What are the implications of the words “pinpoint” and “optimal” when market behavior is so uncertain?

In other words, is it possible to find a single decision that will maximize the odds of earning a handsome payoff when the outcome of any decision is uncertain?  In a rather extreme example, in the highly uncertain world of gambling, can I make some decisions that are clearly better than others in light of the uncertainty?

Let’s say that all of a sudden I have the urge to gamble, and head for Monaco.  I don my tuxedo, and enter the Monte Carlo casino, where I see 3 different tables offering 3 different games.  I have €1,000 to spend, but the house has imposed the constraint that I must pick a single table and commit myself to that table for the entire evening.  Now, let’s say that at each one of the 3 tables, the wager amount for a single bet is €10 (admittedly, a far-cry from what I should be prepared to spend at Monte Carlo), which allows me to play 100 games (€1000 total wallet size ÷ €10 per game) at each table.  So, how does the evening unfold?

Since I am not a gambler, I will have to fabricate some numbers to convey the point.  Let’s say that Table A offers a 49% chance of winning, and each win produces €18 (for a gain of €8 based on my €10 bet); Table B offers a 10% chance of winning, and each win produces €85; whilst Table C offers a 32% chance of winning and each win produces €25.  Needless to say, everything is all but certain inside Monte Carlo, and as a rational man I should stay out.  But if I do venture in and wish to risk my money, can I pinpoint the table that will optimize my returns?

To answer this question, I must travel through several centuries of mathematical thought, and invoke the laws of probability.  I know that if I flip a coin a sufficient number of times, I can say with great certainty that 50% of the outcome will be heads, and the other 50% of the time will be tails).  Notice, the key here is that I must flip the coin a “sufficient” number of times.  Due to the vagaries of random chance, a small number of throws may not reveal the true nature of the coin – with just 7 coin tosses it is possible that all 7 times I see heads.  But, with 700 throws, it is quite unlikely that I’ll see 700 heads.  Instead, I’ll probably see close to 350 heads and close to 350 tails.  This conclusion is driven by a theorem known as the Central Limit Theorem, which was originally put forward by the French-born mathematician Abraham de Moivre.  It states that if we know the probability of an outcome from some event (like a coin toss), we will see that outcome occur as often as the probability multiplied by the number of times the event occurs.

In our hypothetical Monte Carlo excursion, the gambling event can occur 100 times (given my €1,000 allowance and €10 per gamble – i.e., per event).  This means I can expect the following (as I hear de Moivre’s voice from centuries past):

Table A: 100 Events x €18 Won per Event x 0.49 Chance of Win per Event = €882 Expected Winnings

Table B: 100 Events x €85 Won per Event x 0.10 Chance of Win per Event = €850 Expected Winnings

Table C: 100 Events x €25 Won per Event x 0.32 Chance of Win per Event = €800 Expected Winnings

With this arithmetic, de Moivre guides us to Table A – indeed, once can say that he has pinpointed Table A for not in spite of the uncertainty, but in light of the uncertainty. Now, it’s important for us to recognize that the power of de Moivre’s insights rest on understanding the uncertainty – i.e., on “quantifying the chance” of an outcome.  Let’s say that Table A is a Roulette Wheel.  As the host spins the Wheel and we all place our bets, it is impossible to state exactly whether or not I will win or whether or where the ball will land.  There are too many factors to humanely consider:

1. The bounciness of the ball
2. The initial rate of spin with which the host turns the wheel
3. The amount of lubrication in the bearings that bind the wheel to the axle
4. The amount of humidity in the room which can slow down the wheel
5. The air currents in the room when the Air Conditioning comes on
6. The initial height from which the ball is dropped onto the wheel
7. Etc, etc, etc.

And even after knowing all of these factors, the equation used to predict the balls final resting position is nonlinear and the solution is going to be chaotic, as shown in the figure above.  We simply cannot predict where the ball will land.  But, there is hope!

