Introduction
Longtime readers of Mathematically Safe will remember that my first forays in the world of FPL analysis was a piece after the 2015/16 season when I correlated underlying player statistics (such as shots, passes, etc.) with the actual points scored by a player. Back then, I had just two seasons worth of data, so at the conclusion of the 2018/19 season with five seasons behind me I decided to review the formulas in order to find out which players over and underperformed this season, and to give myself the best chance of using the underlying numbers to find undervalued players next season.
The focus of the article quickly snowballed though and I started to look at additional factors which I have also previously studied in an attempt to produce a comprehensive study of how to set a team up in FPL. The principal goals of this analysis evolved, and have now become:
 Part One: To identify the underlying stats which correlate with FPL points
 Part Two: To understand to what extent the underlying stats can predict performance on a weekly basis
 Part Three: To understand whether fixtures make a difference to the FPL performance of a player
 Part Four: To theorise on the optimal structure of an FPL squad considering the value of the player and the abundance of alternative options in the same position
Executive Summary
Full analysis follows, but those of a TL;DR (too long; didn’t read) disposition, here are the main findings.
There is evidence that combinations of metrics related to onpitch actions, such as shots or touches in certain areas of the pitch, correlate strongly although not perfectly with FPL points over the course of a season.
The aforementioned models provide a good understanding of what was driving the FPL performance of players over the course of a season, but one a weekly basis the performance of players against expectations has been – and will continue to be – erratic.
There is evidence to suggest that fixtures have an impact on the likelihood that a player will return points, although there is variation between category of player and position regarding the degree to which this will happen.
Rotation (transfers in and out) according to fixtures is more beneficial among the expensive assets.
Money should be invested in the Defence and Midfield positions, whereas Goalkeepers and Forwards should have limited investment (with the exception of one Premium Forward if you can stretch to that).
I have expanded upon these in Point Five at the foot of this article.
Methodologies
Before I deepdive into the numbers, a few notes on the data set used here.
Size of data set
 Only players who completed at least 900 minutes in the season (equivalent of 10 full games) have been included in the analysis
 There are 1,554 unique player records in the data set covering five seasons, sourced from OPTA via the Fantasy Football Scout members area.
 120 Goalkeeper records; 569 Defenders; 668 Midfielders; 197 Forwards
 305 records from 2014/15; 320 from 2015/16; 305 from 2016/17; 319 from 2017/18; 305 from 2018/19
 For each player, the data set includes FPL data from each game (sourced via the FPL website) and the probabilities of the player being on the winning, losing or drawing side in each game, sourced from the footballdata.co.uk website
Adjusted Points
There is one metric that is universal in FPL and that is minutes played. The points accumulated from appearances (1 point for up to 60 mins; 2 points for over 60 mins) have been removed from the analysis to keep the view of the onpitch actions as clean as possible. Therefore, this analysis refers to ‘adjusted points,’ which is a direct reference to the removal of appearance points.
‘Expected adjusted points’ are what a player would have been expected to return (in adjusted points) according to the models that are outlined below. From now on, I will refer to them as EA points.
Attacking / Defending Defenders
Considering the proliferation in recent seasons for full backs to take on a more attacking role, there are effectively two types of Defenders in the game. I have decided to segment the players accordingly to look at the underlying numbers that suit their strengths. The segmentation cutoff is 18% for proportion of touches in the final third relative to the total touches. Therefore, if a player has 170 touches in the final third out of 1,000 overall touches (17%) then he is a Defensive Defender, and a player with 180 final third touches (18%) is an Attacking Defender.
Category of player
The players have been divided into categories according to their price in their first game of the season
Part One: Identifying the underlying stats which correlate with FPL points
Top level summary

There is evidence that combinations of metrics related to onpitch actions, such as shots or touches in certain areas of the pitch, correlate strongly although not perfectly with FPL points over the course of a season.

The most difficult to predict (e.g. the category of player where underlying stats most deviate from actual performance) is the Defending Defenders. The strongest correlation exists for the Midfielders
Introduction
The objective of this analysis is to develop a series of formulas for understanding what a player should be scoring in FPL using the underlying stats of what they actually did on the pitch. For instance, if a player has taken 30 shots on goal in a season but hasn’t scored, the analysis of the FPL mind would think either “he’s crap” or “he’s due a goal.” Deciding which of the two is true of the player in question is a subjective analysis which factors in many other inputs such as quality of the team, perceived morale of the player, etc. but the fact remains that the stats of an average player should score at least a couple of goals from those numbers. This method of analysis is designed to find what “at least a couple of goals” actually equate to in FPL terms.
The way I’ve done this is to perform linear regression on a series of underlying stats and the FPL points. In short, it puts a numerical value on the influence of Y (underlying stats) on X (FPL points). ‘Adjusted R_{2}‘ is the value given to the correlation. The values range from 0 to 1.000, and can be thought about in the following terms:
 0: complete randomness where Y has no influence on X. For example, the number of words in a newspaper has a 0 influence on the phases of the moon
 1.000: a perfect correlation where X can be predicted by Y.
The formulas that have been developed all have a strong R_{2} value, as shown above. These values are not 1.000, therefore not a perfect “cause and effect” relationship, but strong enough to indicate a relationship not entirely dictated by luck.
Goalkeepers: Price is not a significant barrier to performance
Goalkeeper Expected Adjusted Points Model =
(goals conceded * 1.37) + (saves * 0.26) + (touches * 0.05) + (recoveries * 0.07) + 8.50
As the scatter plot above shows, the 0.757 Adjusted R_{2} value is not a direct 1:1 relationship, but there is a strong positive correlation. This suggests that a combination of goals conceded, saves, touches and recoveries can be a strong predictor of FPL points. The most interesting aspect of this data is the wild distribution of value categories. There is a number of premium Goalkeepers in the topright corner who have overperformed against the model’s expectation (those who sit above the diagonal trend line), but generally speaking there is little pattern to whether an expensive or cheap Goalkeeper over or underperforms against the expectations.
