On 11 June, 2026, 22 men from Mexico and South Africa will take to the pitch for the opening game of the 2026 Men’s Football FIFA World Cup, in Mexico City Stadium. By all accounts, neither of these teams will win the tournament. At time of writing, Mexico are being given odds of 80/1 of winning the cup (i.e. 80/81 chance of losing, 1/81 chance of winning), and South Africa are thought to be even less likely to win, at 1000/1 (in case you are interested, the current favourites are Spain at 11/2).

That does not mean that this match is without excitement though. One of the best things about sports, is that the excitement of a match depends much more on how comparable the teams are, than on the ability of any one individual team. So it is still an interesting question to predict which team will win this match. What’s more, there are far more statistics than simply which is the winning team. Can you predict how many goals the match will be won by? What is your expectation for the number of players sent off? How much would you bet on the goalkeeper eating a pie on camera (believe it or not, this is a real bet that took place, and was quite the scandal in the end!)?

Now, as a disclaimer, I am not endorsing betting and none of this blog post should be interpreted as advice (financial, betting, or otherwise!). But I do enjoy dealing in hypotheticals and probabilities, and World Cup can give us an interesting window into how some aspects of financial mathematics may work.

A quick aside: If you are totally new to football, you can read this brief summary of the rules. Officially, football only has 17 laws, though this is slightly misleading as each has many sub-points.

Let’s Play a Game

The statistic I want to focus on is a bit of an uncommon one, but I promise there is method to my madness. I want a statistic than can vary continuously and go both up and down over time. I therefore will look specifically on the number of goals scored per minute over the course of this first Mexico vs South Africa match. Let’s suppose I offer you the following (hypothetical) deal:

You will pay me €25 now. In return, I will then pay you, in Euros (€), 1000 multiplied by the number of goals scored per minute, once the match is over.

Do you take this deal? How little would I have to ask you to pay me for you to take this deal? What information might you want to know before agreeing to this deal?

To decide how much you would pay me you need to work out an idea of how much I will end up paying you. This is akin to knowing how many goals will be scored, and then dividing it by the number of minutes. As a basic starting point, we could look at the average number of goals per game. 

According to this article, which looked at all 39750 football games in the top 5 European leagues between 2000 and 2022, whilst the most common score line is 1-0, the most common number of goals scored is 2 as this can be achieved both by a 1-1 score and a 2-0 score. A game is 90 minutes so you might expect to earn

\( \frac{2}{90} \times 1000 = 22.222\dots .\)

This would mean that paying me €25 is a bad deal! In fact, this would suggest that you should not take the deal. I am paying you €22.22 on average so you should definitely not pay more than €22.22. If you want a greater level of certainty that you will earn money, you may even refuse to play if I ask for more than €20 (or even less if you are particularly risk averse!). 

But wait! If you are even a penny off, then you could risk losing money. And I expect you will lose money, because our above calculation has made an assumption. Those who know football well will know that at the end of each 45 minutes of play is what is known as “injury time” – a number of minutes added on to compensate for the time spent managing injured players and infringements of the rules. It was reported in 2025, that the average length of a Premier league match is actually 100 minutes and 36 seconds! Using this fact, you might then expect to earn

\( \frac{2}{101} \times 1000 = 19.80198\dots ,\)

which is, notably, less than €22.22.

Your appetite for risk is an important factor when playing this game, not just if you want a buffer for there being a small error in your calculations. Though the above suggests the time can range from 90 minutes to around perhaps, 110 minutes, that does not make a vast difference to the amount of money you’ll be paid. 2 goals scored in 90 mins earns you as we saw, around €22.22, whereas 2 goals scored in 110 minutes earns around €18.18 – only about €4 difference.

On the other hand, what if the total goals is wrong? Though 2 is the most common number of goals scored, recall that the most common score is 1-0. A score of 1-0 in 100 minutes only earns you €10, which is a big difference and a risk you have to decide if you’re willing to take.

Two Teams, Both Alike in Dignity

There is other information you may also want to know, such as the history of matches between Mexico and South Africa. Unfortunately, we only have four international matches to go off, which is not a huge sample size:

Further, the last time these two countries played each other was 16 years ago, which is too long ago to draw useful conclusions from. So what about the individual country’s track records? From data on Wikipedia, we can see that, as of the 2022 World Cup, Mexico have played 60 games, scored 62 goals, and conceded 101 goals. On the other hand, South Africa have played 9 games, scored 11 goals, and conceded 19 goals.

There are multiple ways of using this data. Mexico have scored roughly 1.03 goals per game, and conceded roughly 1.68 goals per game, whereas South Africa have scored roughly 1.22 goals per game, and conceded roughly 2.11 goals per game. So you may use that to say the total score of Mexico’s games averaged 2.72 (to 3sf), or that the total score of South Africa’s games averaged 3.33 (to 3sf). Or you may say that you expect roughly \(1.03 + 1.22 ≈ 2.3\) goals to be scored, or \(1.68 + 2.11 ≈ 3.8\) goals to be conceded.

There is no right or wrong option here! Possibly worth noting, though, is that all of these lie between 2.3 and 3.8 (as, indeed, do the scores of the last two matches these teams played). So you can expect me to pay you somewhere between \(\frac{2.3}{101} = 22.77\dots\) and \(\frac{3.8}{101} = 37.62\dots\).

There is one more pair of variables that I have as of yet not mentioned, but which are often the two most important pieces of data when playing this game: what the score currently is, and how long it is until the end of the game. If the score is 0-0 and it’s the 5th minute of extra time, you would be unwise to play this game at all. The likelihood is, the whistle will blow at a score of 0-0 and you will earn nothing. If, however, it’s 2 minutes into the first half and the score is already 1-0, I would be unwise to allow you to play this game for only €25.

Moving Forward

Why is this relevant to the world of finance, then? Well, imagine instead of me paying you a statistic based on the outcome of a football match, I pay you the price of a stock at some fixed point in the future? This is now a commonly traded financial product called, fittingly, a “future.” You may have also heard of a “forward,” which operates in much the same way except these are non-standard and not traded on exchanges. 

Years of mathematical modelling and financial maths have led to mathematicians and traders accepting a basic formula for the price of a future (i.e. the amount of money you should expect back, and therefore the maximum you should pay to “play the game”):

\(F = S_0 \times e^{rt}\).

In this formula, \(F\) is the price of the future, \(S\) is the current price of the stock, \(r\) is the risk-free interest rate and \(t\) is the time, in years, until I pay you (known as the “time to maturity”). 

This includes most of the same variables we were considering when looking at our football match! It doesn’t actually include the historical prices of the stock, but many traders may well adapt this formula slightly to take that into account. The inclusion of the interest rate here is to consider whether you would be better investing the money elsewhere – yet another aspect to my game that you could consider.

Looking to the Future

Through looking at our humble football game, we have uncovered some key factors to think about when trading financial products. But we’ve barely scraped the surface! Thankfully the tournament is on until mid-July though, so I will be back next month with another of the most traded financial products. Enjoy the first match!

Posted by Sophie Maclean

Sophie Maclean is a mathematician and maths communicator, currently studying for a PhD in Analytic Number Theory at Kings College London. She has previously worked as a Quantitative Trader and a Software Engineer, and now gives mathematics talks all over the UK (and Europe!). She is also a member of the team behind Chalkdust Magazine. You can follow her on Twitter at @sophietmacmaths

Source: Spektrum.de