We can predict the probability of winning, and we can do so using 2 different methods.  First, we can look at the fact that there are 37 pockets on a European Roulette wheel, and the odds that our ball will land in any pocket is therefore 1/37 = 0.027, which means we have almost a 3% chance of winning.  Alternatively, we can take a sample of all the previous people that have played in the prior 6 months and look at what fraction have won.  This gives us what is known as a “Frequentist Probability”, and can be used within the context of de Moivre’s principles to help guide us to the “optimal table” on which to place our bets.  The discovery of these probabilities is one of the fundamental pursuits of the entire discipline of Econometrics, and has become pivotal to achieving Pricing excellence (further exposition on this important topic can be found in the “Modeler’s Mechanics” of our blogs, and within our white papers).  As shown in the figure to the left, this probability discovery process leans heavily on historical market data (and remember, the past does not provide a definitive glimpse into the future, but does provide a very good glimpse into the probabilities of many different futures), with a heavy dose of computing power to produce predictions that have so far proven to dramatically improve the pricing manager’s decisions when compared to using their human instincts alone.

For instance, companies will often either adopt an Every Day Low Pricing (EDLP) or a High-Low Pricing (HLP) strategy.  The former seeks to keep prices low by achieving enormous economies of scale and tight supply-chain operations, whilst the latter seeks to lower prices to almost unprofitable levels a few times per month for select products in the hope that it will consumer attention and fuel the sales of additional products in the store.  A major problem with HLP strategies is that the momentary dip in price can wreak havoc on demand predictions for not only the low-price product, but for other products that are swept up within the consumer frenzy.  In one of Canada’s largest retailer, we found that their ability to predict demand to within +/-15% of actual demand occurred only 32% of the time.  But, with probabalistic methods and the recent advances of scientific pricing, this same retailer was able to predict demand to within +/- 15% of actual demand about 87% of the time!  Note, we are not pinpointing the demand value here, nor are we optimizing which specific products to invent and stock.  Rather, we are pinpointing a price that will maximize demand and revenue by understanding the probability of the market’s needs.

I believe that in order to respect the important points that several respondents to the “At the Mercy of the Market” blog have raised, it is important for us to be careful and augment words such as “pinpoint” and “optimal” with the phrase “expected returns.”  In a world of uncertainty, predicting the expected results using the Laws of Probability rather than the absolute results using a Crystal Ball is indeed the best we can do.  It is extremely important for us, and all other scientists / modelers, to inform the audience that we are in no way aspiring to peddle a crystal ball.

And then there are those rare occasions where we encounter a street musician whose music soars so high that we are forced to refer to him simply as a “musician,” for using the adjective “street” would be nothing short of a criticism.  About 2 years ago, this is what I encountered at one of Washington D.C.’s busiest Metro (subway) stations during the morning rush hour.  It wasn’t until much later in the day that I discovered the musician in whose masterly hands the violin “sobbed and laughed and sang” was the great virtuoso Josh Bell.  In the middle of the morning rush hour, 1,097 commuters passed by and all heard soul-stirring music at a price of their own choosing that just a few days earlier fetched more than $100 a seat at Boston’s Symphony Hall.  Josh Bell played to a rush hour herd, and demanded no price for priceless music.

His income depended not on the value he provided to those 1,097 passersby, but the overwhelming value he provided – for, if he failed to stir, we listless commuters would feel no compunction to pause and forfeit even a meager fraction of our purse.  And stir he did, with a masterly performance of Bach’s Chaconne from Partita No.2 in D Minor.  Of the almost 2,000 pedestrians that filed by, only 27 gave money for a total of $32.  In other words, for a performance that was described by the Washington Post as “pearls before breakfast,” less than 3% of us offered any payment (for “a man whose talents can command $1,000 a minute”).  Did the service deserve such scant payment, or was there more to the revenue than just the greatness of the service itself.  This is a question that goes right to the root of just how complex the endeavor of pricing can be.

