Fig 1.
Relationship between the performance of managers over seasons of FPL.
(a) The relationship between managers’ ranks in the 2018/19 and 2017/18 seasons. Each bin is of width 5,000 with the colour highlighting the number of managers in each bin; note the logarithmic scale in colour. (b) The pairwise Pearson correlation between a manager’s points totals over multiple seasons of the game, calculated over all managers who appeared in both seasons.
Fig 2.
Summary of points obtained by managers over the course of the 2018/19 season.
(a) The mean number of points over all managers for each GW. The shaded regions denote the 95% percentiles of the points’ distribution. (b) The difference between the average number of points for four disjoint tiers of manager, the top 103, 104, 105, and 106, and the overall average points as per panel (a). Note that managers are considered to be in only one tier so, for example, the top-104 tier contains managers ranked from 1001 to 104.
Fig 3.
Decisions of managers by tier.
(a) Distributions of the total net points earned by managers in the gameweek following a transfer, i.e., the points scored by the player brought in minus that of the player transferred out. The average net points for each tier is also shown below; note the difference between the top three tiers and the bottom tier. (b) Distribution of the fraction of better transfers a manager could have made based upon points scored in the following gameweek. Faster-decreasing distributions reflect managers in that tier being more successful with their transfers. (c) The distribution of points from captaincy along with the average total for each tier.
Fig 4.
Analysis of the team value of managers.
(a) The change in average team value from the initial £100M of all managers, along with 95 percentiles; note the general upward trend of team value over the course of the season. (b) Distributions of team values for each gameweek for those who finished in the top ten thousand positions (i.e., the combination of those in the top 103 and 104 tiers) versus lower-ranked managers. The distribution for those with higher rank is generally to the right of that describing the other managers from an early stage of the season, indicating higher team value being a priority for successful managers. (c) The relationship between a manager’s team value at GW 19 versus their final points total, where the heat map indicates the number of managers within a given bin. The black line indicates the fitted linear regression line, showing that an increase in team value by £1M at this point in the season results in an average final points increase of 21.8 points.
Fig 5.
Summary of use and point returns of the bench boost chip.
The managers are grouped into two groups: those who finished in the top ten-thousand positions (Top 10k) and the remainder (Top Million). (a) Fraction of managers who had used the bench boost chip by each gameweek. We see a clear strategy for use in double gameweek 35, particularly for the top managers, 79.4% of whom used it at this stage. (b) Distribution of points earned from using this chip along with the average points—23.2 for the Top 10k and 13.8 for the Top Million—shown by the dashed lines.
Fig 6.
Schematic representation of the approaches taken to identify similarity between the composition of managers’ teams in each GW.
We view the connections between managers and players as a bipartite network such that an edge exists if the player is in the managers’ team. To determine the relationship between players’ levels of popularity we use the co-occurrence matrix which has entries corresponding to the number of teams in which two players co-appear. Using this matrix we perform hierarchical clustering techniques to identify groups of players who are similarly popular within the game, where the number of clusters is determined by analysing the within-cluster sum of squared errors. The similarity between the teams of two managers is determined by calculating the Jaccard similarity, which is determined by the number of players that appear in both teams.
Fig 7.
Analysis of team similarity of managers.
(a) Size of each of the first three identified clusters over all managers for each gameweek. Note that the first cluster is generally of size one, simply containing the most-owned player in the game. (b) An example of the network structure of these three clusters for gameweek 38, where we can see the ownership level decreasing in the larger clusters. The diagonal elements of this structure are the fraction of teams in which the player is present. (c) The Jaccard similarity between the tiers of managers and also over all managers; note that the higher-performing managers tend to be more like one another than those in lower tiers, also note the fluctuations in similarity over the course of the season indicating that a template team emerges at different time points.