BenCrabtree was crowned Fantasy Premier League champion for e 2016/17 season, with an impressive score of 2564  by mainly using a 3-4-3 formation. Often this involved rotating the third defender spot between a trio of low priced centre backs and full backs.

This was a popular strategy among last season’s top managers, who also were flexible enough to opt for 3-5-2 when strong third striker options dried up.

This analysis will explore to what extent 3-4-3 is essential to a successful FPL season, with a goal of finding the best formation that can get closest to Ben’s title winning average  Gameweek score of 67.5.

Method

To do this I calculated every players’ average points per game (PPG). Then excluded anyone with less than 15 games as an attempt to avoid outliers.

Next I focused on creating price brackets. I ended up with three levels for Goal Keepers (Low, Medium, High), and five for the other positions (Bargain, Low, Medium, High, Elite)

I then looked at the prices by position, to come up with an even spread across the price brackets.  Once I had the brackets defined I used several players with prices immediately above and below the bracket price, ensuring that the average price of the selected players was close to my bracket price.

For example with goalkeepers the brackets are 4.5, 5 and 5.5.   To determine the average points for the 4.5 position I used players with prices from 4.3 (Hennessey) all the way up to 4.8 (Mignolet). The average price was 4.55 which was close enough. In total 14 players fell within that price range and the average of their PPG was of 3.6

Goalkeepers

Defenders

Admittedly there was a very small sample size at the 6.5 range, just 6 players.

Midfielders

Forwards

Finding The Optimal Line Up

I tried to come up with a mathematical formula that would give me the optimal line up, but my maths is not up to that level of sophistication, so I decided to crack it with a sledge hammer instead. After a few Google searches I managed to teach myself enough Visual Basic to enable me to write some script that did the following:

For each valid starting line-up, determine every possible permutation of player positions and price, ensure the total of the player prices are within the budget and sum up the team points, save the line up which has the most points. I varied the budgets based on the types of players that would be on the bench.

The assumption being that benched GK are 4.5, Def and Mid are 4.75 and Forwards are 6.0   I also included an additional formations where the third forward was classed as bench fodder at 5.0   I also limited the number of elite defenders to a maximum of four players due to there being so few of them.

The code also takes into account the captaincy, it takes the player position with the highest PPG and captains that position, so basically just doubles his points. It does not take into account any other game chips.

The Caveats

There several caveats that I’m already aware of

1. I’m using the end of season prices for players. Generally the better performing players will have higher prices at the end of the season than they had at the start of the season, but I’m using the start of the season budget amount of £100m. I’m trying to achieve a score close to the winning teams but in all likelihood they will have better total points because they picked up players before their prices increased and they have a significantly higher end of season budget.

What this analysis should do though, is give the best overall formation regardless of whether it can compare with the overall winner’s score.

2. There is no rotation taken into account. For example when using the 3-4-3 formation last season’s winner managed to garner significant points from his low budget defenders by correctly picking the player who would excel on each given week. Turning three budget defenders into the equivalent of an elite defender requires a lot of skill and a fair amount of luck. With a large sample size of four million Fantasy Premier League managers  it’s not unthinkable that a few people get it right for a high percentage of the season.  It’s probably a prerequisite for making the top 1,000 in the rankings.
3. Form. With all the players used in the analysis I took their average points per game. It’s an average of their good weeks and their bad weeks. However, a Fantasy manager has the ability to guess when a player’s form will take a hit, due to knowing the upcoming schedule, transferring him out for another player with a better schedule and hopefully better form to come. Similar to the rotation comment above the more successful managers will be the ones that correctly predict a change in form and transfer in players about to go on a good run of games whilst transferring out players before a bad run starts.

With a  four million sample size there are going to be some managers who optimise points by correctly predicting form. This analysis does not cater for form

4. The average points are used for the price bracket, not the highest points, managers correctly selecting the top performers in the price bracket will optimise their scores above and beyond the scores produced by this analysis.
5. This analysis assumes that you can field a full team every week with the positions that are identified. For example if the formation states you need an elite midfielder that will score on average 5.9 PPG, then you need to field an elite midfielder in that position for 38 GWs. If that elite midfielder misses games and has to be replaced by your bench guy who only scores 2.8 PPG then you’re not going to be able to maintain a season long average. Of course if a player gets an injury then you can replace them with another similar elite player, it’s more an issue relating to random weekly benching, as we often see with the teams playing in Europe.

Given all the caveats it’s fair to assume there are more factors influencing my results being a lower score than a higher score.

380 million permutations were evaluated. (3x5x5x5x5x5x5x5x5x5x5x13). Taking 4 hours to process.

The Best and Worst Formations Are…

Here are the results in highest PPG order

(where x signifies the benched forward is £5m compared to £6m)

There is only a two point difference between the best formation 5-3-2x and the worst formation 3-5-2.   It’s interesting to see that the worst formation was 3-5-2, which was used by many successful managers at the end of last season, whilst 3-4-3, the most successful formation overall, was third from bottom on the list.

This tells me that the bench (rotation) must play a significant part in the overall score.

The optimal line up for 532x was:

In terms of the objective, which was to try and determine an optimal lineup that compared favourably with the winning score these results are 11 points too low. But these based on average players at the price range. When we substitute in actual players with high PPG in the price ranges, you get this a more comparable figure

The recommended 532x formation was based on the average PPG across several players, but there were two players last season that were outliers, Junior Stanislas of Bournemouth and Spurs striker Harry Kane. If we switch the formation by replacing an elite mid with a bargain mid and a low forward with an elite forward we get this.

66.2 PPG gives 2516 points per season, which would be fifth in the FPL Overall Ranking.

The flaw is that this uses average weekly points and assumes the players will play for 38 games.

Looking at players in similar prices ranges to the recommended 5-3-2x formation, who played a lot of games and use their total season’s points we get this.

Assuming that when a player doesn’t play, a bench player will contribute 2.5 points.

Total Points = 2174 + 108 bench points = 2282

This team if left unattended for the season, with decent bench, would have finished in the top 17,000.

Conclusion

I don’t think that the formation is a key differentiator, success is more dependent on player selection and timing, transferring in players as they are about to hit form, getting lucky with captaincy and the making good bench rotation decisions.

What I’m taking from this analysis is that you can really use any formation you like the look of and still be successful, as long as you utilise your bench correctly.

So for the start of the season I’m going with the following line-up, my rotation will be concentrated around all the defenders and the four 6.0 priced midfielders. The aim is to rotate the best seven players from the nine focusing on home fixtures and weak opponents.

The best for 2017/18 could be a mixture of 5-3-2 and 4-4-2.

After some quick analysis of the defenders and midfields schedules, I believe I can attain 60% home fixture for the defenders and an 80% home fixture for the midfielders, with most fixtures being against teams in the bottom half of the table.