Beyond Josh Bell’s performance and the payment it merited, there is a litany of other factors that affected his earnings power (or pricing power if he were to charge a price).  First and foremost, there were 3 possible locations at which Bell could have positioned himself (see figure below):

1. At a location of high transient pedestrian traffic (between the entrance door to the subway station and the escalator bank that leads to the underground train platform).
2. At a location of stationary traffic waiting for a subway train to arrive (i.e., on the underground platform).
3. At a location where the acoustics of the Metro arcade would create the most perfect sound possible within the subway station.

Of the 3 possible locations, Bell perhaps chose the worst location to generate earnings.  No matter how good his music, rush hour traffic has no time to stop.  It wasn’t their purse that the commuters failed to contribute, but their precious time.

The attributes that govern your power to generate revenue transcend the product itself.  Bell’s performance at the L’Enfant Plaza Metro stop highlights several fundamental truths of pricing science:

1. Could being situated at one of the locations where stationary traffic was high have yielded more revenue?
2. Or, perhaps could being situated at a location where the sound would be even more magnificent have yielded more revenue?
3. What if the perfect acoustic spot had only scant stationary traffic?  Then, sadly, we can surmise his income would be lower even though the quality of the product would be it’s highest.
4. To complicate matters even further, what if Bell chose a different day for his performance?
5. What if he played on a sunny, spring day where spirits are higher instead of a dreary winter morning?
6. What if he played on payday (in the Federal government, payday typically lands on the 2nd and 4th Friday of the month) instead of an arbitrary day?
7. What if Bell advertised with a sign around his neck that he was indeed Josh Bell?
8. What if underneath the sign, Bell posted a requested donation of $5 for his performance?

By not focusing on these questions, and concentrating solely on his music (i.e., the tangible product itself), Bell failed to create a high market price for his product, and earned only $32 dollars from a 43 minute performance that in a proper venue would have earned 6 figures.   All of these factors would have dramatically affected the revenues Bell earned that morning.  But, identifying the 12 square inch box out of the 15,000 square feet of space in which Bell would have obtained maximum revenue (i.e., gotten an “optimal price” for his public performance) is an optimization problem of mind-boggling complexity, and simply cannot be solved without data and quantitative analysis.  After all, the analysis is not just about where Bell should stand to optimally balance sound quality with foot traffic, but also about how this optimal location varies with changes in any of the above 8 questions.  The lessons here are deep, and profoundly shape our responsibilities as pricing managers.

Before you jump to match your competitor’s price, you should recognize the market’s willingness to offer you payment that goes beyond the value of the product itself.  It is important for you to optimize the marketing attributes of the product in order to optimize the price of the product.  You are not at the mercy of the market. Through your actions you can greatly influence the market price of your product. As a pricing manager, you should not just view the setting of price as your only responsibility.  You have access to much data about your market and your previous sales and your customers, which you can leverage to determine the interplay between all of the marketing attributes of the product and the price of the product.  The price you are able to make is inextricably linked to the actions of your marketing managers, your category managers, and your product and sales managers.  And once those actions are executed, you can digest all of your data to pinpoint the optimal price you can charge in the market.  Last but not least, as a pricing manager, you are the final decider of the trade-offs your enterprise should make to maximize immediate earnings and establish a long-term competitive advantage:  Should you play your violin where it sounds the best but generates the least income or do you play it where it sounds the worst but stands to generate the most income because of high foot traffic?  If you do the latter, will those that pay you today have the loyalty to pay you again tomorrow?

So, before you give in to the seduction of lowering your prices to beat your competitors, remember to identify and carefully influence all of the attributes (i.e., don’t just make great music, stand in a great location) that will compel the market to pay you your just reward for the goods and services you provide.  The crux of price optimization is not about touching price at all, but touching all the other things that make a price.

