Scotland's World Cup knockout hopes: What they need to advance

Scotland's hopes of reaching the knockout stages of the World Cup for the first time are now out of their hands following a 3-0 defeat to Brazil in their final group-stage match. The result leaves Steve Clarke's side third in Group A with three points and a goal difference of -3, meaning they must rely on being among the eight best third-placed teams to progress.

With several groups still to be decided, Scotland fans face an anxious wait until Sunday to learn their fate. BBC Sport breaks down the scenarios that could see Scotland advance.

How third-placed teams qualify

Of the 12 teams that finish third in their groups, eight will advance to the last 32. If teams are level on points, the rankings are determined by goal difference. Scotland currently sit on three points and a goal difference of -3. According to Opta, teams with three points and a -3 goal difference have only a 42% chance of advancing, compared to 63% for -2 and 84% for -1.

As it stands, five third-placed teams are ranked below Scotland, and five have the same number of points. Four of those five still have a game to play. Scotland's chances took a further hit after South Africa's surprise win over South Korea, which moved South Korea into third place on three points with a better goal difference.

Results Scotland need

With nine groups left to play, Scotland need at least four of the following scenarios to occur:

Thursday

• Group E: Both Ecuador (v Germany) and Curacao (v Ivory Coast) to fail to win. Or Curacao to win by at least four goals and Ecuador fail to win.
• Group F: Sweden to lose to Japan by four or more goals.
• Group D: Paraguay and Australia, both on three points, play each other. A draw would send both through. Scotland need Paraguay to lose by two or more goals, or Australia to be beaten by at least four goals.

Friday

• Group F: Senegal and Iraq to draw. Or Iraq to beat Senegal by no more than two goals.
• Group H: Uruguay to lose to Spain.
• Group G: Iran to lose to Egypt.

Saturday

• Group L: Croatia to lose to Ghana by at least three goals.
• Group K: DR Congo v Uzbekistan to be a draw. Or Uzbekistan to win by no more than three goals.
• Group J: A carbon copy of Group D, with Austria and Algeria on three points. A draw sends both through. Scotland need Algeria to lose by two or more goals, or Austria to be beaten by at least four goals.

Scotland's fate will be determined by the outcomes of these matches, with the final group games concluding on Sunday.