Nothing Average about the Average Price

One of the great myths of everyday folk psychology, and one especially relevant to smaller businesses with a more limited range, is the idea that most customers pay the average price for a product or service.  It has a certain intuitive appeal – that’s why it’s the average because most people are paying it. The reality, as any shopkeeper or restaurant waiting team member knows, is that this doesn’t seem to happen very often in practice and the majority of customers seem to consistently be paying either more or less than the average price on a frequent basis, depending what we have on offer. Why is this and how can we manage these discrepancies ito better control margins/sales?

A quick but very basic statistics lesson, grossly over-simplified deliberately to extract the key things we need to know in order to manage prices.  The average, as most people know, is more accurately known as the mean and it is simply the sum of a group of items, divided by the number of items. If we have three sandwiches on offer priced at £1.50, £3.50 and £4.00, then the mean price of a sandwich is £3.00. So far, so good. The mean is a measure of what is called central tendency and it is just one way people look for the middle-of-the-road option, albeit it’s the best known one. The reason most people don’t go for average-priced options very often, aside from the fact that no individual product is often to be found at that price )as in my sandwiches example) is that gravitating towards the mean requires the customer to actually work it out and, in most cases, we don’t.  We simply infer what the average must be from what we see in front of us and make our (often unconscious) evaluation of what we’re willing to pay on the basis of that ‘estimated average’.

As most of my statistics students know to their cost (or boredom), there are two other common measure of central tendency.  One is the mode, or the most common value in a set. Let’s imaging I have five brands of ketchup in stock, with prices of £1.20, £2.50, £2.50, £3.00 and £3.10. The mode here is £2.50 because there are simply more brands at that price than any other price point. Out of interest here, the mean/average price here is £2.46, slightly lower than the mode.  The other measure of central tendency often cited is the median, or the price-in-the-middle if you like. To calculate this, we just arrange the prices in ascending order and literally look for the value in the middle; again it’s £2.50 because this is the third number among five numbers place in ascending order. Now, do either of these get us any further in understanding, and then trying to manage, which option most customers go for?  No, not really, because although the mode and median at least have the advantage of being real prices people could actually go for, unlike my mythical £3.00 sandwich earlier which didn’t exist anyway, neither the mode nor the median predict what most people will go for any more reliably.  So, what are we to do?

As I said earlier, the problem here is that most people don’t work out the average, they just make an assumption of what the average must be on the basis of what they see in front of them. Neither the mode nor the median seem to gives us that, at least on a consistent basis. A neglected measure of central tendency that is really exerting influence here in FMCG buying situations is the mid-range point. Now, I said earlier that customers don’t generally spend time calculating the average – the maths can sometimes be hard and a waste of cognitive effort to do so – but that doesn’t mean they aren’t unconsciously performing other calculations. Experiments of how people mis-calculate averages in psychology have consistently found that the mid-range is being calculated by the brain, even though most of the time we aren’t even aware of it.

The range in statistics is simply the difference between the most expensive item and the least expensive one. If my most expensive sandwich is £6.00 and my least expensive one is just £1.00, then the range in terms of my sandwiches is £5.00.  Turns out that what most customers do without even knowing it is to base their decision on half this value, the mid-range value in statistical terms. In other words, if you ask a customer leaving my shop what the average price of a sandwich was, a significant majority will “guess” that it is £2.50 (half of £5.00). Sometimes this is the same as the mean, the mode or the median, often it is not.  The two important things to note here are that the mid-range will be given by an overwhelming majority of my customers as their estimates of the average and, crucially, it is based on only two pieces of data – the highest price and the lowest price, all of the ones in between and the number of brands to choose from being completely irrelevant,  Ok, so if we want to forecast what ‘average’ our customers are working to, then the mid-range is the best option to go for.  Ah, but how do I then manage that so they go for the option I want to promote? How can I use that knowledge to promote particular products or brands?

People have an in-built tendency to simplify information and, in particular, to go for two options; high and low. This is called the binary bias in psychology and we can think of it as the customer unconsciously sorting brands into the “cheap ones” and the “dear ones”.  They do this sorting on the basis of the mid-range and, on the whole, they will go for either the least-expensive or more-expensive cut-off point depending on the skew (or imbalance) in the number of items in that cheap/dear category.