If there is a lot more to purchase, or a lot more stuff that can be incorporated into the products you make, each party in this supply chain needs to have the financial ability to entertain such a large set of choices.  Looking at income growth and inflation alone conceals the true nature of spending power.  It is not as much about whether or not our incomes today are keeping up with the prices of things we bought yesterday. It’s about whether or not our incomes are keeping up with the additional things we can buy. It’s about whether or not manufacturers’ incomes can keep pace with the exploding set of ingredients they can choose to put into their products, and whether distributors can cost-effectively stock and sell an ever-widening mix of products, and so forth.  The rate at which these new things emerge is faster than the rate at which incomes grow – and therein lays the crux of the pricing problem (firm birth data obtained from U.S. Census Bureau and Income data obtained from U.S. Bureau of Labor Statistics):

Even though inflation may be growing at a rate that is in line with wage growth, the burgeoning number of items available to consumers (and perhaps even critical to consumers – just a decade ago there was no anti-bacterial lotion, and yet now you can’t walk 10 feet in a hospital without walking past an anti-bacterial gel dispenser) makes consumers have less spending power.

This spending power is a 2-dimenional thing, but we have tended to focus on only one of those dimensions – i.e., we’ve levied most of our focus on inflation versus income growth, and have not focused as much on product variety versus income growth.  Today, there are many more things to buy both directly and indirectly (for instance, when we purchase a car today that contains twice as many parts as a car from 20 years ago, we are indirectly purchasing “more things”) and this breadth of choice bites deeply into our spending power.

It is not just whether or not the prices of things that we bought 20 years ago have grown in pace with our incomes, its whether or not the sheer number of products and the total global value of those products have kept pace with the total global value of our incomes. And by this measure, spending power has failed to keep pace.  The obvious response as a seller is to flock to everyday low pricing – but, this “obvious” response actually fails to respond to the right problem (which is one of burgeoning product assortment).  Price reductions alone will not bring spending power up to the levels of power we had just a generation ago.  And the problem is only going to worsen, for innovation will continue to accelerate and the diversity of goods and services offered in the global economy will continue to mushroom.

So, what’s a pricing manager to do in the face of this shrinking spending power headwind?  First and foremost, recognize the strong interplay between your marketing efforts and your pricing.  Every dollar invested in marketing will impact the prices that you can charge for every product in every market (or, for B2B vendors, sales & marketing dollars directly impact the prices that you can charge for every product that can be sold to every customer – so, if you have 100,000 customers and 50,000 SKU’s, you have 5 Billion customer-item combinations that you need to understand).  Marketing effectiveness and pricing excellence are joined at the hip, which means that marketing managers and pricing managers must couple their decisions optimally.  This is especially true now because your marketing voice is drowned out each day by more than 3,000 other voices.  The chart below shows the sharp rise in advertising expenditure in the U.S. alone (data obtained from Coen Structured Advertising Dataset):

Secondly, recognize the strong interplay between your product assortment and your pricing.  In the face of ever-widening product choices, being able to identify the right bundles of products for the right customers or customer segments is pivotal to combating ever-narrowing spending power.  Remember, everyone’s Achilles heel in this race to sell is the explosion of assortment mixes.  If the crux of the problem is product assortment, then therein lay the solution.  Identifying which products to co-sell with other products, and what price that entire combination should have for every single customer or within any single market is the key to winning this race.

Instead of each player receiving $1500 at the start of the game, we would each receive $1000 (to reflect the $50 Trillion of wealth that has been lost in the last 18 months), and instead of collecting $200 for passing “Go”, each player would collect only $100 (to reflect the massive wage losses seen in the last 12 months). To further reflect the broader economic climate, no loans were permitted in the game (i.e., players were not allowed to mortgage their properties to receive cash from the bank, nor were players permitted to issue loans to one another). With these altered rules, our goal was to see how purchase behavior and wealth would unfold on this artificial economic landscape. The results were rather eye-opening, and sheds light on the fundamental dynamics of price in a down economy.