Goalkeepers: 2018/19 review and future prospects
Looking at 2018/19’s data, we can see that the standout player was Liverpool’s Alisson who, like Ederson, proved their worth to the title challengers by overperforming against the model. Jordon Pickford was another who significantly outperformed what was expected of him, keeping Everton’s leaky defence buoyant throughout the season.
However, the season’s principle overachiever was Cardiff’s Neil Etheridge who saved a number of penalties at the start of the season. The fact he overperforms massively despite not being in the top 10 Goalkeepers for expected points speaks volumes. I shall return to the Cardiff backline shortly.
The question of whether a player or team is “crap” or “due”, as mentioned above, is open to interpretation. I would argue that the presence of Ederson, Alisson, Kepa on the list of overachievers is testament to their qualities as Goalkeepers that made their clubs spend big on acquiring their signatures. Bernd Leno on the other hand was the biggest underachiever of all the Goalkeepers. Does this mean he’s crap or due a better season next time around and revert to the mean? There are handicaps to consider, but 2018/19 being his first full season in the Premier League didn’t hinder the overachieving Alisson, and playing behind a disorganised defence didn’t stop Pickford. I would say the jury is still out.
Defending Defenders: Cheap options rarely excel, but as a group nonattacking Defenders are underestimated
Defending Defenders Expected Adjusted Points Model =
(goals conceded * 1.11) + (interceptions * 0.10) + (touches * 0.02) + (recoveries * 0.10) + (attempts set pieces * 0.96) + (blocks * 0.30) + 0.38
The Defending Defenders (less than 18% of their touches are in the final third, indicating that they tend to stay deep and don’t involve themselves in the attacking phases very often) are the least predictable group with an Adjusted R_{2} Value of 0.672, which is strong but comparatively low compared to other positions. As the scatter plot above shows, there are numerous players which stray far from the model’s line. What is more predictable is the performance of the premium players, who are largely congregated to the right of the chart above the vast majority of MidPrice (Lower) and Budget Defenders: there is a greater evidence of “you get what you pay for.” I have highlighted on the chart two of the three outliers in the extreme upperright which have come from 2018/19. The significant overperformance against what was already a very high expected target (also highlighted in the chart below) shows how dominant Liverpool’s Virgil van Dijk and Manchester City’s Aymeric Laporte have been.
Defending Defenders: 2018/19 review and future prospects
Some key themes about over and underachievers emerge from the chart above.
 The top two premium assets to fall short of expectations are the Tottenham centre backs, Toby Alderweireld and Jan Vertonghen. Considering Lloris hit his EA points almost exactly the failing of the Defenders cannot be blamed on an abundance of soft goals conceded. Rather, their major issue was a lack of goals (one between them) despite a combined 23 attempts on goal. If either are still at the club next season, I’d expect that they are due a goal or two.
 Three of the top six underachievers are Fulham Defenders, which should surprise very few people who saw them defend last season.
 A moment of appreciation for the Cardiff defence, with three of the top 10 overperforming Defenders playing for the Bluebirds. If you combine this with Neil Etheridge being the top overperforming Goalkeeper, it is apparent that they could (perhaps should) have been relegated far sooner than they did.
Tangent: Are Defending Defenders underestimated as FPL assets compared to Attacking Defenders?
A note about the popularity of Defending Defenders: throughout my time playing FPL there has been a propensity for managers to rate Attacking Defenders more, with the potential for goal returns inevitably seen as being higher due to their more advanced position on the pitch. Attacking Defenders will score more on average, but only by around 11% (deeper analysis of this will follow later in the article). The chart below shows 2018/19 data and highlights the popularity of the Attacking Defenders over the Defending Defenders.
The average is a 59.8% vs. 42.2% split in favour of Attacking Defenders, which isn’t a real reflection of their actual performance. They started off much closer, but the emergence of several attacking fullbacks in the cheaper price categories swung interest away from the Defending Defenders. There was a spasm for blank gameweek (BGW) 31, when many FPL managers were faced with the prospect of 12 teams not playing and had to adapt accordingly. Personally, I played my Free Hit chip then (with little success, it must be said) as did many others, and there came an influx of cheaper Defenders from lowerranked teams in order to accommodate Liverpool’s powerful attackers. West Ham’s Declan Rice, a Defending Defender who was nevertheless playing in Midfield for example, attracted attention and his ownership dramatically increased from 160,016 in GW29, through 297,830 in GW 30 to 742,644 in GW31. Immediately afterwards, it fell back down again.
Attacking Defenders: A more predictable group than Defending Defenders, with high price barriers into the elite performers
Attacking Defenders Expected Adjusted Points Model =
(goals conceded * 1.38) + (interceptions * 0.14) + (touches final third * 0.07) + (recoveries * 0.19) + (shots on target * 2.04) + 4.31
The attacking Defenders are categorised as such by their willingness to get forward; 18% or more of their touches during a season are in the final third. Their involvement in the attacking phase offers them more opportunities to shoot, which is a key component that makes this model far more predictable than the defending Defenders (adjusted R2 value of 0.81 vs. 0.672, evidenced visually by the points being congregated closer to the trend line).
As with the Defending Defenders, there is a clear barrier to entry into the upper echelons of the trend line: a premium player can have a bad season, but a Budget or MidPrice (Lower) player will seldom break into the elite group. Indeed, of the top 47 players by EA points, there are only three cheaper players: Trent AlexanderArnold from 2017/18 (which preceded the annotated player’s stellar season in 2018/19), and the 2018/19 Wolves pair Jonny (in the mid50s, with TAA) and Matt Doherty (annotated in the chart). It is interesting to note that these three were all star performers yet all underperformed against the model’s expectations.
Annotated at the topright of the chart – the elite – are the 2018/19 Liverpool duo TAA and Andy Robertson who racked up an extraordinary number of assists and are expected to rocket in price next season. Next to them are three premium spots making up the top five for EA points: all of these are Chelsea’s Marcus Alonso from successive seasons. He truly redefined what a Defender can be in FPL.
