With their first World Cup win in 36 years secured, Scotland fans are already deep in permutation territory. John McGinn's goal gave Steve Clarke's side a nervy 1-0 victory over Haiti at Boston Stadium, propelling them to the top of Group C – a position few had imagined before the tournament.
But the celebrations are tempered by arithmetic. The single-goal margin means Scotland now cannot finish on three points with anything other than a negative goal difference. According to Football Meets Data, a -1 goal difference offers an 87.5% chance of progression – a scenario that would unfold if Scotland lose their final two matches by a single goal each. That probability drops to 69.4% at -2, and 47.3% at -3.
“Scotland's 1-0 win over Haiti, their first World Cup victory in 36 years, leaves them top of Group C but reliant on goal difference for progression.”
Scotland's ineffective attack could prove costly. Their expected goals (xG) at Boston Stadium was just 1.05, with only McGinn's strike and Scott McTominay hitting the post. Set-piece deliveries were poor, resulting in a set play xG of 0. The saving grace was a defence that stood up to pressure to keep a clean sheet. Had Scotland scored another goal against Haiti, a goal difference of zero would have been possible, bringing a 96% chance of progression.
"Winning games at major tournaments isn't something Scotland do regularly," said former Scotland talisman James McFadden on BBC Scotland. "The resilience shown – that's what has been forged in this group. It wasn't enjoyable but I would have taken an ugly 1-0 win beforehand. The next two games are going to be tough, but they have dealt with the pressure of this game."
With eight third-place finishers advancing to the last 32, three points might be enough for Scotland to make history – but the path is precarious. Fans will now be poring over the permutations, wondering if the 1-0 win was enough to carry them through.