Introduction

In my previous post on the Fantasy Premier League (FPL), I outlined an approach to assembling an FPL team. I received recommendations from friends (some of whom who are ranked pretty highly in the Singapore league) on building and managing a team. First, in building a team, it may be worth spending more on first team players and choosing the value-for-money players for the bench, given that they would not be clocking points unless first team players drop out of their respective squads. This was something I did not consider. I’ll implement this for Data United next season. Second, there should be a dynamic approach to choosing players from week to week to maximise points earned. Two insightful considerations were (1) player form and (2) “differential” players - players who are expected to perform exceedingly well for a certain Game Week (GW). Maximising points per GW by choosing in-form and “differential” players depends on the assumption that past performance can be used to predict future performance. In this post, I test this assumption.

Form in the FPL

Many believe that form is important in predicting player performance. It is typically defined as how well a player is currently performing. Digging deeper into the form statistic provided by the FPL, I discovered that form is calculated as the average number of points scored in games the player participated in in the preceding 3 GWs. This is rather simplistic.

In this section, I test whether form as defined by the FPL can be used to predict future performance. I perform the following for all players who have clocked 10 or more games in the season thus far:

  1. Calculate form for each player: the average of each player’s bonus points (BPS) in the past 3 games (as opposed to the past 3 GWs in the FPL system).
  2. Run a regression of BPS on past week’s form: this is the equivalent of using form to predict the next GW’s performance.
  3. Save the coefficient and p-value on the form variable.

I find that form had a statistically significant effect on BPS for only 14 out of 366 players (3.83%) at the 5% significance level. The figure of 3.83% is worse than pure randomness. That is, if we came up with a bunch of random numbers from a normal distribution to mimic a player’s performance during a season, repeated this for many players, and calculated form using the same formula, we would find a statistically significant relationship between “performance” and form for 5% of all these fake players.

Another controversial result is that for 10 out of these 14 players, form had a negative impact on BPS. The graph below shows the distribution of impact (coefficient) of form on performance for these 14 players.

We can safely conclude that the FPL’s form factor does not help much in determining players’ performance in upcoming GWs. This is not to say that the concept of form is not important. Perhaps, we just have not found a mathematical definition of form that can help predict games, assuming there is one.

Does Form Matter?

To get inspiration for my own mathematical definition of form, I searched Google for possible formulas. Strangely, there were few results. There seemed to be no consensus on a formula for player form, which suggests that we are not entirely clear what form is. The only common principle on form was that it involved some combination (average or sum) of points scored in the previous games. Fortunately, we can test whether this broad principle holds by using past performance to predict future performance.

Let’s assume that form can be measured by some weighted average of performance in the past 5 games. A regression of performance on performance in the past 5 games would allow maximum flexibility for the weights:

Our criterion for determining that some broad notion of form matters is where we find statistically significant relationships between past performance (in some of the 5 games) and current performance. Our criterion for determining that form does not matter is if there are close to no statistically significant relationships at all. With that, we can begin the testing.

Model 1: Past Performance vs. Future Performance

Let’s use Mohamed Salah as an example to illustrate the methodology for testing the hypothesis that past performance can predict future performance.

Case Study: Salah

First, let’s take a look at Salah’s performance so far. The red solid line is his average BPS score. The red dotted lines represent the 95% confidence interval - 95% of his BPS scores should fall within this range.

Note that Salah rarely had a series of games where his BPS was stable. However, fluctuations in BPS are extremely common, even for Ben Foster, the most consistent player in the FPL. The difference lies in how large the fluctuations are, and this can be measured by the Coefficient of Variation (i.e. standard deviation divided by mean BPS), a metric that I used to select the FPL team in my previous post.

Next, we examine how Salah’s performance in any game relates to his past games using the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF). The ACF tells us how correlated (vertical axis) performance in one game is with previous games (horizontal axis). For example, a correlation of 0.9 for the 1st lag means that performance in each game is highly related to the previous game. The PACF measures a similar effect, but it removes the effect of all prior lags. For example, the partial autocorrelation value for performance in each game and performance 5 games earlier (lag 5) removes the effect of performance in the 4 games preceding each game (lags 1 to 4).