Attacking Defenders: 2018/19 review and future prospects
The standout Goalkeeper was Alisson. The standout Defending Defender was Virgil van Dijk. The standout Attacking Defenders were Andy Robertson and Trent AlexanderArnold. The Liverpool defence won’t be cheap next season, but evidence suggests they would be worth investment still.
There are two players from 2018/19 that have really caught my attention as investment prospects for next season. The first is the aforementioned Jonny at Wolves (Jonathan Castro Otto in the above charts). Matt Doherty collected all the FPL headlines and will subsequently rise in price next season to £6.0m. Jonny was far more understated and his price has been kept lower at £5.5m. Like Doherty, he underperformed against the model last season but it is not unreasonable to expect Wolves to invest in another Central Defender to work with Coady and Boly. If that happens and they tighten up, Jonny’s attacking instincts could be complimented by increased defensive returns.
A similar analysis can be applied to Leicester’s Ben Chilwell. On the opposite flank, Ricardo Pereira grabbed the headlines with many outofposition turns on the right of an attacking three, and has risen to £6.0m. Chilwell has risen to £5.5m but with Leicester’s upward trajectory there is a chance he experiences a rebound on the whopping 31.4 lost EA points this season. Leicester would need a more reliable central defensive option than Wes Morgan (and to keep Harry Maguire) and possibly a Kasper Schmeichel upgrade in goal, but if that occurs then I’d bet on Chilwell providing better value for money than Pereira next season.
A final word here goes to Everton’s Lucas Digne. As I mentioned in the Goalkeeper section, Everton’s defensive prospects were looking up at the end of the season and Pickford was an outstanding performer. A central defensive replacement for the outgoing Zouma is required, but of equal interest here would be the transfer in of an effective no.9. Whilst crosses are not part of this model, it is worth noting that Digne lobbed in a frankly ridiculous 280 crosses in 2018/19. The next highest was Watford’s Jose Holebas, 71 behind. If someone of the profile of a Soloman Rondon turns up at Goodison Park before the start of August, then Digne will be the first name in my squad even at £6.0m.
Midfielders: The strongest correlation, where you get what you pay for
Midfielders Expected Adjusted Points Model =
(chances created * 0.29) + (shots on target * 1.82) + (touches penalty area * 0.14) + (passes received final third * 0.02) 6.58
There’s a similar pattern for the Midfielders as with the two categories of Defenders, that it is very difficult for cheaper players to have outstanding EA points. Only one of the top 34 performers is from the MidPrice (Lower) bracket – the extraordinary 2015/16 Riyad Mahrez for Leicester – and none are Budget players. Indeed, there is only one Budget Midfielder to score more 70 EA points in a season (Deli Alli during his breakout 2015/16 season).
There are two standout points at the farright of the chart which far exceed the expected points of any other point, and both are Liverpool’s Mohammed Salah in 2017/18 (where he exceeded the EA points dictated by the model) and 2018/19 (where he was about on par). The chart below demonstrates this further for the 2018/19 season.
Midfielders: 2018/19 review and future prospects
What is interesting next season is the pricing of Salah (£12.5m) and his teammate Sadio Mane (£11.5m). Both players shared the Golden Boot in 2018/19 but in terms of EA points, the Egyptian’s onpitch actions should have brought in 51% more than Mane. Salah’s actions on the pitch far exceed that of Mane’s, and it is only due to Mane being the season’s biggest overperforming Midfielder in any position that meant he got close to Salah. With this in mind, I fully expect Salah to provide better value than Mane next season, and if we assume he continues to play a pivotal role in Liverpool’s campaign, the numbers here suggest he is a player worth investing in whatever the price.
Willian at Chelsea is a curious case. Frequently relegated to the bench by a succession of managers, his actions on the pitch deserve far more than the returns he’s been delivering. As mentioned earlier in this post, the underperformance against the model can be read in a couple of ways, and while I think some players are ‘due’ a backbounce to expected levels next season I don’t think this will be the case. Chelsea’s impending transfer ban and Hazard’s departure may increase his game time, but I get the impression that a change of scene would be more beneficial for him as he’s unlikely to be the fulcrum of that side in the future.
In direct contradiction to Willian, I will be seriously considering James Maddison at Leicester next season. He passed the ‘eye test’ with flying colours in 2018/19 and I had estimated him to come in at £8.0m next season, so I was very surprised to see him priced at £7.0m. Although the numbers here show that he didn’t convert his performances into enough FPL points, falling below the model by nearly 28 EA points, I expect him to do well next season.
Forwards: Strong correlation, but with erratic outliers and lowprice gatecrashers into the elite performance group
Forward Expected Adjusted Points Model =
(shots on target* 2.10) + (touches final third * 0.02) – 4.14
The distribution of performance among Forwards is similar to that of Goalkeepers, in the sense that price does not seem to be a guarantee of a successful season. There are far more examples of cheaper strikers making it into the upper reaches of the EA points positions, such as Odion Ighalo in 2015/16, Charlie Austin in 2014/15, Jamie Vardy in 2015/16.
There are a couple of points of interest in this data. The first is that Harry Kane is almost in a league of his own considering his propensity to shoot from just about anywhere within 30 yards of the goal: three of the top four EA points positions are occupied by him.
Forwards: 2018/19 review and future prospects
The second is that 2018/19 provided two examples of Forwards at opposite ends of the quality spectrum. PierreEmerick Aubameyang was the season’s biggest overperformer in any position, scoring more than 48 adjusted points higher than the model’s expectations. His records from previous seasons suggest that this is due to his quality rather than luck, and is a definite contender for investment next season. At the other end, Fulham’s Aleksander Mitrovic was the highest EA points scorer thanks largely to his 47 shots on target in the 2018/19 season (1.24 per game), but sadly his appalling conversion rate (23%) meant that he frustrated many FPL managers throughout the world who were monitoring the underlying stats.