Let’s take a simple example. Sticking with sandwiches, let us go back to my original example and imagine I have more options available; £1.00, £1.00, £1.20, £2.00, £2.25, £2.50, £3.10, £3.10, £3.10, £3.95 and a premium offer at £6.25. On the basis of the mid-range and binary bias combined. most of my customers here would actually buy the £2.50 option. Why? Because the mid-range is about £2.63 and there are more options below that mid-range (five differently priced items) than there are above it (three prices). The number of different options available at a price is irrelevant, so this is different to relying on the media, it’s the number of prices that really matters. Although there will always be customers who are the occasional exception, this works most of the time and is way more reliable a predictor of the best-selling option than any other central tendency route!

How can I use this now to promote a particular sandwich option? Suppose I want to sell more of the £3.10 sandwiches. That’s easy, just increase the mid-range value to above £3.10 and make sure I have more price options available below it than above.  For instance, I might carry a very small number of super-premium sandwiches at £7.50, which would move the mid-range to £3.25. As there would still be more price options below £3.25 (a total of six now) then there were above it (a total of three including the new super-premium one), this tactic would work. Most customers would go for the £3.10 one because of our natural tendency to gravitate to the mid point and go for the category (cheap/dear) with the most “choice”.

And of course the same would work in reverse. I might want to really push that £2.25 option because, despite its price, it has the highest profit margin. An easy way to achieve that would be to do reduce my premium offer from £6.25 to £5.55 (moving my mid-range value to about £2.27) and put my £2.50 option up to £3.10 too, thus ensuring there were less price options available above £2.27 (i.e. now there’s just £3.10, £3.95 and £5.55) than there were below it (£1.00, £1.20, £2.00 and £2.25).

So there we go… the key take-aways here… Our customers don’t work on averages when deciding what to buy, just their unconscious perceptions of what they assume the average to be. The real value they gravitate towards is simply half of the mid-range. Left to their own devices, they will go for the option just above or below that point. To manage which option they go for, however, we need to exploit the binary bias too.  In other words, we need to make sure that the mid-range is where we want it to be and that we make sure that there are more options to choose from below that mid-range value than there are above it.  Simple, really 🙂

The Variety Paradox

As a small convenience retailer myself many years ago, one of the most difficult decisions I ever had to face was how many varieties of a product I should stock. It’s by no means an easy decision.  My logic was always that I needed to keep a big enough range so as not to appear to have too limited a choice available, particularly in comparison to the Waitrose store a couple of streets away, while at the same time not overloading my little shop with a stock range that was costly in both financial and spatial terms.  Tricky problem!  Turns out, however, that my logic at the time was fundamentally flawed when you consider the human brain.

Years later, after a roundabout journey into academia, I found myself particularly irritated one morning while at a conference in Chicago.  It wasn’t the conference itself that was the cause of my irritation but, rather, the untimely interruption of a guest speaker for the conference organisers to announce the death of Margaret Thatcher.  Much disruption subsequently followed and everyone insisted that there was a break in proceedings for British guests to digest the news. Has to be said there were only two of us from the UK among hundreds attending anyway, and neither of us were particularly bothered one way or the other (sorry!), but the real issue for me was that the speaker who ended up being curtailed was the one person I’d actually gone to the conference specifically to hear!

That speaker was Colombia’s very own Sheena Iyengar, author of the best-selling book The Art of Choosing.  In my view, Sheena is one of the best experimental psychologists ever, her work being both meticulously and creatively designed to a level of elegance most of us can only ever aspire to – an even greater achievement when one consider’s Sheena is also blind.  Her most famous experiment, perhaps, identifies what has come to be known as “the six jams rule” or, to give it its correct academic title, the Choice Paradox.  In this particular series of experiments, which I am grossly oversimplifying here, Sheena demonstrated that too much choice is a very bad thing, especially for the retailer pressed for space.  When presented with displays containing 24 varieties of jam, only 3% of participants in the study actually bought anything, while reducing the display to a mere 6 varieties increased sales ten-fold.  So what’s going on here and why were my assumptions all those years earlier so wrong?