Intuitively, if performance in each game can be predicted by performance in preceding games, we should see significant lags (bars that exceed the dotted lines), excluding lag 0 for the ACF.

From the graphs above, we see that Salah’s performance in his past 16 games cannot be used to predict his future performance.

The Model Proper

How do we repeat this analysis for all players without having to plot and interpret the graphs individually? Simple: linear regression. The PACF for 5 games prior, for example, is equivalent to a linear regression of performance on 5 lags of performance. We can easily develop linear models for every player in our dataset using a for loop.

The regression models had the identical specification: current game’s performance against performance from each of the past 5 games. I applied a filter to include only players who played at least 15 games to ensure a sufficient number of observations for each player model. The results:

  1. None of the preceding 5 games could be used to predict performance in the following game for 269 of 306 (87.9%) players.
  2. Performance from 1 of the 5 preceding games could predict performance in the following game for 27 of 306 (8.8%) of players.
  3. Performance from 2 of the 5 preceding games could predict performance in the following game for 6 of 306 (2.0%) of players.
  4. Performance from 3 of the 5 preceding games could predict performance in the following game for 3 of 306 (1.0%) of players.
  5. Performance from 4 of the 5 preceding games could predict performance in the following game for 1 of 306 (0.3%) of players.
  6. There were no players whose preceding 5 games could predict their performance in the following game.

The results suggest that even a broad notion of form does not apply to a majority of players. In other words, in general, form does not predict future performance.

Model 2: Past Performance and Relative Team Strength vs. Future Performance

What if we considered which team the players played against? The regression models would be more complex, but would imply a more comprehensive definition of form. Each player model included as many of the following as the data allowed:

  • Relative strength: (based on team tier)
    • Stronger: the player was in the stronger team in the fixture
    • Equal: the player’s team was of equal strength to its opponent in the fixture
    • Weaker: the player was in the weaker team in the fixture
  • Relative strength x Performance from 1 game ago
  • Relative strength x Performance from 2 games ago
  • Relative strength x Performance from 3 games ago
  • Relative strength x Performance from 4 games ago
  • Relative strength x Performance from 5 games ago

In short, this model configuration considers the predictive power of past performances and the relative strength of the opponents played against. Because some players played fewer games, not all of the variables above were included in the player models. As such, the number of variables actually used differed from player to player (either 14, 15 or 25 variables). In addition, due to the high demand for data from a model with this many variables, models could only be developed for 164 of the original 498 players. The results can be summarised as such:

  1. For 134 of 164 (81.7%) players, past performances and relative team strength had no predictive power on future performance.
  2. For 20 of 164 (12.2%) players, only 1 to 3 of the past performance and relative team strength variables in their respective models were predictive. Because there was no standard number of variables in each player model, the proportion of significant variables ranged from 6% to 20%.
  3. Only for the remaining 10 of 164 (6.1%) players were there 4 or more predictive past performance and relative team strength variables in their respective models. The proportion of significant variables in these player models ranged from 25% to 50%.

Conclusion

In this post, we analysed the relationship between players’ form and performance, as measured by the FPL’s bonus points (BPS) statistic. First, we showed that FPL’s form statistic could not be used to predict players’ future performance. Hence, we searched for an alternative formula for form. We defined form very broadly - as any mathematical combination of performance (BPS) in players’ preceding 5 games against opponents of varying difficulty. Using this broad notion of form, statistically significant relationships between form and performance were found to be the exception. That is, for most players (81% to 87%), form did not matter.

What can we learn from these results?

  1. Be careful when using FPL’s form statistic. It does not predict future performance. A more logical approach would be to develop your own form statistic that has a statistically significant impact on players’ future performance.
  2. Be skeptical about form. I’m sure we have all felt “on form” at some point when playing competitive sports, or have this unexplainable sense that our favourite players in the EPL are “on form”. But, the statistics seem to dispute the claim that form exists at all.