A bat and a ball cost £1.10 in total. The bat costs £1 more than the ball. How much does the ball cost?
On this week’s Scoutcast, Joe raised the idea of unfairly unfashionable players; a group of players that we often overlook to our detriment. This led me to thinking about what it is that can bring us to making poor snap decisions, holding onto outdated impressions for too long and eventually back to a book I believe everyone should read.
For those unfamiliar, ‘Thinking, Fast And Slow’ is a best-selling 2011 book by Nobel Memorial Prize in Economic Sciences laureate and psychologist Daniel Kahneman. The book focuses on our decision-making and uses two characters to describe how our brains generally approach this: System 1 and System 2.
- System 1 – is fast, automatic, exerts little or no effort and is engaged involuntarily. This makes up about 98% of all of our thinking and is the “thinking fast” of the book’s title.
- System 2 – is slow, deliberate, effortful and must be consciously engaged. This makes up about 2% of all of our thinking and is the “thinking slow” of the book’s title.
Like physical effort, mental effort is hard. It consumes calories, puts us under stress and must be actively opted into and maintained.
If you were asked ‘What is two times two?’, you would likely find this quite straight-forwards. You probably did not even have to calculate the answer, arriving at four by instinct. You probably recognised the problem as something you had solved before and produced the answer from memory without ever having to do any mathematical calculations. You also have no control over this, the answer of four came to you whether you wanted it to or not. Not dissimilar to the famous ‘Don’t think of an elephant’, which immediately and involuntarily causes you to think of an elephant.
If you were asked, ‘What is 59 times 73?’, you would likely find this considerably more difficult. You may require pen and paper, you may have to recall multiplication methods taught to you at school and you most certainly will have to put effort in. You do have control over this one, the answer will only come about by way of you choosing to find it and will not appear otherwise. Give it a go.
- 2×2 makes use of System 1.
- 59×73 requires System 2.
You will likely have felt the difference between engaging each of these systems and you will almost certainly have felt the effort required when System 2 was called upon. Your heart rate will have risen, your blood pressure increased and an outside observer paying close attention may have noticed your pupils dilating. These are all sure signs of mental strain.
It is for this reason that System 2 does not get involved much in our every-day lives. It comes with a cost. Our brains prefer System 1.
Most every-day problems do not require difficult computations to solve. We have evolved to rely on System 1, in fact our survival depended on it, and it generally does a very good job. Taking the time to work out if that oncoming mammoth stampede is going to flatten us or not would have resulted in our extinction. Walking at a comfortable speed, chewing food, reading the words written here. All of these are done automatically and effortlessly by System 1. Even if System 2 has to get involved, for example in choosing where to walk, what to eat or whether to open this article, it probably quickly delegated the decision making back to System 1; I’ll walk where I normally walk, I’ll eat something I’ve eaten before, I only open articles written by Simon March.
It is also possible for something that previously required System 2 to transfer to System 1, in fact this is key to learning and mastering skills. At one point, you did not know the answer to two times two instinctively and had to work it out. That is no longer the case. Similarly, most of us are capable of a basic game of chess but almost all of us will have to give each move some thought, especially as the game progresses or competent opposition is encountered. A master chess player, however, would defeat us with very little effort at all. They are experienced to the point that recognising and responding to a vast number of chess moves is automatic. They identify the game state and deploy the required strategy from memory without having to consciously examine and determine this cause of action before doing so.
Fantasy Premier League is a game of decisions. Understanding how we make these decisions and identifying the context around those is key to success. Many of us fall into the trap of believing we are using System 2 – the thoughtful, deliberate side of our brain – for these decisions when we are in fact using System 1.
Answer this, ‘Is Harry Kane (£11.7m) a good goal-scorer?”. The answer is clearly yes. If you were asked why you answered in this way you would be able to start producing reasons such as his finishing ability, movement and impressive goal-scoring record. You did not, however, think of these reasons before you answered, the answer simply came to you instinctively. You were using System 1. When pressed, you then fact-checked with System 2. But even then, do you know what his goal-scoring record is? You may well still be using System 1. You recall he has a good record, but you probably do not know what this is without either giving it some thought, estimating from memory or looking it up. It is in this way that we can very easily believe we are making conscious, deliberate and well-reasoned decisions when we are in fact not.