One startling feature of the game that remained consistent between “normal rules” and “recession rules” was that the price of any property on the board, or the price of any house/hotel was publicly displayed for all to see. This price conveyed essential market information about the value of “the goods”. Yet, despite the publicly known value of a property, property prices always deviated from the stated value once a buyer wished to purchase the property from a player that already owned it. Moreover, different buyers were prepared to pay different prices for the same exact property and in all cases the offered prices were higher than the stated value of the property (i.e., the price paid by the original buyer). This pattern was held true despite the recessionary conditions that were imposed on the game. There are a few important observations to note here:

1. Different people were prepared to pay different prices for the same good.
2. Those prices were always higher than the stated value of the good.
3. Buying & selling still occurred despite lowered wealth levels.
4. Buying & selling still occurred despite the unavailability of credit (no mortgages were allowed and no player-to-player loans were allowed).

We observe these same characteristics when… Monopoly is played under normal rules – so what was so different about how things turned out in our “recessionary-rules” Monopoly? Well, the first thing to note is that there was no difference at all on these 4 major characteristics of the game. In other words, despite overall lower levels of wealth and the unavailability of credit, we still see that buyers were prepared to pay prices that were above the lowest price stated on property value card and each player was prepared to pay a price different than what other players wanted to pay. Attenuation of wealth and credit did not reduce the price dispersion in this economic system, and in fact revealed that buying behavior did not rest on who provided the lowest prices for which properties. Rather buying behavior, and the prices that transacted, continued to rest on the specific utility or value that each player individually felt they could derive from a given piece of property. Even though the property is the same, each player’s valuation of that property is different (see Graph) – and no amount of wealth erosion or credit crunch could change this fundamental fact of the market.

So, now we come back to what were the differences between what we observed in “recession-rules” versus “normal-rules” Monopoly. First and foremost, purchases took longer. Players waited longer to accrue savings before deciding to purchase any property. Secondly, there was much heavier buyer concentration and interest in trading properties at the low-end of the pricing scale than at the high-end (not too much interest in Boardwalk, but Baltic was hot). Third, there was much more price dispersion for the low-end properties than for the high-end properties in ”recession-rules” Monopoly as opposed to “normal-rules” Monopoly. The key take-away from this is that with many more buyers for the same good, the odds are higher that there will be a broader spectrum of how each buyer values this good and the net result will be a greater dispersion in offer prices. In other words, the market becomes even more segmented for the low-end properties and this gives rise to a wide variation in prices. As a seller holding the property, the question of should I sell now or sell later where a different buyer with a higher valuation comes along is more important for those properties that we can predict will have more price dispersion because of their “average” low price.

Lesson Learned: Look at your prices and your product assortments simultaneously – don’t drop the wrong thing. In other words, don’t drop prices without thinking about dropping your assortments. If you have 10,000 SKU’s, create product bundles and price each bundle optimally and recognize that offering the lowest price in the market does not increase your chances of weathering this economic storm and may in fact lead to self-created demise.

A single price captures everything that makes you special.  It embodies the value the market sees in your product, the value of your product in this particular season, the value your brand wields in the marketplace, the degree to which your product satisfies the needs of specific customer segments, the degree to which buyers are willing to pay for your reputation, the degree to which buyers are loyal to your product despite competing products, etc.

Once you reveal your prices to the world, your competitors instantly know how much brand equity you have, they immediately see how much value your product has in this particular season, they immediately see your reputation is strong, they are able to assess the amount of loyalty you command, and so forth.  By putting your prices out there for all to see, you implicitly give your competitors a leg-up.  To compete against you, all they need to do is see your price and shoot for something just a tad lower.

What would a future world look like where you only… show your prices to your customers and to no one else?  Only those who are committed to buy your product are actually privy to the price, and this price is zealously protected like the Coca-Cola recipe from all of your competitors.

