, has had three touches of the ball in the opposition box in 146 minutes. One goal has been scored – a double deflection less than half an hour into the opening game.

Despite all their endeavour, all the heat they put on Morocco late on and a few big decisions that went against them, Scotland failed to register a shot on target on Friday, the first time that's happened to them on this stage since the 1986 World Cup.

They wanted to be a bazooka, but so far they're positively popgun. Taking the last Euros into account, Scotland have had five shots on target in their last five tournament matches. Their three goals across those five contests have come from two deflected shots and one own goal.

And yet, if the football data experts are to be believed, the chances of them progressing are high. The mad psychology is that win, lose, or draw, this might be the most glorious week in the long story of the national team, the moment they finally make it out of a group and into the nirvana of the knockout rounds.

A first-ever win over Brazil would do the job beautifully. Cue a Tartan Army carnival in Miami to wipe the floor with anything that's seen in Rio.

A draw would spark the same merry chaos. The avoidance of defeat would need to be a hell of a Scotland performance, one that would merit a place in the last 32.

Where the mentality gets interesting and, perhaps to some, complicated is if Scotland lose by a goal or two, or even three, and still make it into the next round. They could be utterly brilliant and progress and they could be utterly unthreatening and progress. They could play to keep the score down, pack the midfield, hoof everything downfield and never venture a shot on Brazil's goal and still make it through.

A strange kind of glory? Or, when you've lost out on goal difference so many times before, does it actually matter a damn?

Is the bottom line everything? Does the end justify the means? Never mind the quality, just rejoice in the qualification?

Would a win over Haiti followed by two defeats be acclaimed as a riotous success if it's enough to scrape into the knockouts as one of the best third-placed teams?

A point, or three, against Brazil and nobody needs to contemplate such existential issues. A result and Miami won't know what hit it, but they'll love it.

Clarke has been criticised in places for a supposed risk-averse approach against Morocco, a game that Scotland finished by having a forward line of Lyndon Dykes, Ross Stewart, Scott McTominay and Ben Gannon-Doak. If that was caution, it's hard to imagine what abandon looks like.

Clarke can't please some people, that much is obvious. No matter what he does, there is a constituency of fans out there that will slam him, some for legitimate reasons based on the paucity of the last Euros, many others because they just don't like the guy.

Calling on him to be gung-ho from the get-go against Morocco, or Brazil, is deeply flawed because that's exactly what those teams want Scotland to do.

Clarke is trying to find a balance that sits somewhere between ambition and pragmatism and hasn't really found it yet, but he's trying. Everybody's an expert in telling him what to do.

Steven Naismith, the assistant manager, spoke in Charlotte on Sunday about the fine line that Scotland had to walk against Morocco and will have to walk against Brazil, an infinitely more technically adept team with searing pace out wide and world-class finishers.

Scotland can try to go toe-to-toe with them in the manner of a middleweight taking on a heavyweight. There's only going to be one winner there.

"If you look at Brazil in the last game [against Haiti] before half-time, it's 3-0," Naismith pointed out. "The game that's been on today [Spain led Saudi Arabia 3-0 after 24 minutes]… So there has to be a game plan, but that doesn't mean we're sitting around in our 18-yard box for 90 minutes because taking into consideration the conditions and the opposition, it's impossible to do."

The heat in Miami will be oppressive, considerably hotter than Boston. Expecting Scotland to 'go for it' like mad dogs in a meathouse betrays a serious lack of understanding of the weather here.

"It's at moments in the game where we feel as if we're dominating, then we need to take risks and be ready," Naismith said. "But there's going to be hard moments where we need to set our shape and wait.

"Some of their players have got similar traits to Morocco's forward players. We'll go and do what we need to do to get through the group.

"That's ultimately what we're here to do. But we need to make sure we're solid because, as you've seen in some of the results, teams are ruthless when they get the opportunity.

"I sat here last week and said, if we qualify out of the group, it's the first squad to do it. I think this squad deserves to do it. I think we've got the players to do it and I think we've got the manager to do it.

"The magnitude of these games is definitely as [big] as any games [the players] have played in, but you know you can be punished at any one moment. You've got to be switched on."

Naismith talked about Scotland getting into the final third and then making poor decisions, which is a quality thing and, despite the reputations of some of these Scotland players they went up against more accomplished operators last Friday in Boston and they'll be doing the same again on Wednesday in Miami.

"When we've got possession, and we've got a good feel in the game that we're in control, we need to take risks to try and score," he said. "That's the bit that needs to change.

"We don't need to go, 'if we lose 4-0, we've still got a chance of going through'. We need to take the chances, definitely, but I'd rather have a proper game plan than just going, let's go for it."

That's the essential weirdness of Scotland's situation. If they're trailing 1-0 late on, do they push, or do they settle? If they're trailing 2-0, do they commit more people forward or chase the game and run the risk of conceding more and taking themselves out of the tournament on goal difference in the process?

These are dilemmas you hope they don't have to face. Dan Marino, the greatest Miami Dolphin, once said of a player's mindset: "You have to feel you're the best at what you do. You don't have to come out and say it. But you have to know it within yourself."

Brazil will know it, that's for certain. Scotland need to believe it, too.

A game of football, but also a fascinating and complex game of psychology. What a denouement to the group this promises to be.