The fact that Mitrovic was the highest EA points scorer for the season reveals something fascinating when viewed in conjunction with the first chart of this section: none of the top 12 performances from Forwards occurred in 2018/19. In fact, if we exclude Harry Kane’s outrageous attempt from 2017/18, there haven’t been any in top performances in the last two seasons. By contrast, six of the top ten defensive Defenders and six of the top ten attacking Defenders have come in the last two seasons, suggesting a shift from Forwards to Defenders.
Tangent: Are Premium Forwards worth the investment?
It is notable that there is a far wider disparity between the over and underperformers than in any other position. Four of the top five overperformers for the season were Forwards, as were two of the top five underperformers. Looking ahead to next season, I believe that the fall in expected points that has been seen in 2018/19 raises questions over whether the premium options remain value for money: they are not performing as they did in 2016/17, so why would we pay 2016/17 prices for them? The obvious answer is ‘because Aubameyang and Aguero have demonstrated they can smash the model through sheer quality.’ That is true, but we have also seen plenty of overperformance from MidPrice (Lower) options like Callum Wilson, Raul Jimenez, and Solomon Rondon. The wilder variations in performance mean that I will probably be looking at a single premium striker and will make plans to react early when it becomes apparent which MidPrice options are scoring the goals.
Part One: Summary
There is a pattern within the data that suggests Defenders (both Attacking and Defending) and Midfielders have high barriers to entry into the group of elite performers, meaning that cheaper options will rarely excel compared to the pricier players. By contrast, price is not a barrier for outstanding performers in the Goalkeeper and Forward positions, indicating that there may be scope for setting a team structure that accommodates comparatively less money in these areas. We will explore this more in Part Four.
With regards to finding correlations between game points and onpitch actions, there is ample evidence that the performance of players in each position can be explained by underlying statistics, although none of the correlations are perfect. Midfielders have the strongest correlation, whereas Defending Defenders have the least, although this is still strong.
The formulas developed here will allow us to track underlying statistics over the course of the season to understand which players are under and overperforming, and it is then up to the user of the data to make a determination about what that means for an individual player. The next question we need to ask is whether these formulas are effective predictors of points on a game by game basis in order to use them to identify which players transfer in, which is the focus of Part Two.
Part Two: To what extent the underlying stats can predict performance on a weekly basis?
Top Level Summary
The formulas developed in Part One provide a good understanding of what was driving the FPL performance of players over the course of a season, but one a weekly basis the performance of players against expectations has been – and will continue to be – erratic.
Introduction
I first created the underlying stats models shown in Part One three years ago, and since then I have been using them to monitor who is under and overperforming. Regular readers of this blog and those who follow me on Twitter will know that I sometimes publish the results of these. The question has to be whether these models can be used to foresee a spike in FPL performance.
Analysis: Random events, longterm pattern
I have persisted that they cannot because the events that occur on a weekbyweek basis are, taken in isolation, random.
I will sometimes use the example of rolling a dice. If I were to roll it 60,000 times it will be predictable: I will get somewhere close to 10,000 1s, 10,000 2s, and so on. However, if I were to roll the dice 12 times, there is no guarantee that I will get two 1s, two 2s, two 3s etc. This is because the path to the mean (the expected) is not smooth when viewed closeup. If we look in the sequence of 60,000 dice rolls we would probably see a run of ten 6s at some point. If we were to have viewed only those events, they would strike us as an anomaly, but when viewed as part of a larger sequence of events we understand that they were just a bump in the road.
The same is true of FPL. What happens on a weekly basis, or even during a run of several games, might be part of the norm or it might be a bump that will get smoothed out over time. The problem is that we really don’t know until after the fact which it is for sure, as I will demonstrate here.
When does a trend become established?
The below chart shows Mohammed Salah’s EA points (the number of points my model expected him to score) cumulatively over the course of the 2018/19 season in blue, and his actual cumulative FPL Adjusted Points output in green (Adjusted Points are actual points minus appearance points). Below that is the difference between his EA and actual Adjusted points on a weekly basis. To reiterate from Part One, the model for Midfielders is:
Expected Adjusted (EA) Points = (chances created * 0.29) + (shots on target * 1.82) + (touches penalty area * 0.14) + (passes received final third * 0.02) 6.58
The first thing to note is how infrequently the weekly difference between Expected and Actual output are aligned (bottom half of the chart). I would say that only during eight of the 38 games did his actual performance in FPL terms match his performance on the pitch as defined in the EA model. This means that for 30 of the 38 games his performance and the model’s expectations were not aligned.
However, over the course of the season (top half) the two lines meet and Salah finished, after 38 games, with the points that the model thought he would. The road to get there wasn’t smooth, and as an FPL manager it was difficult to know what to read into his numbers. I was a manager who had Salah at the start of the season and persisted through his underperformance of the first nine weeks. My view was that he was ‘due’ points and I was proved correct.
By the time gameweek 23 came around his actual stats were cumulatively far in excess of his expected numbers, suggesting a reversion to the mean (e.g. a move downwards towards the expected points) was due. The model suggested that I should sell. I didn’t. His weekly FPL points subsequently began to fall well below his expected FPL output. There then followed another period of cumulative underperformance, and by the end of the season it had evened out.
Salah provides a neat example of the effectiveness of the model because he ends up where he was expected. However, below are the 2018/19 numbers for Crystal Palace’s Luka Milivojevic and Leicester’s James Maddison (both £7.0m in 2019/20), the former of which dramatically overperformed consistently against the model thanks to his abundance of penalties, and the latter who significantly underperformed.
What would we make of these charts throughout the season? Strict adherence to the model would have us selling Milivojevic because his performances after gameweek 18 would surely fall back to the expected points line (they didn’t) and we would be holding Maddison because points were surely just around the corner (they weren’t). We would have lost out in both cases.
