A fairer football sweepstake

With the FIFA World Cup about to begin, many people will be planning on participating in a sweepstake. Everyone pays a nominal entry fee, is then randomly allocated one of the competing teams, and at the end of the competition the participant with the winning team wins all the money.

But you know what it's like. If you draw a team that's an outsider, you rapidly lose interest as the team heads for early elimination.

Here we look at an alternative sweepstake version which could be claimed to be fairer and more engaging than the traditional format. This idea was first described in an earlier article in 2020, and has been updated for this article by including data from the 2022 World Cup.

Shirt number sweepstakes

In this fairer version, there are up to ten participants and each is randomly assigned a unique integer between 0 and 9 for the whole tournament. They then receive a set number of points whenever the last digit of a goalscorer's shirt number matches their assigned number. For example, if a participant is assigned the number 3, then they receive a fixed number of points whenever a player wearing shirt number 3, 13 or 23 scores.

This keeps participants engaged throughout the tournament, as they can score points in every game. They will almost certainly be invested in several players in each game, and will be cheering for both teams! Also, the sweepstake can even be started after the tournament has begun, with scoring counted only from then onwards.

Another big appeal is that it is fairer than the traditional sweepstake as it is designed so that each participant has a similar chance of winning. This is achieved by weighting the points awarded for each goal according to how often that shirt number usually scores, as we will describe now.

The table below shows goal-scoring frequencies (including own goals) in the World Cup from 2002-2022 for each number forming the last digit of a shirt number. As number 9 has scored 2.5333 times as many goals as number 8, then to make it fair, number 8  should receive 2.5333 times as many points as number 9 when they score a goal. Similar calculations were carried out by dividing the highest total (190 for shirt 9) by each of the totals for the other shirt numbers. This gave the weightings, or points allocations, for goals scored by each shirt number. 

For example, Shirt 0 Weighting = 190 / 160 = 1.1875

To keep the calculations user-friendly, let’s round the weightings to the nearest 0.5 and double them to make them all integers. This gives the proposed points system as follows.

Illustrating this using the 2022 World Cup game between England and Iran; player numbers 7, 10, 11, and 22 each scored once, and player numbers 9 and 17 each scored twice. This would translate to number 0 receiving 2 points, number 1 receiving 3 points, number 2 receiving 8 points, number 7 receiving (3x4 =) 12 points, and number 9 receiving (2x2 =) 4 points.

So how fair does this points system turn out in practice? Applying it to the last six World Cup tournaments gives the following:

We can see that there are six different winners (numbers 2, 6, 1, 4, 3, and 0), and if we included a runner up prize this brings a further two sweepstake numbers into the picture (7 and 8). This implies that the sweepstake system proposed is relatively fair in that many of the participants can expect a reasonable chance of obtaining a prize. Furthermore when comparing the points scores between the winner and runner up, it can be seen that they are generally very close, suggesting an exciting sweepstake.

About the author

Slim Khan is an Analytics Consultant at Minitab and is particularly interested in mathematics and statistics related to games and sports.