Numbers That Numb – The Amazing Maze

Numbers That Numb – The Amazing Maze
June 21, 2013 Tony Mckenna (Macattack)

By TTT subscriber Anthony McKenna. 

Take a dice; take countless die; place in washing machine; hit fast spin. Watch the swirl of tumbling complexity. Sit down, or at least stand back. Try to make sense of the bombardment. Seek sequences, see patterns. Analyse, rationalise, seek truth, fathom falsehoods. Think logarithimically, think linearly, err greatly. Assess, appraise, be aghast. Be amazed.

It gets worse: the faces of the die are not conventionally dotted from 1 to 6, but different number formats, sometimes of several digits, catching your eye. Fractions, percentages, decimals, integers, odds and evens, round numbers, square roots – a numerical plague of biblical proportion. Amidst the maelstrom, fail to make sense; defer to emotions; make nonsensical conclusions.

Numbers are, in short, mind-numbing – an invitation to embark on a tortuous traverse through a maze. Successful orientation is compounded by the sheer volume of numerical data, and the volume is exploding.  It’s like opening the door to your back garden to be greeted by the Savannah – mowing the lawn will take an age.

And if the task is epic, it is further compounded by our limitations in terms of understanding numbers and utilising them to understand the Beautiful Game. Emotions do get in the way of our willingness to embrace numbers. Even if you possess a Black Belt in Sudoku, there are still problems … it’s all in the mind.

The Tortoise & The Hare

The Statistician’s biggest challenge is the strangled bias of human emotion; opinion takes centre stage long before Statistics accrue to the point of reasonable sample sizes. Emotions are the Hare, Statistics the tortoise. The tortoise may outpace in the longer term, but emotions, and the expression of such, have the advantage of immediacy and social visibility. Numbers, conversely, are garnered incrementally: slow burn undercurrents that must, by definition, concede the floor to the swifter impact of subjective gut debate … at least for some time.  Then something breaks.

On January 3rd and June 3rd respectively, elite and esteemed TTT Statisticians Andrew Beasley and Dan Kennett became active, once more carpet bombing the Social Media. Twitter was on red emotional alert.

Tweets by Andrew Beasley (3.1.13):

“Cole… 2 Goals 1 Assist… Total 3… Mins Played 794… Mins per Goal or Assist 264.97”

“Bale…7 Goals, 1 Assist…Total 8…Mins Played 2451…Mins per Goal or Assist…306.28”

Tweets by Dan Kennett (3.6.13):

“Downing Chances Created: 14 in 633 mins v teams above (2 per game), 51 in 1561 mins v teams below (2.9 per game)”

“Downing Chances Created: 57 in 1721 mins (3 per game) since Fulham (end of LB experiment brought back into team), 8 in 473 mins before”

You go to buy a jacket. You see one you like.  You happen to be in a rush and, in your haste, your reliance on a guestimate will do. You choose a jacket that seems approximate to your size. Later, you will try it on.

But for now, re-read the tweets by two of TTT’s finest. If you have not seen them before, or the reaction to them, absorb and assess. Do the tweets fit? One set of tweets addresses numbers contrasting Goals and Assists for two different players, the other set indicates the creativity output of another player.  What unites each set is that they depict LFC players in a positive light; players whom populist opinion had already condemned.

Bridging The Gap

Dyscalculia is the overlooked twin of the more mentioned dyslexia, though not an identical twin so to speak. Where the latter denotes a problem with words, the former is about problems with numbers – and it may surprise some that there is such a word. I am not a Statistician or an Analyst, nor do I have a gifted mathematical mind. There was a time when I thought I may be affected by Dyscalculia, such was my struggle with numbers. Fortunately, this is not the case.

As we shall see, however, even without such a diagnosis, the mind’s grasp of statistics and numbers is still challengingly obfuscated by its own limitations. Emotion becomes King; it is easier. A refusal to abdicate is premised on strength of feeling and preference for a short cut – why take a longer route?

But perception is altered, disturbingly so. Emotions are the spectacles through which we look at mirrors, the type of mirrors in Fair Ground Fun Halls. What we see, judge and assess can be filtered as a distortion of reality. Someone put hallucinogenic illusions in your coffee, even if it tastes good.

