Vinicius fortune: quantifying luck in the World Cup draw

Julien Guyon explains how bias, variance and luck affect teams in this summer’s tournament – and explores wider relevance for portfolio managers

The premiers of 2026 World Cup co-hosts USA, Mexico and Canada at the draw ceremony in Washington, DC

AP Photo/Alex Brandon/Alamy

Key points Summary Q&A

• Observers can scientifically determine how lucky or unlucky a team was during the World Cup draw by examining bias and variance in the draw process.
• The results show the draw process was biased towards some countries including Canada and against others, including Turkey. 
• A luck index measures the probability that the group stage draw could have been worse – namely, that a team could have ended up in a stronger group.

These summaries are generated by an LLM, but edited by humans.

For the next six weeks, living rooms, cafes and bars around the globe will hum with football chat as the 2026 Fifa World Cup unfolds. A perennial point of debate is the tournament draw, with some fans grumbling that their country was unluckily placed in a group of tough opponents, and others perhaps relieved that their team benefited from an easier draw.

But is there a scientific, quantitative way to determine how lucky or unlucky teams were during the tournament draw – and in the process gain some insight into financial markets and value-at-risk?

The 2026 World Cup has an expanded field of 48 teams, broken into 12 groups of four. Teams were sorted into four pots, based on Fifa rankings, and groups were randomly made by drawing one team from each pot. The exceptions to using Fifa rankings were the three host countries – Canada, Mexico and the US – which were placed in Pot 1, and some relatively high-ranked teams that qualified after the draw took place in December 2025 and had their placeholder in Pot 4, the pot of weaker teams. This created some bias, in particular towards Canada, which was favoured by the procedure (it would otherwise have been in Pot 3), and against Turkey which qualified through late playoffs but would otherwise have been in Pot 2.

Together with my student Thomas Buchholtzer at École nationale des ponts et chaussées, Institut Polytechnique de Paris, we ran 150,000 simulations of the official draw procedure to quantify and visualise biases in the draw, as well as rank teams from the luckiest to the unluckiest during the draw.

For each simulation, we measure the strength of a group as 98 minus the sum of the relative ranks 1–48 of the four teams in the group, based on an a priori ranking of the 48 qualified teams, so that a perfectly balanced group has strength zero, and tough groups have positive strength. To rank the 48 teams, we use either the Fifa rankings or the Elo ratings at the time of the draw. Elo ratings are a system that ranks players or teams taking their relative strength into account, most famously used for chess rankings. Elo ratings tend to reflect the teams’ values a little better than Fifa rankings, as their calculation takes goal difference and home advantage into account.

The 48 probability distributions of group strength based on our draw simulations are shown below – one for each team. The blue dotted vertical line represents the average of the distribution; the more this line is to the right of zero (the grey vertical line in small dots), the more the draw procedure is biased against the team, and vice versa. The orange solid line represents the strength of the group that was actually drawn.

Since the draw pots were built using Fifa rankings, distributions of group strengths are less spread out and tend to be more centred on zero when we use them to measure teams’ strengths. Since the US was ranked thirteenth in the Fifa rankings and twenty-eighth in the Elo ratings, we observe a bias in favour of the US when using Elo ratings. Similarly, since Norway was ranked twenty-sixth in the Fifa rankings and eleventh in the Elo ratings, we observe a bias against Norway when Elo ratings are applied to the original draw. When we use Elo ratings, we conclude that the draw procedure was mostly biased against Turkey and Norway, and in favour of Canada, the US, South Africa, and Bosnia and Herzegovina.

To measure how lucky a team is during a draw, one must disentangle the pure element of luck from the possible bias in the draw procedure. For instance, Turkey ended up in a strong group (their orange line is to the right of zero), but were lucky during the draw (their orange line is to the left of their blue dotted line).

To isolate the pure element of luck during the random draw, we measure the probability that the group stage draw could have been worse – namely, that a team could have ended up in a stronger group. I call it the ‘luck index’. It is the area under the probability distribution curve to the right of the orange line and corresponds to the notion of p-value in statistics. The luck index is a number between 0 and 1, close to 0 if there is a very small probability that the draw could have been worse (very unlucky team), and close to 1 if there is a very large probability that the draw could have been worse, ie, a very small probability that the draw could have been better (very lucky team), given the draw procedure.

 

Averaging over Fifa rankings and Elo ratings, Switzerland appears to be the luckiest team. Other lucky teams include Canada, Czechia, Egypt, Germany, Mexico, Qatar and South Korea. Not only was Canada favoured by the draw procedure, it was also lucky during the draw. Among the unluckiest teams are France and Senegal (because they drew Norway), Australia and the US (because they drew Turkey, the highest-ranked team in Pot 4 by far), Austria and England.

This process measures bias as well as variance. Some teams, such as Turkey, end up in a strong group not because they are unlucky during the draw, but because the draw procedure is biased against them. Even in the absence of bias, variance is an issue. A draw procedure may be unbiased for all teams – the probability distribution of group strength is centred at zero for all teams – but may generate much more variability in group strength for some teams than for others. A team with little variance in group strength may be very unlucky but end up in an easier group than another luckier team with large variance in group strength.

This method is analogous to comparing the losses of two financial portfolios. Portfolio A may have posted a relatively small loss compared to Portfolio B, but may have been ‘unluckier’, in the sense that only a very small proportion of scenarios would have led to a larger loss for Portfolio A. This observation has motivated the introduction of the concept of VAR as a risk measure (VAR in the sense of value-at-risk, not video assistant referee!).

Given a time horizon, say one day, a 5% VAR of $1 million means the maximum loss over one day is $1 million, excluding the worst scenarios, where the cumulated probability does not exceed 5%. This corresponds to the notion of quantile in probability theory: one fixes a probability level, here 5%, and measures the value x, called the 5% quantile of the loss distribution, such that the probability that the loss is larger than x is equal to 5%. VAR is often used by firms and regulators to assess the quantity of assets or reserves that are needed to cover possible losses.

Our methodology for assessing luck in the World Cup draw could be adapted to measure whether a financial quantitative investment strategy was lucky or not, and more importantly, to assess the quality of a strategy, by comparing the probability distributions of the profit-and-loss of various strategies. Of course, this requires building accurate probabilistic models for the outcome of the strategy, by modelling the joint dynamics of the financial assets traded in the strategy; this was not a problem in our World Cup study, as the draw rules are given. Generative models of financial time series are currently being developed to do precisely this.

Julien Guyon is a professor of applied mathematics at École nationale des ponts et chaussées, Institut Polytechnique de Paris, and an adjunct professor at New York University and Columbia University. He is Risk.net 2025 Quant of the Year for his research on volatility modelling. He previously published research examining bias in the 2014 World Cup draw and the risk of collusion in the initially planned 16-groups-of-three format for the 2026 World Cup, which has prompted Fifa to revise both its draw procedure since 2018 and its format for the 2026 tournament.