The brain is a fantastic information-processing machine, a biological computer capable of handling extremely complex tasks.  It is also an inherently “lazy” computer too, however, as it consistently attempts to perform routine decisions (such as buying a jar of jam) at an unconscious level in order to conserve information-processing capacity for more important things, such as finding lunch while avoiding becoming someone else’s lunch. A large selection of jams on a shelf takes far more processing in order to make a choice than one containing a smaller array of options, so provided there is at least some choice open to us then we are far more likely to buy if there is a more restricted range.  And, over the course of her studies, Sheena concluded that six varieties of jam was the optimal range-size to go for, a range that works equally well for many many other FMCG products.  Moreover, the context the display is placed in also has a strong moderating effect, the six jams rule being even more effective in smaller retail outlets.

If we think about it, the Choice Paradox also goes some way to explaining the success of discount retailers such as Lidl and Aldi, all of which typically stock a considerably smaller range. Now, while it would be foolish to suggest here that price is not the key determining factor, it clearly is and comes out as the main reason for frequenting a discount store in survey after survey.  Nevertheless, my own work has found that the second biggest reason for choosing say a Lidl over a Tesco is the perceived saving in time.  Consumers report saving this as much as they do money and this is easily confirmed by observational studies of actual time-in-store.  Put another way, the lower prices bring a direct financial benefit to the consumer, while the effects of the Choice Paradox allows us to make quicker decisions from a more limited range and save valuable time too.

In my view, the Choice Paradox is an even more helpful a psychological advantage for the local c-store than it is for the discount retailers. Time is prized more than money by some, and almost as much as money by others, meaning the on-the-doorstep location combined with the more “limited” (for which substitute “optimal”) range is potentially a very under-exploited source of competitive advantage for the canny local shopkeeper using behavioural science to get his/her stockholdings right!

When Ads Rhyme, Sales Climb!

Ever noticed how the slogans that work best tend to be short and sweet?  Every little helps has been one of the most successful tagline in Tesco history, for instance, while Because you’re worth it has certainly stood the test of time for L’Oreal.  Notice too that many of these also tend to rhyme.  For those of us of a certain age, it’s definitely the case that Beanz Meanz Heinz while we’ve needed little reminding of late that Coughs and sneezes spread diseases.  There are very good reasons why these simple slogans stick with us for years and why those that wax lyrical tend to stimulate the most extra sales.

It’s all to do with the way the brain processes information.  We have evolved to favour quick-and-dirty ways of acquiring and retaining useful details about the world around us and for very good survival-related reasons.  The brain is a wonderful computer but, like any other computer, it has a finite process capacity.  Monitoring a harsh complex environment, full of natural predators and man-made perils, is a heavy-duty task for the brain to perform, one that requires a considerable amount of available processing capacity.  So, to ease the cognitive load, our brains undertake a lot of this processing at an unconscious level, freeing capacity for more important things.

The key to maximising this unconscious processing ability is to rely on a phenomenon psychologists call cognitive fluency.  This simply means paying particular attention to information that is short-and-to-the-point and is easy to both understand and, if necessary, recall from memory at a later date.  Short catchy phrases achieve fluency very well, while those that rhyme do so considerably better still.  And it’s not just about ease of acquiring and/or recalling relevant information either.  A number of studies over the past twenty years have found that the extent to which we view information as being credible is also a function of processing fluency.  In other words, where a product or brand has a catchy tagline – and even more so when that tagline rhymes – we actually believe the information to be more credible and accurate, increasing the likelihood we will buy that product/brand.

So, next time you are drafting an ad or simply creating some quick point-of-sale materials, remember the golden rule of cognitive fluency if you want to maximise sales: When Ads Rhyme, Sales Climb!

Too Many Rabbits from Hats?

