Published on 13th December 2022

**Key Highlights**

- The World Cup tournament is a great learning experience and opportunity, ranging from life lessons to the practical application of mathematics and science.
- The prediction model used here gives Argentina more marginal advantages than France to win the 2022 World Cup title. On a balance of probabilities, France is the greatest threat to Argentina’s quest for the World Cup title in this mathematical model.
- If Croatia beats Argentina, then it will be very hard for France or Morocco to beat Croatia to the title.
- The matching fate that has placed France against either Argentina or Croatia in the World Cup has diminished the chances of the defending champions of reclaiming a repeat title. France must battle a slippery and razor-thin margin of 0.5% separating it from either of the two teams, hence a likely draw with a final decision through penalty shootouts. The penalty precision of Croatia is to be dreaded by any opponent.
- Morocco can win the World Cup under the surprising model scenario that tends to favour the perceived underdog, in this case going uphill and overturning the mean marginal advantages the opponents have over it: 1.3% for Croatia and 2.3% for Argentina.

**Transformative Significance of the World Cup**

In a world of diversity, the World Cup remains a potent integrator as football fans decorate our screens every four years. Each tournament is unique, the forward-ever technological advances being a key modifier of every subsequent World Cup experience.

The first time I watched the World Cup, we were students in a rustic school without electricity. The head teacher was kind enough to power his TV from his car battery to allow us to revel in the unifying ecstasy of the adored game. West Germany beat Argentina 1-0 to win the tournament. The years was 1990. Internet was still unheard of in Kenya. From this exhilarating experience fortified by engaging slow-motion replays, our interest in mathematics and sciences soared high as we came to terms with the reality that education was the sure promise for us to own better TV sets in future to watch subsequent World Cup tournaments, or better still, leapfrog from the countryside and visit those distant and more developed countries that host the World Cup. The World Cup, as such, inspires dreams and transforms lives.

TVs have evolved exponentially since 1990 and so has the technology for sharing written, audio and visual information. The speed at which knowledge and technology are evolving leaves little doubt that the 2026 World Cup will be a more electrifying experience as 5G, big data, AI, IoT, and Big Data, among others, become pervasive.

The World Cup tournament is rich in many life lessons, ranging from teamwork, mentality, tenacity, hope against odds and time, and even the wisdom of protecting small gains instead of craving for more at the expense of protecting existing marginal advantages against counterattacks. Do you remember how Brazil had its marginal advantage crashed by Croatia just three minutes to the final whistle? Could it have been better for them protecting the goal difference they had anchored already. The Swahili put it proverbially, “*Usiache mbachao kwa msala upitao”* (Don't throw away your old rag for a borrowed mat).

But can the World Cup also be a tool for endearing mathematics and science to young learners, demystifying the dreaded subjects by demonstrating their real-world application? A version of the many possible answers to this question featured in 2018 through a mathematical prediction model. This article will show how.

**World Cup Prediction Model**

The World Cup Prediction Model presented here is a mathematical model conceptualised and calibrated in 2018. The model converged on **nine crucial variables** for winning the matches. It was then used to predict the outcome of the 2018 World Cup matches with amazing accuracy. The model gave France 1.9% mean marginal advantage over Croatia in the 2018 World Cup. The methodology used to come up with the model was based on the following fundamentals:

- Probability and statistics
- Numerical analysis
- Geometry and spatial thinking
- Projectile motion
- Trend analysis and pattern recognition
- Decision matrices
- Expert elicitation surveys
- Common sense

Simplified, this approach reinterprets the football pitch as a mathematical construct, a probability space accommodating random variables. Readers should note that other experts and scholars have also been engaged in football modelling using mathematics to arrive at a team’s probability of winning. Prof. David Sumpter, for example, has written extensively on Soccermatics, which is the mathematics of football as articulated in his writings and lectures of postgraduate students. The model shared here is, however, rather simplified yet effective, so as to be comprehensible to younger learners from senior secondary school.

