Thread by @fpl_gents

Regression to the mean. A very long #FPL {THREAD}

After seeing the skill/luck debate I felt it would be fitting to share what I've learned from the book “Thinking Fast and Slow” by Daniel Kahnemann.

The concept can be applied to examine players but also our own results.

The book is about biases that cloud our reasoning and distort our perception of reality. It turns out there is a whole set of logical errors that we commit because our intuition and brain do not deal well with simple statistics.

The term ‘regression to the mean’ refers to the idea that things tend to even out over time, or at least gravitate in the direction of an even split. The concept can be applied in business, psychology, genetics and even to glean new insights from common FPL trends.

By making ourselves properly acquainted with this concept we'll train our brains to better spot when this counterintuitive phenomenon is taking place. It will allow us to be more able than our competitors in assessing a player’s form...

And because our approach is backed by science it’ll make us more confident in our decision-making. Minimizing instances of bad judgment and addressing the weak spots in our reasoning is after all one of the best ways to improve our FPL game.

Kahnemann says that “The very idea of regression to the mean is alien and difficult to communicate and comprehend… Many statistics teachers dread the class in which the topic comes up, and their students often end up with only a vague understanding of this crucial concept”.

Before I give some examples of when the concept is relevant, I want to make clear what some common misconceptions are.

One misinterpretation is that an individual will regress to the mean of all data, but that is certainly not the case.

What it does mean, however, is that data will tend to regress back towards some expected value. Extreme data points—like the top-scoring right back in FPL in a given year—involve some amount of skill and some amount of luck.

In the subsequent year it is not likely last year's top players will experience the same luck.

Another misinterpretation is that it gets confused with the fallacious law of averages, which states that an unusual number of successes must be balanced by failures; for example...

... that a winning football team is due for a loss. The correct regression principle implies that the best-performing teams will, on average, continue to perform above average, but not as well as they had previously...

since their stellar performances were more likely affected by good fortune than bad. If Liverpool won 10 straight times versus Spurs, 10 straight times does not mean that they will always beat Spurs; their perfect record exaggerates how much better they are than Spurs.

On the other hand, each victory would not increase the probability that they would lose the next time they played.

Regression to the mean in scores should not be misinterpreted as implying that abilities are converging to the mean.

The correct conclusion is instead that those teams that are currently the most successful generally aren’t as talented as their lofty records suggest. Most have had more good luck than bad, causing their performance to overstate their ability.

When their performances regress toward the mean, their place at the top might be overtaken by other teams that perform above their own ability.

Now that we have cleared some misconceptions, let’s try to understand the concept better.

Kahnemann mentions that one of the reasons why it’s such a hard concept to grasp is because even when a regression is identified, it will be given a causal interpretation that is almost always wrong. Because there is never a cause for regression to the mean, only an explanation.

To better understand what he means by this let’s look at an example: If a defender has, let’s say, returned points in all of his first 5 gameweeks of the season and subsequently has the most points of any player in the game, this probably means he has an above-average talent.

But it also most likely means he’s been lucky. If on the other hand another player, say an attacking one, has zero returns after playing all games in his first 5 gameweeks, he has probably a below-average talent but were also unlucky during this period.

Now if you were to predict the next 5 gameweek scores of these two players you’d expect them to retain the same level of talent, so the first player will have an above average score and the second player a below average score. Luck however is a different matter.

Since you have no way of predicting the players’ luck in the second time period your best guess must be that it will be average, ie. neither good nor bad. This means that in the absence of any other information, your best guess about the players’ score in gameweek 6 to 10...

...should not be a repeat of their performance in weeks 1 to 5.

The most you can say is: The player who did well the first 5 weeks is likely to be successful in the following weeks, but less so than before, because the unusual luck he probably enjoyed before is unlikely to hold.

Similarly the player who did poorly will still be below average but will improve because his hypothesized streak of bad luck is not likely to continue. The more extreme the original score, the more regression we can expect, an extremely good score would suggest a very lucky run.

Now if you’d evaluate all players in their second time period first instead, weeks 6-10, then you will find exactly the same pattern of regression to the mean. The players who did best on week 6-10 were probably lucky that period and had done less well in weeks 1-5.

The fact that you observe regression when you predict an early event from a later event should help convince you that regression does not have a causal explanation, but our minds work from associative memory and will try to find a cause, or potentially make it up.

This is where we may start to see ghosts and falsely make connections between events that simply isn’t there. So when the real explanation probably is that the player was unusually lucky the first weeks, we will not settle for this because our mind prefers a causal explanation.

That is why pundits are paid quite well, because we want to hear their interesting theories for why the regression effects we see actually occurred.

There is a major difference between regression towards the mean with teams and with players, and it’s important to understand the differences between the two. It’s much harder for an entire team to maintain a peak performance over an extended span than an individual player...

but eventually both are due to slow down. There is also an obvious connection between the two in that if an individual superstar is due to slow down then it is likely their team are liable to slow down as well.

For example, if Paul Pogba dominates throughout the course of an eight-game win streak and he clearly is the primary reason why Man U is winning then there should be an understanding that his eventual slowing down could lead to Manchester United cooling down as a team.

So different teams will be affected in varying degree when it comes to a players form because it depends on how important he is for the team.

After Salah’s record FPL season in 17/18 when he scored 303 points there were many of us who expected next season to be at least as good.

Player’s usually take a little time to adapt in a new environment so it’s not that likely their first season is going to be their best. However, after only a couple of games into the season, which was Salah’s second in Liverpool...

...I read someone on twitter mentioning his reduced output was probably just a regression to the mean. I think his insight was quite profound if we look at how Kahnemann sees it.

A lot of others who tried to figure Salah out blamed tiredness from World Cup.

Or the injury he had from the CL final, and yet another explanation was that he had been figured out by the oppositions’ defence and goalkeepers. These are all good examples of reasonable explanations and could very well have had an impact, but I still find it interesting that...

despite all of our explanations there is often a simple statistical trend that underlies these results. This does not mean we should completely disregard our own opinions and intuition, there is definite room--and need--for those, but I’m trying to point out how powerful this...

...principle can be, either combined with our own intuitions or on its own if we are uncertain about what to actually think about a situation.

We’ve looked at how the regression to the mean could be applied to a player’s or team’s form but we could also apply it on our own performances as managers. Having a very bad season probably means we’ve been very unlucky, and vice versa.

Knowing about the regression to the mean means we can more easily clear the fog when things are not matching our own expectations, and it will subsequently help us keep our cool in both ups and downs.

The effects of regression can be difficult to disentangle. Luckily awareness of the phenomenon itself is already a great first step towards a more careful approach to understanding luck and performance.

If there is anything to be learned from this principle it is..

the importance of track records rather than relying on one-time success stories. I hope the next time you come across an extreme quality in part governed by chance you will realize the effects are likely to regress over time and adjust your expectations accordingly.

Thanks for reading and I hope you find it interesting enough to share @DhillonAjit @FPL_Batman @FPLGOAT7 @FPLBrain @FplStrategy @aritravo_auddy @FPL_SOS @Reuser5 @FPL_InHindsight @allaboutfpl