Tangent: A statsbased model is not perfect when understanding objective reality, but it still outperforms subjective analysis for identifying targets
Formulas such as the ones I created in Part One can only ever be an indicator for these reasons:
 The path to the mean Expected Points is not smooth. It has many seemingly random bumps in the road that only level out over time. The numbers in any given week is unlikely to correspond to the model exactly and is probably a bump. This is because football, as with so much in life, is random on a shortterm basis
 There is no way of knowing how long the longrange should be. We are working within 38 games because that is the length of a season, but should we be looking at two seasons? Or five? Or ten? The underperformance of Maddison or the overperformance of Milivojevic in 2018/19 might be a mere bump in the context of a ten season model.
 The model assumes that only the selected underlying metrics are important, but the R_{2} values are not a perfect 1.000, proving that there are other external factors at play that we cannot see or do not incorporate. These include such unquantifiable variables like morale of the player. However much we put into the model, it will likely never be enough to be perfect. (note: Artificial Intelligence in the distant future may be able to predict every action of every person with accuracy, but let’s not go down that rabbit hole here).
Ultimately, this model has been very useful at pointing me in the direction of players to look at, but it cannot be relied upon as the sole decision point for FPL transfers on a weekly basis. It is very important to make a sound judgement on whether the expected points in any model are a true reflection of the ability and performance of that player and team, and that sound judgement needs to include a variety of alternative methods such as the ‘eye test’.
Despite the above, I argue that the large scale analysis of data within models such as the ones developed here are important for an FPL manager because while the view it provides is not a perfect correlation with reality, it is a very strong correlation nonetheless. The advantage of a statsbased approach is that you are able to objectively assess all players across multiple weeks. The ‘eye test’ approach will never be able to provide the scale or objectivity statistical models can: can you honestly say you have watched, catalogued and contextualised all players in all games in every minute? If you can (you can’t, I’m sure), your perspective would still not be objective.
Part Two Summary
Statsbased models provide a great method of understanding where to focus your attention, providing a sound footing for the subjective analysis of unquantifiable factors.
Part Three: Do fixtures make a difference to the FPL performance of a player?
Top Level Summary
There is evidence to suggest that fixtures have an impact on the likelihood that a player will return a successful point haul (six or more points), although there is variation between category of player and position regarding the degree to which this will happen. It is notable that expensive Goalkeepers, Attacking Defenders and Midfielders are more influenced by fixture ease, whereas MidPrice (Lower) players throughout the positions are not especially influenced by fixtures. The indication here is that rotation (transfers in and out) according to fixtures is more beneficial among the expensive assets.
Introduction
The objective of this analysis is to understand whether the favourability of a team in any given game has a bearing on the potential for FPL points for it’s players. The prevailing logic among FPL managers is that certain opponents provide enticing opportunities for points, and certainly among “echo chamber” communities like that of #FPL Twitter herd mentalities develop where fear of missing points drive managers towards transferring these players in (this type of momentum is known as a ‘bandwagon’). However, for every success story there is seemingly another example of thousands of managers getting burned. A notable 2018/19 example came in GW7 when Harry Kane ‘blanked’ (scored nothing more than his two appearance points) against Cardiff after more than 373,000 managers brought him in, the majority doing so with the intention of captaining him. I have previously explored the impact of ‘fixture ease’ on FPL points, but I feel that it is necessary for this article to include an updated and more succinct analysis.
Methodology
The category of players are the same as Part One, with players divided into: Budget, MidPrice (Lower), MidPrice (Upper) and Premium. The criteria by which players have been assigned a category again based on starting price. Positions are also the same, with the standard FPL designations used but with Defenders split into Attacking and Defending (based on proportion of touches to be made in the final third). Players who have played 900 minutes or more have again been included, whereas those which fall below the threshold have been excluded.
Where I have deviated from Parts One and Two is that I am looking at FPL points, rather than Expected Adjusted Points. I have made this decision because I am no longer looking for underlying causes of points but rather the impact of a fixture on total FPL output.
What the visualisations are showing
The charts you will see below show three views of the same data. The following example is for all players combined:
 At the top of the visual, the bars show the percentage share of events within the category where six or more points were scored. The coloured segment of the bar represents the number of times a player scored more than six points, relative to the grey segment where less than six was scored. The probability of the players’ team winning the game according to bookmaker odds range from 0% to 100%, and these have been grouped into five even categories: rank outsiders who had 020% chance of winning, heavy favourites who had 80100% chance of winning, and three groups in between.
 The bottom of the chart shows the number of events within these categories, which is important to consider when drawing conclusions. For example, a category of player might score six or more points on 50% of occasions, but this is a lot less powerful as a finding if it is based on two events than if it were based on 500.
 The single stacked bar on the right shows the split between events of under six and six or more. This is to provide overall context. The data here shows that amongst players who play at least 900 minutes a season, they will score six points or more 16.21% of the time. Put another way, if 10,000 players played one game each, 1,621 would score more than six points.
Please note that the segmentation of data into groups of over and under six is arbitrary: around 5.5 it is the target that you should be aiming for per player per week if you want to have any chance of winning FPL and so the threshold of six can realistically be labelled as a successful week for a player.
Goalkeepers: There is a definite trend for Premium players to benefit from fixture ease, but the pattern is far less clear below that price range.
The first notable feature of the Goalkeeper data is that it has the highest proportion of success of all the positions: in 23% of cases a Goalkeeper will score six or more FPL points, which is almost one in four.
The most interesting points in the data above are as follows:
 There is very little difference in the ability of MidPrice (Lower) and MidPrice (Upper) Goalkeepers to score FPL points, and for both categories, their own ability to improve output as the fixtures get more favourable breaks down the higher they go.
 MidPrice (Lower) are no more likely to register a successful game in the 4060% range as they are in 6080% range (although there are very few of the later events so this must be taken with a pinch of salt) and MidPrice (Upper) experience a similar plateau. This is likely due to the impact of save points and increased activity in these more difficult games.
 The one player category which does show evidence of fixtures playing a role is the Premium Goalkeepers, where the likelihood of six or more points increases with the ease of the fixture.