In 2022, the model has been enhanced such that it uses the **mean marginal advantages** as differentials for predicting **three scenarios** in each match, complete with expected goal differences. The model has been giving accurate predictions with a performance index of 70-80% during the group stages, 100% during the knock-out stages, and 90% during the quarterfinals. All the predictions and the accompanying narratives can be accessed from the Facebook page of Nashon Adero | Facebook. The longer version of this model is accessible from December 6, 2022 (impactborderlessdigital.com)

**Simulated Scenarios**

The model is used to generate three scenarios for every match whose outcome is predicted. All the scenarios are possible, considering the entire match from start to the extreme phase of penalty shootouts.

The **first model scenario** is the **business-as-usual (BAU) scenario**, where it is assumed nothing extraordinary will take place so that the expected team composition and the demonstrated skills of the team members can be assumed to be steady and following the known trends and patterns, mainly from historical precedence.

The **second model scenario** is the **surprising scenario (SS) **that assumes the perceived underdog will be lucky enough to score more on the variable of serendipity. From the data and results studied over the period of applying this model, serendipity tends to be in the ratio 7:3 in favour of the perceived underdog.

The **third model scenario** is the **augmented favour** **scenario (AFS)** that assumes a shift in serendipity to be in favour of the perceived frontrunner, the way it happened for Portugal vs Switzerland at the knock-out stage. This scenario has been rare from the observations made so far.

**Mean Marginal Advantages and Telling Inequalities**

The model predictions are based on parameters linked to the nine crucial variables that help to determine the winning probability. The **expected goal differences** between the teams in a match have been established in the model to be taking the form of the following mathematical inequalities:

**Semi-Final Scenarios**

For the 2022 semi-finals, scheduled for 13^{th} and 14^{th} December, the model gives the following scenarios simplified into a narrative depicting the BAU scenario, surprising scenario (SS) favouring the perceived underdog, and the augmented favour scenario (AFS) that further boosts the perceived frontrunner.

**Argentina vs Croatia **– 13 December 2022, 22:00 EAT

Mathematician's model suggesting #Argentina is tottering on a knife-edge 1% mean marginal advantage over #Croatia in the #WorldCup #Semifinals. Based on the model’s goal conversion factor, this is a likely draw if not a very lucky one-goal difference within normal match time. If serendipity swaps in favour of Croatia in the established model ratio of 7:3, penalties included, then Croatia can be sure of a goal difference of 2 over Argentina, a maximum difference of 3 at best. Finally, the worst scenario that will stun Croatia is where serendipity favours Argentina, resulting in a wild 3-4 goal difference over Croatia. Will #Messi do it again? Will Argentina’s record of not losing having reached this far hold?

**France vs Morocco **– 14 December 2022, 22:00 EAT

Mathematician's model suggesting #France is balancing on a thin 1.8% mean marginal advantage over #Morocco in the #WorldCup #Semifinals. Based on the model’s goal conversion factor, this points to a one-goal difference, but hard to reach 2-goal difference within normal match time. If serendipity swaps in favour of Morocco in the established model ratio of 7:3, penalties included, then Morocco can be sure of a goal difference of 1 over France. Finally, the worst scenario that will stun Morocco is where serendipity favours France, resulting in a wild 3-4 goal difference over Morocco. Will #Mbappé do it again? Will Morocco’s record of not losing having reached this far hold?

**Final Scenarios: Argentina Mathematically Favoured in the Matrix**

Scheduled for 18 December 2022, 18:00 EAT

In the following matrix are the possible team combinations in the final match. The calculated mean marginal advantages for each scenario are shown in the cells.

There are four possible team combinations for the 2022 World Cup Final, following from the four semi-final teams that have been determined. The model gives three model scenarios for each match. A decision matrix using the mean marginal advantages for all the three model scenarios has been applied. The matrix, interestingly, sees **Argentina** rise to the top of the competition, going by the mathematical mean marginal advantages.

