Saturday, April 19, 2008


"Just ninetynine-ninetynine!" is what they tell me every time I fail to switch the radio station fast enough, is what they print in the ads, is what the shout in the commercials.

When I was about six years old or so, I recall I asked my mom why all prices end with a ninetynine. Because they want you to believe it's cheaper than it is, I was explained. If they print 1.99 it's actually 2, but they hope you'll be fooled and think it's "only" one-something.

I found that a good explanation when I was six, but twentyfive years later I wonder if even six year's old know that can it be a plausible reason? Why keep stores on doing that? Do they really think customers are that stupid? Or has it just become a convention?

Now coincidentally, I recently came across this paper

via Only Human. The study presented in this paper examines the influence of a given 'anchor' price on the 'adjusted' price that people believe to be the actual worth of an object if the only thing they know is the adjusted price is lower than the retail price. A typical question they used in experiments with graduate students sounds like this

"Imagine that you have just earned your first paycheck as a highly paid executive. As a result, you want to reward yourself by buying a large-screen, high-definition plasma TV [...] If you were to guess the plasma TV’s actual cost to the retailer (i.e., how much the store bought it for), what would it be? Because this is your first purchase of a plasma TV, you have very little information with which to base your estimate. All you know is that it should cost less than the retail price of $5,000/$4,988/$5,012. Guess the product’s actual cost. This electronics store is known to offer a fair price [...]"

Where the question had one of the three anchor prices for different sample groups: a rounded anchor (here $5,000), a precise 'under anchor' slightly below the rounded anchor, and a precise 'over anchor' slightly above the rounded anchor. Now the interesting outcome of their experiment is that consistently people's guess for the adjusted price stayed closer to the anchor the higher the perceived precision of this price, i.e. the less zeros in the end. Here is a typical result for a beach house, the anchors in $, followed by the participants' mean estimate

    Rounded anchor: 800,000
    Mean estimate: 751,867

    Precise under anchor: 799,800
    Mean estimate: 784,671

    Precise over anchor: 800,200
    Mean estimate: 778,264

What you see is that the rounded anchor results in an adjustment that is larger
than the average adjustment observed with the precise anchors. Now you might wonder how many graduate students have much experience with buying beach houses, or plasma TV's for 5,000. But they used a whole set of similar questions, in which the measure to be estimated wasn't always a price, but possibly some other value like the protein value of a beverage. There even was a completely context-free question "There is a number saved in a file on this computer. It is just slightly less than 10,000/9,989/ 10,011. Can you guess the number?". The results remain consistent, the more significant digits the anchor has, the less the adjustment. For the context free question the mean estimate was 9,316 (rounded) 9,967 (precise under) 9,918 (precise over).

The paper further contains some other slightly different experiments with students to check other aspects, and it also contains an analysis of behavior in real estate sales. The author's looked at five years of real estate sales somewhere in Florida, and compared list prices with the actual sales prices of homes. They found that sellers who listed their homes more precisely (say $494,500 as opposed to $500,000) consistently got closer to their asking price. The buyers were less likely to negotiate the price down as far when they encountered a precise asking price.

I find this study kind of interesting, as it would indicate that the use of ninetynineing is to fake a precision that isn't there.

Bottomline: The more details are provided, the less likely people are to doubt the larger context.

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  1. I read that the original reason for pricing items slightly below a round number was that the operator of the cash register was thereby forced to open the cash register, to provide change to the customer. Opening the cash register leaves a record behind, which makes it more difficult for the operator to embezzle money from the employer.

  2. When you daytrade stocks, for example as a market maker on Nasdaq, the round numbers become very significant. This is because large numbers of people put orders in at round numbers. You'll see a lot more sell orders at $100 per share than you see $100.25, for example, and this makes the random price movement near these points not quite so random.

    It becomes profitable to put sell orders in at $99.99 (so your order is put in front of the orders at $100) and then watch the action at $100. Since there are a lot of sell orders at $100, it will take longer than usual to burn through them. If it fails to burn through, then you've just sold a penny under the peak.

    If it looks like it is getting close to burning through, then you buy back at $100 losing only $0.01 per share plus commissions. For a day trader who makes money, commisions on 1000 shares should be around $4 or so.

    P.S. You can't do this at home because your equipment and accounts are insufficient to compete with the big houses. But you can do it, and many people do just that, at a trading house.

  3. Great post, just wish I could access the original paper!

  4. Fascinating, if I were to guess the cause of this, it would be that the later digits distracted the brain (the late digits being the less significant). I'm willing to bet these figures don't hold up in cultures that write and speak numbers in a little-endian form (we use a big-endian form).