Behavioural economics is an important area of decision science, but I can’t help thinking sometimes that advocates rely a little too much on cheap psychological conjuring tricks for their own good and this masks the really crucial aspects that are of most use to marketers and, indeed, to society as a whole. It’s very easy to demonstrate that supposedly irrational consumers will be fooled by an offer such as “30p each, or 3 for £1”, for instance, or that supposedly smart people can’t work out the price of a train ticket if you tell them it was “£10 more than a cup of coffee” and say £11 was the total amount spent.

These examples are amusing, but the underlying message is lost as behavioural economists – and indeed behavioural scientists generally – rely on these tricks a little too much when trying to get the audience or readers’ attention. The literature on heuristics and biases, of which these are particularly good examples, appears especially prone to this “look at me, i’m smart and funny” effect. Heuristics are cognitive rules of thumb, followed by all of us unconsciously in order to save the brain’s limited information-processing capacity for more important conscious things.

The “3 for £1” effect is a good example, falling into that particular group of heuristics that help us deal with situations where there is too much information and so we just extract one or two fragments without thinking and base our judgment on those. I actually did this trick myself for real many years ago when, long before I was an academic and I had a proper job running convenience store. I sold chart singles, for those old enough to remember music being bought that way. The margins were good, about 29p to me and retailing for 99p, but they had a limited shelf-life and became almost worthless when the track in question fell out of the Top Twenty. To recoup my costs and minimise losses, I’d then reduce them to 30p to get rid of the damn things. Usually worked, but one weekend they just weren’t selling and, more as a joke than anything else, I let a bright schoolgirl called Dawn who worked in my shop on Saturdays amend the display sign to add the quirky “or 3 for £1” tagline and we were both astonished to see sales shoot up and our Kensington customers buying rubbish 80s tracks in multiples of three! Yes, as you can tell, my hero at the time was Arkwright from the BBC’s hit Open All Hours, but this was in many ways the start of my own interest in decision-making.

“Dawn’s Deal” as I now like to call it worked because we don’t process all of the information here. We are so used to the fact that “3-for-whatever” always works out cheaper that we don’t actually read the entire sentence. We process the first bit, assume it’s a special offer, and buy three singles instead of just one or two if chart music is our thing. In reality of cause, most customers weren’t fooled by this at all – many just stopped and had a good laugh – but enough were to help us clear the surplus stock.

The key point here is the fact that most customers were not fooled at all. We sometimes find these tricks amusing by focusing only on the exceptions, rather than on the rules themselves. Heuristics are generally very effective in everyday life. As Herb Simon rightly pointed out, they help us to make judgments that most of time “satisfice” (or make do) and they work mostof the time because, to labour my own example, it’s usually the case that “3 for £N” does work out cheaper and we save money. Most of the time is not allof the time, however, and so we can make the occasional error from time to time that (at least when it comes to buying a record) is no big deal. It just gives an otherwise dull behavioural economist something to joke about!

Now, I really love Dan Ariely and have a tremendous respect for his work, but this tendency to focus on the amusing exceptions, rather than on the vast majority of cases where relying on heuristics is beneficial, was undoubtedly amplified by the success of his book Predictably Irrational. It’s an important work, it certainly introduced behavioural economics to a whole new audience, but it has had the unfortunate effect of making many associate work on heuristics with the dumb choices we make, when we should be focusing on the smart ones more. Whole research agendas have subsequently been fashioned around this whole notion of irrationality (which as an evolutionary psychologist, i’d dispute anyway at times) and so important research on successful/optimal applications of heuristics is harder to find and, when it is undertaken, it’s often overlooked as having nothing important (for which read “funny”) to say.

Let’s close with one really good example of what I mean, published in the latest issue of Cognitive Research by Min Zheng and her colleagues over in New York. This particular paper focuses on the important issue of healthy eating and the potential effects, both good and bad, of social pressure on our ability to do that. In a very well-designed series of experiments, the authors tested the extent to which the amount of information we have available effect the degree to which we understand causal relationships between diet and potential health consequences. Around 1800 people participated in these experiments, divided into groups who received varying amounts of information about Type Two Diabetes and the various factors (e.g. diet, exercise, etc.) that may contribute to its onset or exacerbate it. Whether presented in text-based or visual form, it turns out that the ability to accurately judge whether someone was at risk of developing the condition actually declined as the provision of information increased. In fact, a much better predictor of whether an individual participant could accurately predict risk was whether they themselves personally knew someone with diabetes.

