Media

The Placebo Effect – An Overview

There is a major problem with reliance on placebos, like most vitamins and antioxidants. Everyone gets upset about Big Science, Big Pharma, but they love Big Placebo.

– Michael Specter

A Little White Lie

In 1972, Blackwell invited fifty-seven pharmacology students to an hour-long lecture that, unbeknownst to the students, had only one real purpose: bore them. Before the tedious lecture began, the participants were offered a pink or a blue pill and told that the one is a stimulant and the other a sedative (though it was not revealed which color corresponded to which effect – the students had to take their chances). When measuring the alertness of the students later on, the researchers found that 1) the pink pills helped students to stay concentrated and 2) two pills worked better than one. The weird thing about these results: both the pink and blue pills were plain ol’ sugar pills containing no active ingredient whatsoever. From a purely pharmacological point of view, neither pill should have a stimulating or sedative effect. The students were deceived … and yet, those who took the pink pill did a much better job in staying concentrated than those who took the blue pill, outperformed only by those brave individuals who took two of the pink miracle pills. Both the effects of color and number have been reproduced. For example, Luchelli (1972) found that patients with sleeping problems fell asleep faster after taking a blue capsule than after taking an orange one. And red placebos have proven to be more effective pain killers than white, blue or green placebos (Huskisson 1974). As for number, a comprehensive meta-analysis of placebo-controlled trials by Moerman (2002) confirmed that four sugar pills are more beneficial than two. With this we are ready to enter another curious realm of the mind: the placebo effect, where zero is something and two times zero is two times something.

The Oxford Dictionary defines the placebo effect as a beneficial effect produced by a placebo drug or treatment, which cannot be attributed to the properties of the placebo itself and must therefore be due to the patient’s belief in that treatment. In short: mind over matter. The word placebo originates from the Bible (Psalm 116:9, Vulgate version by Jerome) and translates to “I shall please”, which seems to be quite fitting. Until the dawn of modern science, almost all of medicine was, knowingly or unknowingly, based on this effect. Healing spells, astrological rituals, bloodletting … We now know that any improvement in health resulting from such crude treatments can only arise from the fact that the patient’s mind has been sufficiently pleased. Medicine has no doubt come a long way and all of us profit greatly from this. We don’t have to worry about dubious healers drilling holes into our brains to “relieve pressure” (an extremely painful and usually highly ineffective treatment called trepanning), we don’t have to endure the unimaginable pain of a surgeon cutting us open and we live forty years longer than our ancestors. Science has made it possible. However, even in today’s technology-driven world one shouldn’t underestimate the healing powers of the mind.

Before taking a closer look at relevant studies and proposed explanations, we should point out that studying the placebo effect can be a rather tricky affair. It’s not as simple as giving a sugar pill to an ill person and celebrating the resulting improvement in health. All conditions have a certain natural history. Your common cold will build up over several days, peak over the following days and then slowly disappear. Hence, handing a patient a placebo pill (or any other drug for that matter) when the symptoms are at their peak and observing the resulting improvement does not allow you to conclude anything meaningful. In this set-up, separating the effects of the placebo from the natural history of the illness is impossible. To do it right, researchers need one placebo group and one natural history (no-treatment) group. The placebo response is the difference that arises between the two groups. Ignoring natural history is a popular way of “proving” the effectiveness of sham healing rituals and supposed miracle pills. You can literally make any treatment look like a gift from God by knowing the natural history and waiting for the right moment to start the treatment. One can already picture the pamphlet: “93 % of patients were free of symptoms after just three days, so don’t miss out on this revolutionary treatment”. Sounds great, but what they conveniently forget to mention is that the same would have been true had the patients received no treatment.

There are also ethical consideration that need to be taken into account. Suppose you wanted to test how your placebo treatment compares to a drug that is known to be beneficial to a patient’s health. The scientific approach demands setting up one placebo group and one group that receives the well-known drug. How well your placebo treatment performs will be determined by comparing the groups after a predetermined time has passed. However, having one placebo group means that you are depriving people of a treatment that is proven to improve their condition. It goes without saying that this is highly problematic from an ethical point of view. Letting the patient suffer for the quest of knowledge? This approach might be justified if there is sufficient cause to believe that the alternative treatment in question is superior, but this is rarely the case for placebo treatments. While beneficial, their effect is usually much weaker than that of established drugs.

