In 1998, the French men’s team won the football World Cup for the first time in their history. For most of the country, even non-football fans, it was a joyous moment and the trigger for a massive national party, especially as the tournament was in France with the final in Paris.

At least one Frenchman did not join the party: the rancorous politician Jean Marie Le Pen, who complained that the team was not “French enough”, a cowardly reference to the number of black players in the team. Le Pen was already renowned for making racist statements, and ran – and lost – five times as a far-right candidate for the French presidency.

I often remember Le Pen’s ridiculous complaint. France’s black players were some of the best in the tournament and France might well not have been world champions without them.

Football has come a long way in tackling racism in the last two decades, but racism in football is not yet eradicated. There have been recent racist chants in matches across Europe, and high-profile black players have been poorly treated by some parts the mainstream media and suffered racist slurs on social media (Steinberg 2019).

Considering racism in football today, I wondered if there were similar problems in a popular online football game where users pick a team of players from the English Premier League and win points when their players do well. Could I find users who picked teams with no black players?

The Official Fantasy Premier league has over 7 million teams and is played around the world. It is discussed in an abundance of blogs and podcasts, including a regular BBC radio show to discuss tactics and tips.

In a clear sign that racism is a problem amongst some users, last season’s league leader was disqualified after they made racist remarks about Raheem Sterling, a high-profile black player (D’Urso and Anka 2020). The eventual winner was an Oxford university mathematician.

Each user picks 15 players with a budget of £100 million. The best players cost more, so you can’t just fill your team with the most renowned players. Nor can users just select, say, the entire Liverpool FC team: only 3 players from the same team are allowed. Users make initial picks to fill a squad of 15 with 2 goalkeepers, 5 defenders, 5 midfielders and 3 forwards (see Figure 1). As the season progresses, users can transfer players in and out, depending on their budget. Transfers are limited to 1 free transfer per game week, with additional transfers costing points. Users can choose to make unlimited transfers in two weeks of the season by playing a wildcard.

Table 1: Proportion of black players in the English Premier League fantasy game by position. These are based on my own categorisation and there is no official league data on player ethnicity.

I calculated the probability of a user picking no black players simply by chance. Starting with the two goalkeepers, the probability the first goalkeeper will not be black is 60/65 (0.92). For the second goalkeeper we assume the first pick was not a black player, so the probability the second goalkeeper will not be black is reduced slightly to 59/64 (0.92). To get the probability of no black goalkeepers by chance alone we multiply the two probabilities and get 0.84.

The probability that the first defender picked will not be black is 133/214 (0.62) and the first striker is 36/72 (0.50). After filling a team with 15 players, the probability of a user picking no black players by chance is just 0.00079, less than one in a thousand. This small probability arises from the steady reduction of the cumulative probability for each player picked.

Once the matches start, users can transfer players in any position, hence the probability after 15 picks varies by position. The probabilities for transfers in each of the four positions are shown in Figure 2. After 40 picks, the probability of picking no black players by chance is very small, particularly for users changing their strikers where is it smaller than 1 in a billion.