Update III on the Women’s World Cup: is football coming home again?

Over the past weekend, Australia, England, Spain and Sweden all went through to the semi-finals of the Women’s World Cup. The upcoming matches will be tight, but the Lionesses are now favourites to lift the trophy on Sunday.

The Women’s World Cup is down to the final four teams: co-hosts Australia plus England, Spain and Sweden.

The Lionesses have had a couple of tense matches despite not facing their expected opponents in the Round of 16 (Nigeria rather than Australia or Canada) or the quarter-finals (Colombia rather than Germany). Nonetheless, England have now reached three successive World Cup semi-finals.

Those tight matches reflected the convergence between the women’s and men’s games previously noted, as teams from across the globe have become more evenly matched.

Brazil, Canada and Germany were unexpectedly eliminated in the group stages of the tournament before the United States – the top ranked women’s national team – fell in the Round of 16. Similarly, France, another strong team, were knocked out in the quarter-finals by Australia.

This means that the semi-finals are composed of teams currently ranked by FIFA in their top ten – just perhaps not the most likely composition. Sweden are ranked third, England fourth, Spain sixth and Australia tenth.

According to our Elo rankings, among the last four, England were the highest ranked team before the tournament (1388), just ahead of Sweden (1386). But as the tournament has progressed, Sweden have forged ahead of England, thanks to wins over the United States and the Netherlands.

Elo ratings adjust more for wins against stronger opposition. Sweden’s Elo rating adjustment for beating the United States was 13, whereas England’s for scraping past Nigeria was less than one. Sweden’s Elo rating is now 1410 and England’s just 1404.

Spain are the third-best team as ranked by our Elo ratings, although their journey through the tournament has been a little more nuanced. They made small gains thanks to routine wins over Costa Rica (89% chance) and Zambia (87% chance) to move from a pre-tournament rating of 1338 to 1341 by the time they faced Japan. But their defeat by the Japanese moved their Elo rating down to 1331, below what it was at the tournament’s outset.

Since then, knock-out wins against Switzerland and the Netherlands have brought their ranking up to 1349. It has been argued that Spain’s loss to Japan was strategic. By losing, Spain faced a weaker side in Switzerland (Elo rating 1125, FIFA 20^th) than Norway (Elo rating 1271, FIFA 12^th), past whom Japan battled in the Round of 16. Japan then faced, and lost, to Sweden (Elo 1410, FIFA 3^rd), rather than the Netherlands (Elo 1344, FIFA 9^th), whom Spain eliminated.

Such ‘winning by losing’ – often referred to as ‘tanking’ – is a feature that tournament organisers usually try to avoid, since it calls into question the integrity of a sport if teams or participants are not playing to win. But at the same time, tournament organisers like FIFA are attempting a complex optimisation procedure.

Round robin opening stages are common in global tournaments so that all contestants get a number of matches to take part in, hence making their travel and efforts worthwhile. But the manner in which the initial stages feed into bracket-style knock-out tournaments seems likely to throw up such perverse situations.

One proposal to circumvent this is allowing the best teams to ‘choose their opponent’, as Julien Guyon of New York University has proposed. That way, whoever finished top of the group that Spain and Japan were in would have had first pick of opponent in the Round of 16, and would have been to likely chose the easier opponent.

This particular World Cup had an additional geographical constraint – one half of the draw was being played in Australia, the other in New Zealand – and the final is where the two halves meet.

What are the likely outcomes this week?

Despite Sweden being ranked marginally higher than England, the Lionesses have the highest chance of winning the World Cup at 37%. Sweden are at 35%, and the difference is explained by England having the marginally easier semi-final (on paper at least), playing co-hosts Australia. Sweden have to get past Spain.

Table 1: Elo ratings and percentage chance of progress through the tournament

Country	Elo (pre-groups)	Elo (post-groups)	Elo (quarter-finals)	Elo (semi-finals)	Final (% chance)	Win (% chance)
England	1387.761	1401.024	1401.765	1404.374	68.09	37.15
Sweden	1386.196	1395.143	1408.402	1409.503	62.9	35.21
Spain	1341.832	1331.343	1340.994	1348.851	37.1	15.9
Australia	1316.55	1315.574	1318.136	1328.068	31.91	11.74

Source: Results from www.worldfootball.net and www.soccerbase.com, author’s tournament simulation based on Elo rating calculations.

Both will be tight matches, even if the game between England and Australia is slightly more imbalanced. While England have a 68% chance of beating Australia and making it to their first World Cup final, Australia also have a significant shot (32% chance of winning). In other words, if the match were to be repeated 100 times, the Australians would win 32 times and progress to the final. The match between Sweden and Spain is tighter still, with Sweden having a 63% chance of progressing, and Spain a 37% chance.

Australia are not without a chance: there’s a 12% chance that they go all the way and win their ‘home’ World Cup. Spain have a 16% chance of winning.

Where can I find out more?

Women’s and girls' game sees growth after a memorable year: November 2022 report from the FA.
World football Elo ratings: Ratings for national football teams.
Evaluating strange forecasts: The curious case of football match scorelines: study by James Reade and colleagues.
Going with your gut: The (in)accuracy of forecast revisions in a football score prediction game: research paper by James Reade and colleagues.
Handbook on the Economics of Women in Sports: book edited by Eva Marikova Leeds and Michael A. Leeds.