Another source of criticism is the deception of the patient during a placebo treatment. Doctors prefer to be open and honest when discussing a patient’s conditions and the methods of treatment. But a placebo therapy requires them to tell patients that the prescribed pill contains an active ingredient and has proven to be highly effective when in reality it’s nothing but sugar wrapped in a thick layer of good-will. Considering the benefits, we can certainly call it a white lie, but telling it still makes many professionals feel uncomfortable. However, they might be in luck. Several studies have suggested that, surprisingly, the placebo effect still works when the patient is fully aware that he receives placebo pills.

Experimental Evidence

One example of this is the study by Kaptchuk et al. (2010). The Harvard scientists randomly assigned 80 patients suffering from irritable bowel syndrome (IBS) to either a placebo group or no-treatment group. The patients in the placebo group received a placebo pill along with the following explanation: “Placebo pills are made of an inert substance, like sugar pills, and have been shown in clinical studies to produce significant improvement in IBS symptoms through mind-body self-healing processes”. As can be seen from the graph below, the pills did their magic. The improvement in the placebo group was roughly 30 % higher than in the no-treatment group and the low p-value (see appendix for an explanation of the p-value) shows that it is extremely unlikely that this result came to be by chance. Unfortunately, there seems to be a downside to the honesty. Hashish (1988) analyzed the effects of real and sham ultrasound treatment on patients whose impacted lower third molars had been surgically removed and concluded that the effectiveness in producing a placebo response is diminished if the patient comes to understand that the therapy is a placebo treatment rather than the “real” one. So while the placebo-effect does arise even without the element of deception, a fact that is quite astonishing on its own, deception does strengthen the response to the placebo treatment.

plac1

Results of Kaptchuk et al. (2010)

Let’s explore some more experimental studies to fully understand the depth and variety of the placebo effect. A large proportion of the relevant research has focused on the effect’s analgesic nature, that is, its ability to reduce pain without impairing consciousness. Amanzio et al. (2001) examined patients who had undergone thoracotomy, a major surgical procedure to gain access to vital organs in the chest and one that is often associated with severe post-operative pain. As handing out sugar pills would have been irresponsible and unethical in this case, the researchers found a more humane method of unearthing the placebo effect: the open-hidden paradigm. All patients received powerful painkillers such as Morphine, Buprenorphine, Tramadol, … However, while one group received the drug in an open manner, administered by a caring clinician in full view of the patient, another group was given the drug in a hidden manner, by means of a computer-programmed drug infusion pump with no clinician present and no indication that the drug was being administered. This set-up enabled the researchers to determine how much of the pain reduction was due to the caring nature of the clinician and the ritual of injecting the drug. The results: the human touch matters and matters a lot. As can be seen from the graph below, every painkiller became significantly more effective when administered in an open fashion. Several follow-on studies (Benedetti et al. 2003, Colloca et al. 2004) confirmed this finding. This demonstrates that the placebo effect goes far beyond the notorious sugar pill, it can also be induced by the caring words of a professional or a dramatic treatment ritual.

plac2
Results of Amanzio et al. (2001)

The fact that the human touch is of major importance in any clinical treatment, placebo or otherwise, seems pretty obvious (though its power in reducing pain might have surprised you). Much less obvious are the roles of administration form and treatment ritual, something we shall further explore. For both we can use the following rule of thumb: the more dramatic the intervention, the stronger the placebo response. For example, several studies have shown that an injection with salt-water is more effective in generating the placebo effect than a sugar pill. This is of course despite the fact that both salt-water and sugar pills do not have any direct medical benefits. The key difference lies in the inconveniences associated with the form of delivery: while swallowing a pill takes only a moment and is a rather uncomplicated process, the injection, preparation included, might take up to several minutes and can be quite painful. There’s no doubt that the latter intervention will leave a much stronger impression. Another study (Kaptchuk et al. 2006) came to the exciting conclusion that a nonsensical therapeutic intervention modeled on acupuncture did a significantly better job in reducing arm pain than the sugar pill. While the average pain score in the sham acupuncture group dropped by 0.33 over the course of one week, the corresponding drop in the sugar pill group was only 0.15. Again the more dramatic treatment came out on top.