 There are so few events for regularly playing budget Goalkeepers that it is difficult to take any conclusions seriously, but it is notable that games where they have a less than 40% of winning there are particularly weak. They are much stronger in the 4060% range but these events are particularly rare.
Goalkeepers Summary
The conclusions we can draw from here is that Premium Goalkeepers (£5.5m+) will see increased output relative to the ease of the fixtures (when aggregated over the season), but there is not really any reason to invest in a MidPrice (Upper) when for £0.5m you can expect a similar frequency of hauls from a MidPrice (Lower) Goalkeeper. Neither of the MidPrice brackets appear significantly affected by fixture ease (with the exception of when they are rank outsiders).
Defending Defenders: Fixture ease does play a role in probability of high returns, but evidence is slight across all price categories
 The increase in FPL returns as the fixtures improve is evident, however the gradients are very shallow.
 It is interesting to note that the likelihood of a Defending Defender getting a successful return in FPL during a game when the team has a 4060% chance of winning is barely any different between the MidPrice (Lower and Upper) and Premium categories: they will return in 25% of games (give or take less than 0.5%)
 The data doesn’t appear to show much difference between the groups, indicating that fixture difficulty is not a significant factor in points hauls. However, the frequency of games needs to be considered: MidPrice players will play the majority of the time with a 2040% chance of winning, and here they return six or more points in 16.8% of games (Lower) and 19.4% of games; by contrast, Premiums will spend the majority of time as 6080% favourites, and they return in 34.7% of games.
Defending Defenders Summary
Fixture ease is a factor in the output of Defending Defenders, however it is not a major factor in the majority of cases. There is evidence that it is worth investing in Premium Defending Defenders over the cheaper options, which supports the conclusion from Part One, but there is only marginal difference in the out of MidPrice (Lower) and MidPrice (Upper) players, suggesting a “go big or go home” mentality when investing here.
Attacking Defenders: Fixtures favour the expensive players, but less so the cheaper players.
 In contrast to the Defending Defenders, there is a noticeable benefit in investing in MidPrice (Upper) Attacking Defenders compared with the cheaper MidPrice (Lower) category. In games where the team is 4060% likely to win, they will return points in 27.9% of occasions, significantly higher than the 20.5% for the cheaper group.
 In fact, the Premium group are also eclipsed in these games, where the most expensive attacking Defenders will return just 21.1% of the time. To get returns out of these players, they need to be heavy favourites. I attribute this to the fact that if they are not favourites (less than 60% chance of winning), they are likely playing a very strong team with a potent attack.
Attacking Defenders Summary
The gradient of the inclines, which is shallow for MidPrice (Lower) through steep for Premiums, suggests that there is a relationship between fixture ease and price: cheaper Attacking Defenders will not benefit as much from easier games, but more expensive ones will. This suggests investment should be in the players who will be favourites more often. If one is to invest in a cheaper Attacking Defender, make sure you don’t play them when they are rank outsiders.
Midfielders: Cheap players rarely return, regardless of fixture
 The data here is the most pronounced we have seen so far. It indicates that there is no impact of fixtures on the cheaper end of the scale, but a significant impact at the higher end.
 For a MidPrice (Lower) Midfielder (less than £7.5m) there is surprisingly less value in them being a heavy favourite, with the drop from 4060% to 6080% being 3.4 percentage points (14.9% to 11.5% likelihood of a return). By contrast the MidPrice (Upper) and Premium categories increase their chance of returns by 5.4pp and 7.2pp respectively.
Midfielders Summary
The data here shows that the more expensive players are far more influenced by fixture favourability than the cheaper players, suggesting that as much money should be placed in the top two categories as possible.
Forwards
 MidPrice (Lower) Forwards (under £7.5m) are not influenced heavily by fixtures unless they are overwhelming favourites or rank outsiders. When these players are 2080% favourites, they will return in around one in six games (~1618%).
 MidPrice (Upper) Forwards (under £10m) show an incline through the ranges: they will score less when they are not favourites but will score more when they are. However, it is interesting to note that there is not much difference between 2060% favourability, which is where most of their games reside. This suggests that the majority of the time they are returning points in just under one in four (~23%) of games.
 There is a general increase in returns as the Premium’s fixtures get easier, however the volume of returns is not very compelling when compared to their cheaper alternatives or their Midfielder peers. It must be said though that the chances of a return when overwhelming favourites (over 60%) is more than one in three, which is very appealing.
Forwards Summary
The conclusion from this data is that strikers generally get slightly more returns the easier the fixture, and Premium strikers will return especially frequently against weaker teams. However, the MidPrice (Lower) options are low returns in the majority of fixtures.
Part Three Summary
There are multiple ways of interpreting this data because it is aggregated to quite a high degree. However I believe that it reveals something interesting about the approach to FPL strategy.
In the past I have been a proponent of the ‘three way defensive rotation’, which freed up money for attacking players by picking three cheap Defenders and rotating them according to favourable fixtures. However this data reveals that in the MidPrice (Lower) category the favourability of a fixture is not much of an indicator of FPL performance. The concept of rotating three £4.5m Defenders on the hope of catching clean sheets in good fixtures is not going to be any more beneficial than flipping a coin to choose the starter between the three.
By contrast, the Attacking Defenders and Midfielders show some evidence that the more favourable the fixture, the better the Premium and MidPrice (Upper) assets in these positions will do. The same is also true of Premium Forwards and Goalkeepers. This suggests that the herd mentality of chasing expensive bandwagons and switching Premium assets in and out is grounded in logic.
Throughout most of the categories and positions there is evidence that fixtures do have an impact on the returns of an FPL asset, however by looking closer at the data one comes to the conclusion that there is justification for rotating (e.g. transfers in and out of the squad) the expensive players rather than the cheaper ones according to fixtures, which is not something I have practiced in recent seasons.
