What do Scotland need to make World Cup knockouts?

Reaching the last 32 of the World Cup is out of Scotland’s hands after they suffered a 3-0 defeat by Brazil in their final group-stage game.

Scotland fans will now be clinging on to hopes of progressing as one of the eight best third-placed sides.

It means they may need to wait until Sunday to find out whether they will reach the knockouts for the first time.

With a potentially agonising few days on the way, BBC Sport guides you through what to look out for and how Scotland could still make it.

How can Scotland go through as a third-placed side?

By this point, you have probably heard a lot about how finishing third could still get you through.

Of the 12 teams who finish third in their group, eight will progress.

If teams in the third-place standings finish level on points, the rankings are then decided by goal difference.

That means Scotland will need to hope that at least four do not manage to reach three points, or they do so with a worse goal difference than them.

As it stands, there are five third-placed teams ranked below Scotland, and five who have the same number of points. Four of those five still have a game to play

Losing 3-0 means Steve Clarke’s men’s goal difference took a blow, with them now sitting on -3.

According to Opta, teams with three points and a -3 goal difference only have a 42% chance of making the last 32, while it’s 63% for -2 and 84% for -1.

Watch out for these games

In Group D, Australia and Paraguay are second and third respectively and meet in their final game. The losers would end the group with three points, while a draw would leave both sides on four.

On we go to Group E. Ecuador and Curacao have one point apiece and play Germany and Ivory Coast respectively. Failure to win would mean whoever finishes third cannot better Scotland’s tally of three points.

In Group F, Scotland will be hoping second-placed Japan beat third-placed Sweden convincingly. A point for Sweden, though, would leave the third-placed finishers on at least four points.

The key fixture in Group G as far as Scotland are concerned is Egypt v Iran. A win for Egypt will ensure the team finishing third will have fewer than three points.

It is the same situation in Group H where Scotland fans will be rooting for Spain to beat Uruguay so the third-placed team can only finish on two points, while in Group I, a draw between Senegal and Iraq would mean the team in third will have just one point.

In Group J, Austria and Algeria – second and third respectively on three points – meet in their final group game, so Scotland would not want that to end in a draw.

DR Congo and Uzbekistan are vying for third place in Group K.

A win for Uzbekistan would give them three points but, with a goal difference of -7, they would need a big win against DR Congo to move above Scotland in the standings.

In Group L, a point or more for Croatia against Ghana could be bad news for Scotland as it would again leave the third-place finishers with four points.

A big win for Ghana, and Panama not beating England, would be Scotland’s ideal scenario from a mathematical point of view.