'Scotland in need of revival to beat all revivals' - Tom English

As he must, Gordon Strachan continues to cling steadfastly to the hope that Scotland are still in with a chance of a place in the play-offs for the 2018 World Cup.

But Scotland's dismal 1-1 draw with Canada in Wednesday's friendly in Edinburgh has done little to boost a nation's hopes.

Group F is a grim sight for Scotland, who sit in fifth place with one win (against Malta) and four points from four games. On Sunday, at Hampden, they face second-placed Slovenia, who are unbeaten in the pool after a draw away against Lithuania, a win at home against Slovakia, a draw at home against England and a win away against Malta.

This, as Strachan and the Scottish Football Association's chief executive Stewart Regan have stated, is a must-win game. If the hope - some would argue the fantasy - of a place in the play-offs is to remain alive then Slovenia need to be beaten. Anything other than a home win and Scotland are done - and most probably - Strachan will be done, too.

The manager has had the full support of his employers at Hampden. Not long after the 3-0 loss to Slovakia in October and a second 3-0 loss to England in November, Regan threw his weight behind Strachan and against his critics. "We are not going to be swayed by social media," said the chief executive. "We are not going to be bounced by a kangaroo court - we are going to give Gordon a chance."

Mike Mulraney, a member of the board at Hampden, said after the 3-0 double-header: "Do I think we can qualify? Yeah, I think we can qualify. He (Strachan) is convinced he can get us into a play-off place. Gordon is convinced he can do it."

Alan McRae, the president of the SFA, has said the same. So, too, Rod Petrie, another member of the board.

• Match report: Scotland 1-1 Canada
• Poor start against Canada affected Scots - Strachan
• Select your Scotland starting XI to play Slovenia

Strachan said the other day that he didn't know how many points might be required to make the play-offs, that his focus was solely on beating Slovenia and nothing else. His short-term view is wise, but trying to project what Scotland might need in the coming six games in order to make those play-offs is still an instructive exercise that shows the vast scale of the job.

Based on what was required to make the play-offs for the last four major championships, Scotland are in need of something approaching a footballing miracle.

World Cup 2010 qualifiers

Eight teams qualified for the European play-offs for the World Cup in South Africa, from Russia as top seed with 22 points to the Republic of Ireland as eighth seed with 18 points.

These totals weren't the critical numbers, though. Just as the teams in Scotland's current World Cup group will have their victories against the bottom team - in this case, Malta - removed at group's end, so, too, did Russia and the Republic back in 2010.

Their revised totals were the ones that counted. The Republic still scraped in as eighth, and bottom seed, on 12 points. Of the eight nations in the play-offs, the average points required (minus the fodder points) was 14.25. Call it 14.

Right now (taking away the win against Malta) Scotland has one point with six games to play - or five games if you remove the home match against Malta. Presuming every other team in Scotland's group take maximum points from Malta - and they have so far - then in the real world there are 15 points up for grabs, not 18 points. Malta become irrelevant so long as everybody beats them. Even if you take eighth-seeded Republic of Ireland as the barometer from 2010, Scotland have to get another 11 points from those 15. That's three wins and two draws from Slovenia (home), England (home), Lithuania (away), Slovakia (home) and Slovenia (away).

Given that in the last two-and-a-half years the only nations that Scotland have beaten in competitive matches are Gibraltar and Malta, that looks like a footballing Everest.

Euro 2012 qualifiers

Again, results against the bottom team in each group didn't count, so after removing the fodder points, the eight that made the play-offs did so with a revised total ranging from Portugal's high of 16 to Turkey's low of 11.

The average number across the eight nations was 13.75 points. Round it up to 14. We can take the eighth seed, Turkey, as the reference point. Using their 11 points as a guide, Scotland would need 10 more points from 15. Three wins and a draw from the five remaining games that truly matter. A sizeable suspension of disbelief is required in order to see that happening.

World Cup 2014 qualifiers

The eight play-off teams, minus the points they secured against the bottom team in their section, ranged from Greece on 19 points right down to Croatia on 11 points. The average total of the eight worked out at 14.75 points. Call it 15.

If you take Croatia on 11 points as the focal point, Scotland still need 10 more points from the five big games left in their group. That's the best case scenario. That takes you back to three wins and a draw.

When talking about how Strachan believes they can still do it, did anybody at Hampden actually test this theory by looking at what other teams have had to do to make the last eight?

Euro 2016 qualifiers

This was the easiest major championship to qualify for in the history of major championships. Scotland still didn't make it, of course.

All second-placed teams made it automatically and the best-placed third team, Turkey, also got a direct passage to France. The analysis here is of those nations that finished third and, not surprisingly, the average total required to make the play-offs is lower than Euro 2012 and the World Cups in 2014 and 2010.

The average points total required to make the play-offs was 12.25 points. Round it down to 12. Slovenia made it with 10 points to scrape in as eighth seed. In that scenario, Scotland would need another nine points from the five games. Slovenia's total would leave Scotland still requiring three wins or two wins and three draws.

Strachan can't afford to distract himself with this stuff this week, but it's the reality of the situation he is in. If recent history is an indication, then Scotland are in need of a revival to beat all revivals to get themselves in the hunt for the World Cup.