As I am neither a Statistician nor an Analyst but a mere ‘thinker’, I realise that I must wrestle with the numbers. Football has changed in terms of how the game is being interpreted and understood. I must explore the literature; how my mind works in reaction (or may not work appropriately), and why the numbers can be so confusing at times. Here, I share that journey, and what I have learnt; maybe, erringly so. But how I used to watch football will no longer suffice. I need to run with the revolution before it turns too fast.

That revolution has served me well so far; a discovery of many Rumsfield’s ‘Unknown Unknowns’ has been attained. All those years ago, how incredible would be the idea that shots outside the box hardly lead to goals, that corners are over-rated, that Final Third Regains matter.  But there is much more to be discovered. For this, we need to bridge the gap between those who are accomplished ‘Numbers’ guys and those who are not. Lay people like me need to understand that we enter a maze where obstacles abound.

Reasons To Be Careful: Parts 1,2 & 3

Part 1

Numbers, in evolutionary terms, are quite new. Possibly about 10,000 years old, writes Bellos. (Alex’s Adventures In NumberLand). But the author points to a more fascinating and quite astonishing fact. The way we appraise numbers, or quantity, is not entirely reflective of our intuitive equipment; an influence of culture has overwritten our natural inclination. Over 10,000 years ago, before numbers, we utilised our logarithmic instinct to appraise quantity. This is our more natural propensity, yet education systems teach us to understand numbers in more linear fashion; as evenly spaced numbers on a ruler for instance.

This has been demonstrated experimentally. Pre-school children in Western Cultures, before formal education intervenes, share the trait of cultures where no number words or symbols exist: they appraise ratios between amounts.  For example, shown a series of pictures depicting dots 1 to 10, they:

“…see that five dots are five times bigger than one dot, but ten dots are only twice as big as five dots.”(Bellos: Alex’s Adventures In NumberLand).

Conversely, we, as adults, have been westernised to place the numbers sequentially as 1;2;3;4;5 etc.  They become evenly spaced. That said, apparently we do still apply the more intuitive logarithmic approach, particularly when we digest huge numbers (or try to digest as the case may be). We think of them as closer together. We can, for example, tend to equate all Premier League players as being paid ‘huge amounts of money’. But there are significant differences in individual cases; ‘huge amounts of money’ implies the same thing.  Here, we are quantifying amounts with approximations.  Something we would not do to reflect the amount of goals in a football match; a 3 v 1 final score, for instance, is easily understood and untainted by the need for approximation.

This was news. Whilst we have a Language Instinct – born into the world with innate faculties that predispose us towards the way we use and understand the language of words – our minds are not inherently equipped for dealing with amounts the way we do; rather that cultural influences have bent the mind to work in this direction. Worse still, and specifically addressing statistics, our minds do not deal with such entities too easily.

Part 2

“Why is it so difficult for us to think statistically? We easily think associatively, we think metaphorically, we think causally, but statistics requires thinking about many things at once, which is something that System 1 is not designed to do.” (Thinking Fast and Slow: Daniel Kahneman).

Kahneman depicts System 1 and System 2 as personality traits of two distinctively different protagonists in our minds; they are fictional metaphors to help illustrate the different mental tasks we need to perform. System 1 is effortless, reactive and fast-thinking, being intuitive by design. System 2 deals with much slower type of thought processes; this approach, being more deliberate, is damn hard work!

Unfortunately, System 1 bears more influence on our judgement than we bargain for; snap assessments may be useful in many areas of our lives; but not when absorbing statistics it seems.

Preferably, we would like to see our own assessments as indicative of the methodological, slow and careful thinking of System 2; it makes us appear more clever and thoughtful. But this is not always the case; emotions get obstructively in the way. Most times, we will not even see our own transgressions, believing that we are, in fact, prudent and wise.

If in a Maze and you hit a brick wall, turn back; eliminate this blind alley to avoid future calamity. Think; but think slowly. That means take time to listen to System 2. It’s that easy?… No! Often System 2 will take its lead from System 1; there is a tension between the two. We all possess the Yin and Yan of a Janus face; one is outwardly looking in an instant; its swiftness obstructs the other that needs to look in, more methodically.  But this is not all.

Part 3

We possess yet another regrettable biological trait. It is an inclination for the truth of sorts, but not a wholesome one.  We talk about a hindsight bias; but bias can look anywhere, by any means necessary – because self-validation will always commit the vanity sin it is biologically driven to do.