The experimental results mentioned above might explain why popular ritualistic treatments found in alternative medicine remain so widespread even when there are numerous studies providing ample proof that the interventions lack biological plausibility and produce no direct medical benefits. Despite their scientific shortcomings, such treatments do work. However, this feat is extremely unlikely to be accomplished by strengthening a person’s aura, enhancing life force or harnessing quantum energy, as the brochure might claim. They work mainly (even solely) because of their efficiency in inducing the mind’s own placebo effect. Kaptchuk’s study impressively demonstrates that you can take any arbitrary ritual, back it up with any arbitrary theory to give the procedure pseudo-plausibility and let the placebo effect take over from there. Such a treatment might not be able to compete with cutting-edge drugs, but the benefits will be there. Though one has to wonder about the ethics of providing a patient with a certain treatment when demonstrably a more effective one is available, especially in case of serious diseases.

Don’t Forget Your Lucky Charm

This seems to be a great moment to get in the following entertaining gem. In 2010, Damish et al. invited twenty-eight people to the University of Cologne to take part in a short but sweet experiment that had them play ten balls on a putting green. Half of the participants were given a regular golf ball and managed to get 4.7 putts out of 10 on average. The other half was told they would be playing a “lucky ball” and, sure enough, this increased performance by an astonishing 36 % to 6.4 putts out of 10. I think we can agree that the researchers hadn’t really gotten hold of some magical performance-enhancing “lucky ball” and that the participants most likely didn’t even believe the story of the blessed ball. Yet, the increase was there and the result statistically significant despite the small sample size. So what happened? As you might have expected, this is just another example of the placebo effect (in this particular case also called the lucky charm effect) in action.

OK, so the ball was not really lucky, but it seems that simply floating the far-fetched idea of a lucky ball was enough to put participants into a different mindset, causing them to approach the task at hand in a different manner. One can assume that the story made them less worried about failing and more focused on the game, in which case the marked increase is no surprise at all. Hence, bringing a lucky charm to an exam might not be so superstitious after all. Though we should mention that a lucky charm can only do its magic if the task to be completed requires some skill. If the outcome is completely random, there simply is nothing to gain from being put into a different mindset. So while a lucky charm might be able to help a golfer, student, chess player or even a race car driver, it is completely useless for dice games, betting or winning the lottery.

Let’s look at a few more studies that show just how curious and complex the placebo effect is before moving on to explanations. Shiv et al. (2008) from the Stanford Business School analyzed the economic side of self-healing. They applied electric shocks to 82 participants and then offered them to buy a painkiller (guess that’s also a way to fund your research). The option: get the cheap painkiller for $ 0.10 per pill or the expensive one for $ 2.50 per pill. What the participants weren’t told was that there was no difference between the pills except for the price. Despite that, the price did have an effect on pain reduction. While 61 % of the subjects taking the cheap painkiller reported a significant pain reduction, an impressive 85 % reported the same after treating themselves to the expensive version. The researchers suspect that this is a result of quality expectations. We associate high price with good quality and in case of painkillers good quality equals effective pain reduction. So buying the expensive brand name drug might not be such a bad idea even when there is a chemically identical and lower priced generic drug available. In another study, Shiv et al. also found the same effect for energy drinks. The more expensive energy drink, with price being the only difference, made people report higher alertness and noticeably enhanced their ability to solve word puzzles.

 

This was an excerpt from my Kindle e-book Curiosities of the Mind. To learn more about the placebo effect, as well as other interesting psychological effects such as the chameleon effect, Mozart effect and the actor-observer bias, click here. (Link to Amazon.com)

New Kindle release: Curiosities of the Mind (Psychology)

After about six months of work and fun, my new Kindle book is finally ready and … surprise, it’s not math! This time we’ll be delving deep into the ultimate scientific challenge: the mind. Here’s the blurb and the Table of Contents:

Blurb:

Over the past centuries, science has successfully unlocked many secrets of the universe. We understand atoms and molecules, cells and organs, stars and galaxies and have managed to use this newly-found knowledge to build fantastic machines that can bring us from A to B at mind-blowing speeds and cutting-edge medication that can alleviate pain almost instantly. Yet, the grandest secret the universe has to offer remains a perplexing mystery: the mind.

