There is a reason, at the very moment Gareth Southgate and his players were having obscenities and plastic cups hurled at them in Cologne on Tuesday, every leading UK bookmaker was slashing the odds on England winning Euro 2024.

It had nothing to do with a sudden surge of optimism or a flurry of betting activity. After all, who would lump any money on an England triumph after that?

It was because of the way the tournament has begun to take shape: the odds for England were cut along with Italy, Austria and Switzerland. The odds on French, Spanish, German or Portuguese glory drifted accordingly.

If it was a free draw after the group stage, as what happens in European club competition, it would be hard to look beyond Spain, Germany, Portugal and — as poorly as they have played so far — pre-tournament favourites France.

But the path was pre-determined. The knockout bracket looked unbalanced before a ball was kicked. It has been unbalanced further by France’s failure to win their group, meaning they join Spain, Germany, Portugal and Denmark in the top half of the bracket. Belgium, should they finish second or third in Group E, could end up there too.

On paper, the bottom quarter of the bracket looks reasonably strong: Switzerland facing Italy in Berlin on Saturday; England facing a third-placed team (quite feasibly the Netherlands) on Sunday. But Switzerland, Italy and England won one game each in the group stage. Add the Netherlands (or whoever finishes third in Group E — Romania, Belgium, Slovakia or Ukraine) and it becomes four wins from a possible 12.

To spell this out, in the bottom quarter of the draw, a team that has won just once in the group stage will reach the semi-final — where the worst-case scenario would mean facing Austria, Belgium or the Netherlands. The most likely semi-final permutations in the other half of the draw might be Spain or Germany vs Portugal or France.

It was put to Southgate on Tuesday, after a dire 0-0 draw with Slovenia, that England might have got lucky with how the knockout stage is shaping up. “We shouldn’t be seduced by which half of the draw,” the manager told ITV Sport. “We have to take a step at a time. Tonight was an improvement. We’ve got to improve to win the next round.”

In his post-match news conference, it was spelt out to him that England had ended up on the opposite side of the bracket to Germany, France, Spain and Portugal. “We have huge respect for all of the teams you’ve mentioned but equally, there are some very good teams on our side of the draw,” he said.

Not equally, though. As at the 2018 World Cup, fortune has smiled on England and on all the other teams who have ended up on that side of the bracket — not least Austria, who are entitled to claim that, by finishing ahead of France and the Netherlands, they have made their own luck.

In 2018, five of the six top-ranked teams in the knockout stage (Brazil, Belgium, Portugal, Argentina and France) ended up on one side of the draw, while the other half consisted of Spain (who had won only one of their three group games), Russia, Croatia, Denmark, Sweden, Switzerland, Colombia and England.

That World Cup was widely regarded as Belgium’s best chance of winning a major tournament, with so many of their ‘golden generation’ of players at or around the peak of their powers. But they paid a heavy price for winning Group G, beating Japan and Brazil but then falling to France in the semi-final. England’s prize for finishing second to Belgium in their group was a place in the gentler side of the draw, which led to them beating Colombia and Sweden before defeat by Croatia in the semi-final.

Euro 2016 brought a similar imbalance. Italy, under Antonio Conte, excelled in the group stage, but their prize for winning Group E was to be placed on the tougher side of the draw. They beat Spain 2-0 but lost to Germany on penalties in the quarter-final. Germany in turn lost to hosts France in the semi-final. On the other side, Portugal — who had scraped third place in Group F by drawing with Iceland, Austria and Hungary — reached the final by beating Croatia in the round of 16, Poland in the quarter-final and Wales in the semi-final.

Some competitions are based on a free draw, such as the FA Cup. Others, such as the NFL or NBA, see teams ranked on their regular-season record, which should theoretically ensure the two strongest teams in either conference end up on opposite sides of the draw.

International football competitions — including the World Cup, European Championship, Copa America, Africa Cup of Nations and Asian Cup — do not work like that. It is pre-determined from the moment the draw is made: the winner of Group A will play the runner-up of Group B, the winner of Group C will play the runner-up of Group D and so on.

The group-stage draw is seeded, but teams are allocated to each group by a random draw, which raises the possibility of the knockout bracket ending up lop-sided. Because the tournaments are condensed into a four-week or five-week period, with matches played in a host nation, it is felt beneficial to have a pre-determined structure for planning, travel and ensuring each team has enough rest between matches.

There are still inconsistencies. Austria will have a seven-day break between the end of their group matches on Tuesday and their first knockout round next Tuesday, whereas Spain’s opponents in the round of 16 (still to be determined) will have had just four days’ rest.

Everything about knockout football lends itself to variance. But it can be predicted with some confidence that a team that has performed miserably at Euro 2024 will reach the semi-final or feasibly the final. After a difficult group stage, England, Switzerland, Italy and others have had a soft landing. For one of them, it might even prove a springboard.

(Top photo: Andreas Gora/Picture Alliance via Getty Images))