Several heuristics were at wrk here, I guess, but the most important was probably the Availability Heuristic: the extent to which we unconsciously make judgments on the basis of recent experiences of something similar that are less-effortful to recall. Now, when discussing the Availability Heuristic, it’s very easy to joke about how look-a-like brands in Aldi often fool us because of their close resemblance to ones we are very familiar with, which are the exceptions, or even the potentially more serious issue of medical misdiagnoses which are more likely when a doctor has seen a number of patients with symptoms similar to our own. The example of the Zhang et al experiments, however, is a good reminder that most of the time the good old Availability Heuristic actually gets things right!

So where does this leave us? Well, at the time of writing, we are in the midst of a global pandemic and the rest of the world is trying to figure out if the seemingly quirky strategy of the UK Government to base its response on behavioural economics is a good or bad thing. My answer to that is to think about what sort of behavioural economics is informing this strategy – a one that focuses on the science behind when heuristics get things right, or a behavioural economics that’s more informed by psychological conjuring tricks such as my “3 for £1” tactics.

Time will tell, I guess, but there is clearly a need for decision scientists to focus on the more serious business of heuristics – the instances in which they are reliable aids to judgment – than on the relatively rarer exceptions to the rule that simply have greater comedy value.

My message: whether you are trying to stop the spread of a deadly virus or just wanting to sell more cheese, remember the beneficial effects of heuristics that usually serve us well and research those properly, rather than on the seemingly irrational effects of my own Arkwright moment. Put another way, let’s stop pulling rabbits out of hats and just make do with the Easter Bunny!

Memory and the Morning After

hangoverSomething about New Year’s Day that makes many psychologists feel obliged to have an alcohol-related post. Perhaps it’s because the subject is topical, and so the post is more likely to be read, or maybe it’s just that psychologists themselves are experiencing that heavy-headed feeling and are looking for a reason to rationalise their own self-indulgence.  Who knows!  Oh well, if you can’t beat them…

Some readers will undoubtedly be experiencing one or two hazy memories today.  The “did I really do that” effect or the “what happened after 1am” phenomenon, perhaps?  By far the most common case of alcohol amnesia is the inability to accurately recall someone’s face, apparently. Ever woke up with someone’s phone number – maybe someone you seem to recollect being quite “hot” at the time it was written – but find yourself now unable to remember anything more that the fact that (s)he had very red hair and was dressed in black?  More frequent an occurrence than we might think!

Turns out there’s a very good cognitive explanation for this sudden facial amnesia, according to a recent paper by Harvey and Tomlinson in the Journal of Psychopharmacology.  In an interesting series of experiments involving student volunteers – who proved surprisingly willing to indulge themselves with alcohol – the authors found that something strange happens to the way we process and store information about others as intoxication takes hold.  Specifically, whereas the brain normally processes information about other people in a very holistic way, identifying defining facial feature or mannerisms, for instance, as well as more external details such as the size of a person’s ears or the colour of their hair, it appears that alcohol intoxication diverts attention to the latter characteristics only.  Put another way, the more we’ve had to drink, the more likely it is that we will ignore harder-to-process information like the colour of someone’s eyes or the length or their nose, our lazy brains instead simply referencing them by the colour and length of their hair (or indeed its absence!).  The result – we remember the shape of the head and its framing by the hair, but very little else.

So there we are… a nice straightforward explanation for often-temporary facial recall problems.  There’s a serious side to this, of course – Harvey and Tomlinson’s findings have important implications for eye-witness testimony when the victim or witness to a crime are under the influence of alcohol.  But for this New Year’s Day post, it perhaps also explains why those of you who are single (or maybe not!) are unable to quite remember why that guy/girl you apparently spent so much time talking to you last night seemed to be the one of your dreams!  Never mind, better luck next (or I guess this) year…