To see this future world, we can actually look to the past and examine yesteryear’s bazaars.  Prices of the day’s harvest did not appear on some store shelf.  Rather, farmer Jack brought his tomatoes to market and as you held his tomato in your hand, you asked him his price.  And once he told you, you inevitably countered with a lower offer.  After some back and forth, you and Jack settled on a price and the transaction closed.  Jack’s competitor – farmer John –sat at the other end of the bazaar and sold his tomatoes in perfect ignorance of the price Jack just charged.  Researchers have found that in such bazaars there is no single optimal price, and indeed, there is very large price variation for the same good (see Figure below from Epstein & Axtell).  This is ferreted out in multiple computer simulations as well, where the basic laws of buying and selling behavior are imposed on artificial buyers & sellers, and over time the prices offered and counter-offered are seen to drift all over the place, but the drift does narrow over time.

Of course, farmer Jack is just as ignorant as John of his competitors’ prices – he has little idea how much farmer John is charging for his tomatoes.  And if you return day after day to purchase your tomatoes from Jack, you build a rapport and a loyalty – this loyalty is reciprocated by Jack.  He holds the best tomatoes for you, he offers you reasonable discounts in exchange for your loyalty, during times of hardship he may have even give you a free tomato.

Meanwhile, John builds up his own loyal following and sets his own set of prices where no two customers get the same price.  Why should they?  After all, no two customers are the same.  No two customers derive the same utility from a tomato.  No two buyers experience the same satisfaction in the conversation they have with John.  By concealing their prices, Jack and John force their customers to negotiate individual prices, and in the process, Jack and John respectively build “micro-markets” of buyers within the larger market of buyers in this medieval bazaar.

So, did our medieval farmers possess greater pricing wisdom than we do today?  They closely guarded their prices, and achieved the marketing holy grail of one-to-one relationships.  Did they know that their prices were a valuable asset, and therefore should be whispered and meticulously haggled with each individual customer?  Or, did history finally catch up with our farmer Jack?  Was there an economic renaissance where Jack awoke one day and realized that if he broadcast his price to the entire bazaar – even at the risk of letting John know his price – and coupled this broadcast with a marketing message that he has the best tomatoes in the market then he could not only serve many more customers per hour (i.e., he no longer had to spend 10 minutes per customer haggling), he can attract customers.

This historical awakening marks the rise of marketing.  The ascent of marketing is deeply entwined with prices becoming uncloaked.  Your prices are indeed an asset.  They are indeed your most valuable intellectual property.  But, it need not be kept secret because the prices you charge, and can charge, are unique to you.  Only you can charge the prices that you are able to charge.  And that is because you occupy a unique position in the marketing sphere.  There are attributes about you that the market holds dear, and your marketing has influenced the market to hold these very attributes with a unique level of dearness.

That uniqueness gives you the ability to charge prices that need not be the lowest in the market – your marketing uniqueness gives us an optimal price that you can scream to the market with a megaphone and not worry about becoming competitively undermined even if your competitor offers the same exact product.  Because of your marketing uniqueness, your competitors cannot replicate your price.

But, the key is that you need to remember that there is indeed an optimal price that you can charge and you must shy away from the temptation to charge the lowest possible price in the market.  You must recognize that your prices and your marketing go hand-in-hand.  The race to capture customers should not be forsaken with a race to the bottom of the barrel pricing.  Your marketing gives you brand equity, it gives you loyalty, it gives you reputation, it exposes many different customers to you– and all of this gives you a certainly ability to charge prices that lie outside the ability of what our competitors can charge.

We have grown beyond our medieval forbears.  Gone are the days of the bazaar where Jack knew all of his customers by name.  Today, we may not know all of our customers by name – but, thanks to the advent of modern pricing technology and deep analytics, we can know our customers better now than ever before in history.  In fact, our data warehouses and our data mining capabilities allow us to know many more customers with much more intimacy than Jack’s comparatively feeble mind could fathom, and we can optimally market ourselves to all of them and we can mathematically determine the best prices to charge and we can do all of this without spending a single breath haggling.

But, to broadcast prices to the world without using modern pricing science would make us more primitive than our medieval forbears, where in the absence of pricing science they at least knew they had to guard their prices.

If you’re going to let your guard down, do so with prices that you know are optimal for you!