“It seems we have an innate tendency to seek out and overvalue evidence that confirms a given hypothesis”.  (Bad Science: Ben Goldacre).

Any scheme will do? Personally, I would add the following: we also may seem motivated to disregard – or deliberately not seek out – evidence that is contrary to the belief system we hold dear.

We can also be selective with evidence that offers comfort in justifying losing a player. I wonder if this is why we embrace the Stats that tell us LFC win more frequently when Suarez is not playing? This sanctions the notion that his departure will not hurt us greatly.  Yet we do not apply the opposite analysis.

We won more frequently when Carroll did play: he is leaving without too much protest from the fan base. But of course, we paid over the odds for him, and we are prejudiced by that number: £35 million! So, he will not ‘fit Rodgers system’, we say; there, it’s done; sorted, rationalised. Ditto for Carragher; ha … tiki-taka? No chance; but go and seek out his passing stats for last season.

How do we know a component will not fit a system until we try it? Too late; emotional assessment has already suffocated attention to the irrational outcome of the Carroll solution. Take a loss, take a mighty loss, get stung again.

Hearts & Minds

Downing is shit; shits out of tackles; he’s just f***ing shit … and shit sticks. This is analysis … to some people anyway.  Laughingly bereft of an ‘Assist’ for such a long time, the jokes came thick and fast. But people ignored the other Stats; emotions became the isolated tools of analysis, and imperfect tools at that.

This was the season when LFC not only hit the woodwork a record number of times, but were sorely struggling to convert chances in general. Downing, however, had met his own remit; tackling was not one of those requirements, that is a red herring. Or else go and judge Reina on how many goals he scores.

Ultimately, Downing delivered the goods his role demanded: creating chances.  If the Chef prepares a good meal on a plate, is it his fault that the diners failed to devour the delicacy?  It’s a team game, remember? … or, at least, remember when Lucas also used to be shit.

These things matter. Do we want to sell ‘bad’ players who are actually contributing to the cause? We want LFC to progress; our emotional apparatus may thwart progress if we allow it to bully our assessments. The soul search for every fan is the truth; but we are not biologically cut for the task of impartiality.  Our opinions are already cloaked in the emotional and psychological uniform we choose to wear; the constraints of the strait jacket are difficult to remove.

Recognition of this weakness should be an almighty strength, the acknowledgement that our navigation equipment is faulty will enable us not to trust it implicitly and foster caution. We need to take a slower amble through the maze and via other means. Advice from others holds value; other people have already taken a slower, deeper consideration of the route.  Those people are Statisticians and Analysts; embrace them.

Shock & Awe

A closed mind becomes an empty mind. But the dial has been set; hearts and minds have been won.  Emotions have a lockjaw hold; assessments have been made without realisation that the evidence is flawed; now the world is flat. Should anyone try to talk a different walk?  Should anyone tweet anything that remotely depicts Joe Cole and Stewart Downing in a positive light? The car crash of cognitive dissonance looms.

It’s shock and awe. What? That can’t be right; Joe Cole and Stewart Downing? A flurry of tweets in response and the debates are launched; counter-attacks of consternation rail for the truth. People are trapped on the stickiness of emotional flypaper, unable to wriggle free. Rejoinders to the tweets, usually beginning with ‘but’, reach a general consensus: this is not what they see!

But I understand why. As Goldacre (Bad Science) warns: we place an over-confidence in our own assessments. Remember that jacket you bought in a rush? You now try it on, bewildered to find that it actually doesn’t fit.  How could your judgement be so wrong? So close, so upfront, so easy really – or, at least, it should have been.

Your judgement, using no guide other than the human brain, was fallible. If your cranial apparatus failed to measure, accurately, with regard to the mundane task of buying a jacket, how will it fare in the evaluation of more complex undertakings? With an imperfect view, at such a distance, the odds are never in your favour.

A Room With A View

So what do people actually see when watching football? The Armchair supporter, a much-maligned figure of the past, is now the most important consumer of the game; otherwise why would Sky pay so much for T.V. rights?  Obviously, more people watch the game at home, or in a pub, than those housed in the stadia, and there is nothing wrong with that.