  5. Hi Bee,

    With all that the researcher has discovered it still boils down to what your mother told you, which is that perception is the issue. The truth is the numbers themselves are arbitrary as the base of the number system is itself. If these prices were expressed in a different base the physiological under and over points would be different. Ninety-nine ninety nine would mean very little in the base 60 system of the ancient Sumerians or for the two counters among the tribes of New Guinea. In fact many numbers we hold as special have no real significance at all, beyond the fact we have ten digits on our hands. Relative proportion on the other hand does have real significance like 3.14159 or .6180 and the best of all 137. Although, come to think of it, many of the natures numbers are irrational so perhaps this arbitrary accuracy is a strategy nature employs to disguise the real values or at the very least that we don’t barter her decisions :-)



  6. Hi Peter,

    That's interesting, but it doesn't sound very plausible to me. For one, it would only take the allegedly dishonest employee to have a penny bowl to deal with the 99ers. But besides this, the ninetynineing is used on the price-tag, which in countries where the tax is added at the register doesn't correspond to the actual price that is to pay anyway. I am not sure though how long ago this was introduced. Either way, this would fall into the category of 'convention' and left me wondering why it's still used. Best,


  7. Hi Carl,

    Interesting. Excuse me for my ignorance, but what's the merit of this (on the macrolevel)? Best,


  8. Hi Phil,

    Indeed I found it somewhat misleading to call the prices with less zeros more 'precise'. Without any other information, they are all equally precise, it's just that I guess most people perceive a price with more zeros as likely being rounded (in the decimal system) and thus less precise.

    Anyway, I have to admit that I find the results of this study somewhat surprising. To me a price with five niners in the end looks equally 'precise' as one with five zeros - just that the niners are more annoying. Then I'd have said well, maybe it's the randomness of the digits that causes a perceived 'significance' of the digits. But then, if somebody were to ask for $ 762,114 for a beach house I'd find that utterly ridiculous. As far as I am concerned, I mostly set the 'adjustment scale' by the prices of the next cheaper/more expensive product. Same would probably go for other measures. Best,


  9. Hi Bee,

    “I mostly set the 'adjustment scale' by the prices of the next cheaper/more expensive product. Same would probably go for other measures.”

    That is most certainly one of the reasons you are a scientist and also perhaps serves to strengthen your conviction, which I share, that more should think the same.



  10. Hi Phil,

    I'm not convinced more should think the same. In fact, I sometimes wonder how what I think I think correlates with what I do ;-) One of the other experiments in the mentioned paper examines the influence of also providing a 'range' (broad or narrow) for plausible prices. They find that a broad range results in more adjustment than a narrow one, but the anchor-effect is still present. So just providing a scale for orientation doesn't remove the effect. Best,


  11. Hi Bee, the authors have provided so much detail and context - do we know that the study was actually done?

    The more details are provided, the less likely people are to doubt the larger context.



  12. This comment has been removed by the author.

  13. Hello Bee,
    although You stay abroad since years,
    You remember ALDI?
    All prices were percisely in Pfennigs,
    everybody admired the women doing the cash register for their memory.
    Only few realized, that all prices ended
    on 8 Pfennigs :=)
    some sad news for you (maybe): those
    woman lost their "High Priest of
    Wirtschftwunder"-Status some years ago,
    ALDI swichted to bar code technology!

  14. Hi Bee,

    “I'm not convinced more should think the same. In fact, I sometimes wonder how what I think I think correlates with what I do ;-)”

    You have to understand that the key word here is “think”, which is the process that I feel is omitted in most decisions that would show such a pattern of result. QM with its typical probability distribution has highs and lowers focused around an anchor point and yet for the most part demonstrates a symmetrical distribution. Strangely enough when I see a graph or chart that shows a non symmetric or erratic distribution it usually indicates it some how relates to people. Freedom of choice is thus best displayed and most revealing as it clearly demonstrates there is a difference between mind and intellect:-)



  15. 'Bottomline: The more details are provided, the less likely people are to doubt the larger context.'

    I agree entirely with the conclusion to this post. It applies elsewhere, too. For example, a lot of physics papers get published because they contain a lot of detail. Because they're full of detail, the peer-reviewers are more likely to pass them than sketchier papers.

    They simply don't have the time to carefully check the claims and repeat the experiments being made, so they prefer to approve the papers that appear to provide the most details, while rejecting the briefer, sketchy ideas. Even though sometimes key ideas are often very sketchy!

    A round-number price similarly sounds artificial and therefore more greedy and expensive, whereas a more precise, less rounded number looks as if it has been very carefully worked out and is therefore fairer.

    In a lot of old physics papers, especially pre-1930 papers, tend to look more precise than they are accurate, because results and averages are painstakingly calculated and printed to many more significant figures than the accuracy of the data warranted. This ended as a result of the influence of studies by people like Ronald A. Fisher (author of 'Statistical Methods for Research Workers', 1925) who showed how scientific papers deal with treat errors, working out the standard deviation as well as the mean, doing significance tests with carefully chosen null hypothesis, etc.

    As soon as authors were expected to quote a standard deviation for accuracy as well as the mean, it became superfluous to provide the data to a precision in exceeding the precision implied by the standard deviation. E.g. a result with a standard deviation of plus or minus 1% should be rounded to 2 significant figures, 0.1% to 3 significant figures, and so on.

  16. Hi Nige,

    Yes... that's what I had in mind when I wrote this sentence... ;-)


  17. Hmmmm.....The strategy of gasoline pricing has been revealed? :)

  18. You insprired my NINING poem ... since the first line is from your blog post ...


    ninetynining is to take a precision which isn't there

    sixtynining is to take a position which isn't unfair

    fortynining is to take a stake and claim a rich tract

    thirtynining is to fake an age that's no longer fact

    twentynining is to reminisce of years which were prime

    And 109'ing is to drive down the route near I've lived a long time

    ... like for 16 years now!



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