This can work in our favour. If we had to look up Kane’s entire goal history before handing him the captain’s armband we would likely never make it to the deadline. It is efficient to simply know he is a good goal-scorer and use this information to inform our decisions.
However, the things we “know” are sometimes not as accurate as we think they are.
This piece opened with a question about the price of a ball:
A bat and a ball cost £1.10 in total. The bat costs £1 more than the ball. How much does the ball cost?
The answer is 5p. Over 50% of people will answer 10p.
This is not because they cannot perform relatively simple maths, it is because they did not think they needed to. They allowed System 1 to provide the answer unchecked by System 2.
10p ‘feels’ right. It is roughly the correct magnitude and we know that £1 plus 10p is £1.10. So, we accept 10p as the answer, assuming that the bat is £1. However, the difference between 10p and £1 is 90p, not £1, and so this cannot be the answer.
When we allow System 2 to re-examine the question, we arrive at 5p. The bat costs £1.05. The total amount and the difference between the bat and the ball are both satisfied by this answer.
Many Fantasy managers may tell you they make decisions because they “feel right”, and like crossing the road, chewing or reading, these decisions will often come off without issue. Some managers may be lucky enough to draw parallels with the chess master, where they can make the correct Fantasy decisions without having to engage in the amount of effort the rest of us do. This may be due to a particular aptitude for the game, a successful strategy or a long history of making and storing these decisions, their outcomes and the relevant evidence in memory.
However, as the bat and ball problem illustrates, we cannot and should not allow our decisions to be made on instinct alone, unchecked by more vigorous examination.
The ways in which we can fall foul of this are often described by means of cognitive biases. These are shortcuts that allow System 2 to opt out and rely on System 1 to make our decisions.
Some of these biases are well-known in the FPL community: recency bias, confirmation bias, the availability heuristic and so on. I would like to explore these in further detail another day, but for now let’s return to the inspiration for this, Joe’s original observation regarding unfairly unfashionable players.
These are players that we often assign to the ‘ignore’ category. This is System 1 taking something that “feels right” and allowing it to make our decisions for us.
The most common faulty assumption that leads to this is price: expensive players are good, inexpensive players are not. While this generally holds true, as players with strong points histories and positive prospects are priced more highly than those without, this is not the case for every player and thus can lead to us missing good opportunities.
Players may have been mis-priced or undergone a significant change in fortunes since they were initially priced. As the season progresses and we move further away from that point, this factor becomes less and less correlated with actual quality. This goes for both selecting a player, eg. Matej Vydra (£4.8m) and Rob Holding (£4.2m), and captaining a player, eg. Jesse Lingard (£6.5m) and Ilkay Gundogan (£5.9m).
The second-most-common of these is holding onto beliefs that were once accurate but have since been proven to be otherwise. First impressions are a big thing and it takes a lot to change them. Paradoxically, once we have then changed these we find it equally hard to adapt again, assuming that because we have now found the ‘correct’ answer, that will continue to hold true.
Patrick Bamford (£6.5m) is a great example of both of these. The Leeds forward had a reputation in the Championship over being poor in front of goal despite a high volume of chances. This was proven accurate by the data and his record. It was not unreasonable to carry this understanding forwards into this season. However, he began the 2020/2021 Premier League campaign with three goals in three matches. This quickly became six in six. The data did not point to this being unreasonable, despite his previous under-performances on the same metrics. Those who identified and adapted fastest to this reaped the best rewards.
However, Bamford now only has four goals in sixteen matches since Gameweek 16. He has accumulated a number of assists in this time, which has helped to keep his points ticking over and perhaps lull those still holding him into believing he has continued his early season threat. Once again, this decline in attacking output has been backed up by the numbers. Leeds have become more defensively solid and less threatening going forwards, with Bamford himself seeing a significant reduction in his previously impressive statistics. As before, those that identified and adapted to this quickly have benefited the most, with Bamford scoring just three goals and delivering two assists in his last ten matches. With improved fixtures from Gameweek 34, could we be due one more shift in his fortunes before the season ends?
It is in these scenarios that we need to engage System 2 and interrogate our System 1-led assumptions, either proving them to be accurate or learning some new information, perhaps a shift in underlying numbers or a tactical switch, that allows us to assess a player in a new light and, eventually, become the chess masters of the FPL world.
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