**Argentina** tops in two (BAU and AFS) out of the three scenarios and scores a net margin of 7.6% when all the three scenarios are considered. **Croatia** comes second at position 2 in all the three scenarios with a net margin of 2.1%. **France** is third at position 3 in all the three scenarios with a net margin of zero. **Morocco** needs to be lucky in the surprising scenario (SS) to emerge the overall winner against either Argentina or Croatia, but its net margin of -9.7%, being a negative value, implies it must beat many odds to reach there. On a balance of probabilities, France is the greatest threat to Argentina’s quest for the World Cup title in this mathematical model.

Could these mathematical results be an early sign that **Argentina** is best placed to be the winner of the World Cup 2022 and a loss for Messi’s team will be a case study in wasting ready chances? It is now evident if **Croatia** beats Argentina as provided for in the model SS scenario, then stopping Croatia from emerging the overall winner will be the hardest and unforgettable challenge France or Morocco will have to face.

The fate that has placed France at war with either Argentina or Croatia in the 2022 World Cup will test the defending champion to the core. This is because France must battle a slippery and razor-thin margin of 0.5% separating it from either of them, hence a likely draw with a final decision through penalty shootouts. The penalty precision of Croatia is to be dreaded by any opponent.

If Morocco beats France, Morocco will have to work extra hard to overturn the mean marginal advantage that the opponents already have over it: Croatia (1.3%) or Argentina (2.3%). As such, an overall win for Morocco in the 2022 World Cup will be arising from the second model scenario, which is the scenario of surprises.

**The following are the key narratives from this prediction model of the 2022 World Cup Final.**

**France vs Argentina **

Mathematician's model suggesting #Argentina is hanging on a slippery and razor-thin 0.5% mean marginal advantage over #France in the #WorldCup #Final. Based on the model’s goal conversion factor, this isn’t enough for a goal difference and points to a draw within normal match time. If serendipity swaps in favour of France in the established model ratio of 7:3, penalties included, then France can be sure of a goal difference of 2 and at most 3 over Argentina. Finally, the worst scenario that will stun France is where serendipity favours Argentina, hence swapping that 2-3 goal difference in favour of Argentina.

**France vs Croatia**

Mathematician's model suggesting #France is hanging on a slippery and razor-thin 0.5% mean marginal advantage over #Croatia in the #WorldCup #Final. Based on the model’s goal conversion factor, this isn’t enough for a goal difference and points to a draw within normal match time. If serendipity swaps in favour of Croatia in the established model ratio of 7:3, penalties included, then Croatia can be sure of a goal difference of 2 and at most 3 over France. Finally, the worst scenario that will stun Croatia is where serendipity favours France, hence swapping that 2-3 goal difference in favour of France.

**Argentina vs Morocco**

Mathematician's model suggesting #Argentina has a slim 2.3% mean marginal advantage over #Morocco in the #WorldCup #Final. Based on the model’s goal conversion factor, this points to a sure goal difference of 1, at most 2 if lucky, within normal match time. If serendipity swaps in favour of Morocco in the established model ratio of 7:3, penalties included, then Morocco can be sure of a goal difference of 1, at most 2 if very lucky, over Argentina. Finally, the worst scenario that will stun Morocco is where serendipity favours Argentina, resulting in a wild 3-4 goal difference over Morocco.

**Croatia vs Morocco**

Mathematician's model suggesting #Croatia is balancing on a thin 1.3% mean marginal advantage over #Morocco in the #WorldCup #Finals. Based on the model’s goal conversion factor, this points to at most a one-goal difference in not a draw within normal match time. If serendipity swaps in favour of Morocco in the established model ratio of 7:3, penalties included, then Morocco can be sure of a goal difference of 1 and at most 2 over Croatia. Finally, the worst scenario that will stun Morocco is where serendipity favours Croatia, resulting in a wild 3-4 goal difference over Morocco.

By Nashon Adero – a lecturer and Taita Taveta University and a geospatial and systems modelling expert.

nashon.adero@gmail.com

Acknowledgement

Young Kenyans have been part of the modelling and dissemination process. Wilson Kibe, a young graduate from Kenyatta University, has been collecting and collating the datasets that have been used to calibrate the model used for the 2022 World Cup predictions. Hilary Anekea, a young graduate from Moi University, has been key to the social media publicity of this exciting prediction model.