Fantasy Premier League: Where to spend money

Introduction

Fantasy Football is a very popular pastime during the football season. While many outlets are available for Fantasy Football, this post concerns the official Premier League Fantasy Football.

In Fantasy Football, every player in the Premier League is valued and managers (the public) have £100m to spend on 2 goalkeepers, 5 defenders, 5 midfielders and 3 forwards. Players accumulate points for actions such as goals, assists, clean sheets and others.

The skill in Fantasy Football lies in wisely spending money. Big name players, who often accumulate the most points, are also priced the highest -- but is the increase in price tag justified by the increase in expected points.

In this post, points and initial prices from last season's Fantasy Football are compiled and the optimum buying strategy calculated. Following this, conclusions are drawn which suggest how this analysis could be applied to this season's Fantasy Football.

Method

To begin with, a representative number of points is calculated for each price point at each position. While the mean was considered, the final choice made was the median. Using the mean would allow outliers to skew the number of points which is not the aim of this post. Instead this post is designed to allow a team to be selected using only the prices and positions of players, without relying on picking the highest scoring player of any given price/position combination.

Much thought was given to the best way to calculate efficient spending. Points/£ is clearly an important metric, but ultimately, the winning team is the one which gains the largest number of points rather than that with the highest points/£ -- and the two could be mutually exclusive: Consider Team A, which costs £75m and scores 1000 points and Team B which costs £100m and scores 1001 points. Team A is clearly superior in terms of points/£ but Team B will win the Fantasy League.

The method chosen begins by acknowledging that 15 players must be chosen and the minimum price of these 15 players is £64m: (GK -- £4m, £4m; DF -- £4m, £4m, £4m, £4m, £4m; MF -- £4.5m, £4.5m, £4.5m, £4.5m, £4.5m; FW -- £4.5m, £4.5m, £4.5m).

With that as a provisional squad, the remaining money is spent as efficiently as possible: the incremental points/incremental £ are calculated for each more expensive price/position combination. The combination with the highest incremental points/incremental £ is selected and the team "upgraded" accordingly. The sequence then repeats until all £100m is spent. During this process, the number of available players at each price/position combination is considered (there is only one forward, Robin van Persie, who costs £13m so only one £13m forward can be selected).

Results

The number of points expected for the £64m, "bottom of the range" team given above is 37.5 (the goalkeepers and forwards score 0, the defenders 2 and midfielders 5.5). Following the algorithm described above, a legitimate squad can be selected which scores 1,801.5. By comparison, the highest scoring group of 15 players which conforms to the position rules (although not the price rules) scores 2,173 points and costs £131.5m.

The optimal prices for each position are shown in the chart below, alongside the range of prices for each position:

The main point to note here is that big money should be spent not on the glamour positions of midfield and forward, but on defenders and, especially, goalkeepers. This is due to the different relationships between points and price for each position. Below are shown charts of the incremental points (points - points for least expensive in each position) against incremental price (price - price for least expensive in each position):

For the forwards, for example, there is a middle price range for which a small increase in price provides limited, or no, increase in points output. The same can be said for midfielders, but for defenders and, especially, for goalkeepers, an increase in expense is rewarded by a commensurate increase in output.

Conclusions

So, what may be deduced from this which could aid selection this season? The obvious claim would be to suggest that these guidelines be strictly followed, however there are some considerations:

• Only one year has been used here as a sample, so drawing firm conclusion is perhaps inadvisable
• It is likely that the providers of the official Premier League Fantasy Football do some analysis, perhaps like this, and may well adjust their price distributions accordingly
• The distribution of prices is different this year to last: most notable, Gareth Bale is the most expensive midfielder by some margin, changing the range of available midfielders considerably.

Having said that, I'll be selecting my squad according to this piece of work! Additionally, I plan to put together some analytical methods by which to manage my squad throughout the season.