I started playing Fantasy Premier League (FPL) in 2018, back when I had no
idea it would take over my life and every ounce of free time I would ever have. It's a complex game (or so I'd like to think) but the long and short of it is:
Premier League games take place over the course of the year. At the beginning of each season, hopeless FPL 'managers' (when I refer to managers, I mean people like me who sit on the couch and watch these professionals play, and when I refer to players I mean football/soccer players who earn millions of pounds to actually play the sport) like myself
choose a squad of 15 players from the Premier League. When those players play games and do well (score goals, assist, keep a clean sheet)
we get points for their performance. We're given some transfers to use every gameweek to bring in players that we like. There are 38 gameweeks,
and we are ranked on how many total points we have at the end of gameweek 38.
When competing against the 8 million+ players across the planet in a game that is subject to a high level of variance from week to week
(since players can do well one week but suffer a drop in performance the next week for no apparent reason), it is difficult to choose the best players for each gameweek.
Many managers and organizations have built predictive models using machine learning to predict player performance, but they are all subject to a high rate of error - each player produces only 38 data points per season, so any prediction one makes is subject to a small sample size.
Player performance varies over seasons and as players tend to enter and leave the league, it is difficult to find any useful statistical signal.
However, there are some metrics that have helped me make player decisions such as expected goals (xG) and expected assists (xA).
Without trying to reinvent the wheel, my goal was to look for a metric that could supplement xG and xA and is particular to FPL.
The value that each player brings to my team is primarily a function of how many points they score, and how they are priced in the game.
The market element of FPL is what makes the game challenging - we are given a limited budget to select players, who are supposed to be priced
according to their FPL value - i.e. star players like Mo Salah, Kevin De Bruyne, and Harry Kane are priced much higher than the others.
Player prices change based on how many managers transfer them in and out of their teams, creating somewhat of a market system.
I wanted to create a metric that was simple, but still provided me with enough signal to help me make a more informed decision on how much value each player was
bringing to my team - and whether I could identify overvalued or undervalued players.
That's how I (I have not seen this metric elsewhere, but there's a good chance others have used it/come up with similar metrics) came up with Value per million per 90 (VPM90).
VPM90 allows for valuation of Premier League players across two dimensions: price and playing time.
For example, it can help us spot players who are relatively cheap and tend to do well whenever they play. This can be helpful when
we are considering players who haven't played many minutes due to injury/rotation (i.e. the coach tends to bench them a lot) but tend to
score points when they are on the field.
It can also help us examine players who score a lot of points but are somewhat 'overvalued', in the sense that there are cheaper options who
tend to match/exceed their points output.
Lastly, the Adjusted player price used to calculate VPM90 is not the original price of the player.
In FPL, players are separated by their positions (Goalkeeper, Defender, Midfielder, Forward). Each FPL team needs to have 2 Goalkeepers, 5 Defenders, 5 Midfielders, and 3 Forwards.
At the start of each season, the lowest price for the 'worst' (though some players at these low prices are often underpriced and are eventually considered to be steals) Goalkeepers/Defenders/Forwards is £4.0 million, while the lowest priced Midfielders are valued at £4.5m.
Since VPM90 is a metric that measures a tradeoff between price and points scored, I felt it appropriate to adjust the player prices to take this into account -
since managers have to spend that extra £0.5m on a midfielder anyway, a measure of value should measure the value gained for each £million over the minimum price for that position.
This means that Midfielders actually provide slightly more 'value' than their price suggests. For example, if we have a Midfielder and Forward that are both priced at
£7.0m and have scored the same number of points in the same number of minutes, the Midfielder is providing more value (since we have only spent an incremental £2.5m on him compared to an incremental £3.0m spent on the Forward).
Caveat: this minimum price can drop over time if the lowest-priced players experience a drop in price. Here are the current lowest-priced players by position:
| Position | Lowest price |
|---|---|
| Goalkeeper | £3.9m |
| Defender | £3.8m |
| Midfielder | £4.3m |
| Forward | £4.4m |
The player comparison graphs measure weighted VPM90. VPM90 is calculated for each game, and then is weighted with the VPM90 of all the previous gameweeks of that season (weightage is based on minutes played). So if a player has a VPM90 of 2.0 in week 1 after playing 80 minutes, and then a VPM90 of 1.0 in week 2 after playing 40 minutes, the cumulative VPM90 for week 2 will be: $$ 2.0*\frac{80}{40+80} + 1.0*\frac{40}{40+80} \approx 1.667$$