Part Four: The optimal structure of an FPL squad
Top Level Summary
The greater value for money per £m spent is in the Defender and Midfielder positions, whereas the Forwards and Goalkeeper positions offer greater relative value in the cheaper categories of player. Therefore, the ideal squad structure features heavy investment in Premium Midfielders and Defenders, whereas there is little justification for an expensive Goalkeeper or more than one Premium Forward.
Introduction
Using the data and findings from Parts One and Three we can begin to analyse the question of where in the squad should money be invested. In order to do this, we need to consider a combination of several factors, including:
 Number of option in the same price bracket (an ‘exit strategy’ should a player be underperforming)
 Average number of points scored per position / category
 Relative prices of players in each category (a variation on ‘value over replacement player’)
 Impact of fixtures on categories
Average Points and Price Analysis
Parts One and Three showed us that there are lower barriers to entry for good season performances in the Goalkeeper and Forward positions. In these areas of the pitch, whilst the truly exceptional seasons are had by more expensive players, there are frequently cheaper players that break through. The chart below further demonstrates this, with the average points for Budget players relatively high in comparison with Defenders and Midfielders.
The average points per player by category and position we can see that Forwards and Midfielders, especially the Premium and MidPrice (Upper) category players, are where the highest absolute points lay, hence why players in these brackets cost more money. It is notable though that the incline through the price brackets is steeper for Midfielders. This suggests that there is most value to be found in the premium Midfielders than Premium Forwards.
However, this view of the data is skewed by the relative prices of the players. If we look at the same view below, but with EA points replaced with average starting price, we see that the incline in price for Midfielders is equally as steep as the Forwards. It is also slightly difficult to read because the starting points are different (£4.0m for Budget Goalkeepers, £4.85m for Budget Forwards)
What is required is to merge these two charts.
Value for Money Analysis: There is greater value per £m spent in Defenders and Midfielders
The following chart does two things:
 The starting point – average EA points for the Budget category – has been indexed as a baseline value of 1.00. The proportional increase in average EA points per category is plotted relative to the Budgetset baseline index. This allows us to see how much of an impact on EA points a jump from one category to the next will have.
 For example, the Budget Goalkeeper average EA points are 36.7, which are represented by 1.00. The Premium average EA points is 60.7 and represented by 1.65 (=1.00/36.7 * 60.7 = 1.65), in essence noting that Premium Goalkeepers are expected to score 65% more adjusted points than Budget Goalkeepers.
 The chart plots the average starting price of each budget category against the index described in step 1. The gradient (steepness) of the trend line indicates where there are greater gains to be made for your FPL wallet.
This analysis has strayed relatively far into the abstract for the casual reader at this point, so in simple terms the above chart demonstrates there is greater value (low priced bargains who will perform) to be found in the Goalkeepers and Forwards, and it is worth spending money on higher priced Defenders and Midfielders.
Explaining the Value for Money Data: Why steeper lines show that Defenders and Midfielders require more investment
This can be demonstrated by looking at the value of the trend line gradients in the above chart. Let’s take Attacking Defenders as a practical example:
 The Budget category players have an index value of 1.00 and the Premium players have 3.34. This means that Premium players in this position will score (on average) 3.34x more than budget players.
 The average price of these categories players are £4.0m and £6.28m respectively.
 The gradient of the trend line is 1.10 (with an intercept of 3.59). This indicates that the average EA points index value rises against the average starting price by a factor of 1.10x.
 It is therefore possible to predict what the index value would be given the starting price of a player, which allows us to understand how many more EA points he would score relative to a budget player. For example, using the formula: EA points index value = 1.10*starting price – 3.59, on a player worth £5.5m, we can calculate that the index value will be 2.49, meaning that a £5.5m player will be expected to score 2.49x more points than a budget player in the Attacking Defender position. This index value increases by 1.10 for every £1.0m spent (£6.5m = 3.60x (rounded); £7.5m = 4.70x, etc.)
In simple terms, the steeper the gradient of the line, the more value you get per £m spent. The gradients by position are as follows:
 Goalkeepers: 0.40x
 Defending Defenders: 0.97x
 Attacking Defenders: 1.10x
 Midfielders: 0.94x
 Forwards: 0.24x
This shows that the greatest increase in EA points per £m spent is in the Attacking Defenders position and the lowest is in the Forwards. In simple terms, this means that a player like Andy Robertson will outscore a £4.0m fodder player in terms of value per £m spent to a greater degree than a Forward like Harry Kane will against a £4.5m Forward.
What this means for Team Structure
Where this analysis has begun to veer from the weektoweek experience of an FPL manager is in the focus on the average EA points. FPL managers do not fill their squad with random players determined by available budget, but rather try to find the outliers who are performing above average, thus offering greater value. It therefore does not matter if the average EA points of budget Goalkeepers are 36.7 if there is one who is starting regularly and keeping clean sheets. In such circumstances the transition to accommodate them is easy: a more expensive Goalkeeper is sold and money is freed up for investment elsewhere. Where team structure generally and this analysis specifically becomes important is when upgrading a cheaper player to a more expensive option, or even moving sideways. In the aforementioned example the budget Goalkeeper may pick up an injury, at which point the exit tactic relies either on money in the bank to fund an upgrade or an equally priced player performing to a comparable level. However, as any experience FPL player knows, £4.0m playing Goalkeepers are a rare commodity.
The above chart shows the number of players in each category (size) and the average EA points (colour and annotation). When we look at this data in conjunction with the baseline index model above, there are a few points of interest when considering how to structure an FPL team.
Goalkeepers: There is less value for money in expensive Goalkeepers; there are numerous MidPrice (Lower) options which should be the target of investment
As described anecdotally above, the number of playing Budget Goalkeepers is low (average 1.6 per season will play more than more than 900 minutes), meaning that the exit strategy for these players is almost nonexistent without money in the bank or a free transfer. However, there are 9.8 MidPrice (Lower) Goalkeepers per season. As demonstrated previously, the increase in EA points per £m spent is lower than both types of Defenders and Midfielders, meaning that there is less reason to increase spend big in this position and there are plenty of exit options in the MidPrice (Lower) category if required. Additionally, Part Three showed that fixtures are not at this price point, so as a substitute option, I favour a budget backup of my main Goalkeeper, so they can come if the first choice is injured and you don’t spend money unnecessarily on the bench option.