But think about the view all scenarios entail, even in a stadium: the singular angle at your disposal, the obstructions, the distractions. It is a limited view, obscured and corrupted, beyond perfect reach. Furthermore, you absorb emotionally, not rationally, and your human mind, without question, is unable to count the frequency of passing percentages, chances created, clear-cut chances etc. This now sounds like a ridiculous statement.

Is this not what most people, however, actually do?  Opinions take root without counting the things that might count.  Yet the collation of such metrics requires the painstaking slow process of detection; the work that Statisticians and Analysts do; the stuff of Kahneman’s System 2.  We watch football using System 1, our emotional hard drive. It lets us down constantly. You could be wrong! Is it wise to run amok in the Maze?

Where application of considerable thought, time, study and diligence has taken place, how is it feasible to question this with – on the spot – emotional knee jerk reaction?  Your Doctor makes a diagnosis; would you tell them: “hey, this isn’t right?” Or put it another way, as Dan Kennett tweets with captive aptness, humour and ironic twist:

“If Stewart #Downing creates a high quality chance in front of 45,000 people does it actually exist? #zen” (Tweet by Dan Kennett 3.6.13)


Neither Andrew Beasley nor Dan Kennett arrived at their respective Stats as defences of Cole or Downing; in fact, if I recall rightly, they both expressed surprise at their findings. I am not trying to defend Cole or Downing either; rather the core principle invovled – that if numbers ever run at a tangent to your emotional expectation, then we must learn to question our emotions first; then the numbers; then everything else.

Stats alone are not enough – good Statisticians acknowledge that. Debating them is also fine, but it is the immediate emotional assumption of their wrongfulness that is not, just because they do not sanction the belief system you have formulated.

I mentioned ‘everything else’.  That ‘everything else’ includes the role of chance, randomness and luck.  Those whose mantra is ‘nah don’t do Stats’ – not quite the McDonalds ‘nah you’re all right’, but close – will surely have a more difficult job accepting the incidence of chance and luck in the Beautiful Game. But those entities are now taking a serious hold within the Football debate.

Recall our season of record woodwork hits; that, and our failure to convert more chances, was rationalised by some as the players not ‘being clinical enough’; or simply, ‘not good enough’.  Try, at least, to broaden your assessments to incorporate this:

“And so, after all those hours and hours of watching goals, how many did Lames and his team qualify as fortunate, as owing more than a little to luck? The answer is 44.4 per cent, though that varied a little from league to league and competition to competition.” (The Numbers Game: Anderson/Sally).

How blasphemous! That’s practically half! How terrible for those to have to relinquish control when the need is to be in control! Yet, luck is a deity which even the atheists crave: “hope I get lucky”; “I need a bit of luck”; “wish me luck”. It is buried deep in our psyche, and it takes place on a football field. Take time, also, to reflect on how we have fared in the Debatable Decisions Tables over the last couple or so seasons.

Again, as with Stats, the presence of Luck is not to throw all hope at it. Anderson and Sally point firmly to budget, training and optimising the use of players at your disposal etc.  Black Swans and randomness, however, do warrant consideration in the whole scheme of things; a significant part in fact. But as with Stats, wise people know these entities are not the only things where to dip your brush – on football’s humungous palette – to paint a picture. Refusal to engage with any one of these, however, may render your picture incomplete.

Luck, incidentally, takes place off the field too. If it makes you feel better, call it Sturridge: a player tossed between a couple of billionaire Football Club owners, now he is ours. Call it Coutinho – what were Milan thinking of? But, thank you … always.

Journey’s End (for now)

If in a Maze and you hit a brick wall, turn back; eliminate this blind alley.  I’m still in the Maze, but slowly finding my way around the terrain. It’s the Savannah after all.

My grasp of numbers, no doubt, will continue to err; but knowing that the human mind is an imperfect tool – regarding their comprehension and employ – is a start at least.  I can resist the temptation for my emotions to paint the picture single-handedly. I can take numbers, and all the other variables, inherent in the Beautiful Game, including Black Swans, and maybe get closer to the truth.

Mind you, it is exhausting; sometimes you need to take a break from the journey.  Time to hit the ‘Stop’ button on that washing machine; let the die settle until the numbers disappear … close the door to your back garden … mow a bit more of the lawn later … it’s been emotional.

“To be “at sixes and sevens” is a British English idiom used to describe a state of confusion or disarray.”  (Wikipedia)