Defenders: Value per £m spent is high so investment should be high in at least three Defender positions
Across both types of Defenders (Defending and Attacking) the baseline index analysis shows that there is the steepest incline in EA points per £ spent, indicating that money should be invested in the Premium category and there is low value in the budget category. There are also more viable options here: 15.6 players per season in the premium category vs. just five in the budget area. The combination of the highest incline in expected returns and few options in the budget category mean that there is a compelling argument to invest heavily in Defence. It should of course be noted that £4.0m Defenders offer the best sacrificial options in the game (e.g. players to free up money for elsewhere and not be expected to play), so at the start of the season it is almost certainly worth having at least one of these players in your team if you’re not planning to have 15 starters in your squad.
It is interesting to note that the fixture favourability analysis showed that the propensity for Defenders to score six or more points in a game was not very different between MidPrice (Lower) and MidPrice (Upper), suggesting that the more expensive of these two groups will score higher on average when they do return a successful (+6) haul.
Midfielders: Investment should be high in at least two Premium options; the law of large numbers suggests that it is still worth saving money in one or two cheap placeholder options
Midfield Premium options are as close as we get in FPL to guaranteed EA points per £m spent. The R_{2} values from the regression analysis in Part One are the strongest of all the positions (indicating the strongest correlation between onpitch actions and EA points, making them the most predictable position), and the analysis of the baseline index values shows that the more you spend, the higher the returns. In terms of average points per player, the Premium Midfielders are the runaway leaders. Therefore, it makes sense from an FPL perspective to invest as much in the midfield as possible.
However, it is worth pointing out the abundance of options playing more than 900 minutes in the Budget and MidPrice (Lower) categories (110.2 per season). Therefore, there are plenty of escape routes if you pick a cheap player in one or two of your five midfield slots. The average EA points in these positions is low (xx), but the maximum values over the last five seasons have range from 52.986.3 for Budget options and 75.8115.7 for MidPrice (Lower) options, so there will inevitably be a good option you can pivot to. It is therefore advisable not to neglect cheaper Midfielder options in your team because they offer up budget for elsewhere in your team.
Forwards: Value for money is offered by cheaper options; Premium players shouldn’t be ignored though due to their absolute points potential
The Forwards offer the shallowest gradient in the baseline analysis, indicating that the increase in points from Budget to Premium is low per £m spent. However, it is worth noting that the Premium category is second only to Premium Midfielders in terms of average points per player, and as noted earlier the 2018/19 season saw Aguero and Aubameyang hugely overperform against their expected numbers such is the quality of the strikers in the Premier League. So it would be remiss of an FPL manager to completely ignore these players.
The analysis of the Forwards is of interest more in the Budget category. There are 5.2 players playing more than 900 minutes per season and in terms of value per £m spent (relative to the Premium options), they offer by far the best return of all the positions. The MidPrice (Lower) category has even more options (23.2 per season), meaning that there is a strong exit strategy for cheap Forwards. It points towards an advocacy of a ‘one Premium and two cheaper’ strategy in this position in order to fund the Premium options in Defence and Midfield.
Price and Team Structure Analysis: Summary
Ultimately, it is difficult to fit in all the players you want. Based on the analysis, Premium options through each position would be desirable, however this is not realistic. Value for money analysis suggests it is best spent in the Midfield and Defensive areas of the pitch. Whilst a Premium Goalkeeper and a Forward are high points scorers, the value for money is low relative to their cheaper counterparts and so they should be considered the sacrifices here in order to maximise the impact of a squad.
Whilst the information presented here is open to debate, my thoughts on the budget structure for the coming season are:
 Goalkeepers: £8.5m (one MidPrice (Lower), one Budget)
 Defenders: £28.5m (three Premium, two MidPrice (Lower))
 Midfielders: £45.0m (two Premium, one MidPrice (Upper), two MidPrice (Lower))
 Forwards: £18.0m (one MidPrice (Upper), one MidPrice (Lower), one Budget)
Part Five: Conclusions
To reiterate and expand upon the Executive Summary from the start of this article, my interpretation of five seasons worth of FPL data is as follows.
There is evidence that combinations of metrics related to onpitch actions, such as shots or touches in certain areas of the pitch, correlate strongly although not perfectly with FPL points over the course of a season.
The aforementioned models provide a good understanding of what was driving the FPL performance of players over the course of a season, but one a weekly basis the performance of players against expectations has been – and will continue to be – erratic.
There is evidence to suggest that fixtures have an impact on the likelihood that a player will return points, although there is variation between category of player and position regarding the degree to which this will happen.
Rotation (transfers in and out) according to fixtures is more beneficial amongst the expensive assets.
Premium Goalkeepers (£5.5m or higher) are more sensitive to fixture difficulty than their cheaper counterparts. MidPrice (Lower) Goalkeepers (£4.5m) offer the best combination of value for money, fixture robustness and number of options.
Defending Defenders are the least predictable group of players. They perform only fractionally below their Attacking counterparts but are significantly undervalued by FPL managers. It is better to spend money in this position than go for Budget options.
Attacking and Defending Defenders offer the best and secondbest value for money per £m spent respectively. Therefore, heavy investment is recommended.
Midfielders also offer very strong value for money per £m spent. The Premium Midfielders (£10m or higher) are the highest average point scorers in the game, and so should be the principal focus of investment. MidPrice (Lower) Midfielders (£5.57.0m) should not be ignored though due to the number of available players in that range, of which at least one will breakout with a decent season.
Forwards offer low value for money per £m spent, but Premium players (£10m or higher) do offer large point totals. There are numerous cheap options offering good value for money against the Premium players relative to their Defender and Midfielder counterparts. Investment in this area is not recommended due to budget constraints
Thanks for reading. I can be found on Twitter @mathsafe_fpl.