Despite the incredible scientific progress, we still find ourselves wondering what it is, where it is and how it works. This book cannot hope to give you a full answer, but it will provide you with fascinating hints on the workings of this mysterious machine by discussing the strange curiosities manifested in it. You will get to know the most common psychological effects and biases, learn about illuminating experiments from the field of social psychology and find out a lot about yourself and the people around you in the process. For a detailed table of contents, check out the Look Inside feature.

Table of Contents:

– Placebo Effect
A Little White Lie
Experimental Evidence
Don’t Forget Your Lucky Charm
Poor Little Albert

– Chameleon Effect
Just A Harmless Fly
Now 10 % More Likable
It’s All About Empathy

– Childhood Amnesia
A Fundamental Part Of Being Human
The Nature Of Early Memories
Parents, Culture And Gender
The Self And Autobiographical Memories

– IKEA Effect
Labor Leads To Love
Cognitive Dissonances
High Expectations versus Low Rewards
Self-Perception Theory
Of Origami Frogs and Men

– False Consensus Effect
Bungee Jumping Enthusiasts Are Biased
What Would You Do?
A Powerful Defense Mechanism
Friends – A Biased Sample Of Mankind

– Actor – Observer Bias
Everybody’s To Blame Except You
Fidel Castro’s Army Of Students
A Matter Of Culture And Vision
Let’s Talk Later

– Dunning-Kruger Effect
Unskilled And Unaware
Learn To Be Better
Statistical Artifacts And Task Difficulty

– Music and the Mozart Effect
Tones and Overtones
Music And Your Mind
Say No to Marketers

– Appendix
Mean and Standard Deviation
P-Values
Regression to the Mean
Afterword

Click here to get to the product page on Amazon.

CTR (Click Through Rate) – Explanation, Results and Tips

A very important metric for banner advertiesment is the CTR (click through rate). It is simply the number of clicks the ad generated divided by the number of total impressions. You can also think of it as the product of the probability of a user noticing the ad and the probability of the user being interested in the ad.

CTR = clicks / impressions = p(notice) · p(interested)

The current average CTR is around 0.09 % or 9 clicks per 10,000 impressions and has been declining for the past several years. What are the reasons for this? For one, the common banner locations are familiar to web users and are thus easy to ignore. There’s also the increased popularity of ad-blocking software.

The attitude of internet users is generally negative towards banner ads. This is caused by advertisers using more and more intrusive formats. These include annoying pop-ups and their even more irritating sisters, the floating ads. Adopting them is not favorable for advertisers. They harm a brand and produce very low CTRs. So hopefully, we will see an end to such nonsense soon.

As for animated ads, their success depends on the type of website and target group. For high-involvement websites that users visit to find specific information (news, weather, education), animated banners perform worse than static banners. In case of low-involvement websites that are put in place for random surfing (entertainment, lists, mini games) the situation is reversed. The target group also plays an important role. For B2C (business-to-consumer) ads animation generally works well, while for B2B (business-to-business) animation was shown to lower the CTR.

The language used in ads has also been extensively studied. One interesting result is that often it is preferable to use English language even if the ad is displayed in a country in which English is not the first language. A more obvious result is that catchy words and calls to action (“read more”) increase the CTR.

As for the banner size, there is inconclusive data. Some analysis report that the CTR grows with banner size, while others conclude that banner sizes around 250×250 or 300×250 generate the highest CTRs. There is a clearer picture regarding shape: in terms of CTR, square shapes work better than thin rectangles having the same size. No significant difference was found between vertical and horizontal rectangles.

Here’s another hint: my own theoretical calculations show that higher CTRs can be achieved by advertising on pages that have a low visitor loyalty. The explanation for this counter-intuitive outcome as well as a more sophisticated formula for the CTR can be found here. It is, in a nutshell, a result of the multiplication rule of statistics. The calculation also shows that on sites with a low visitor loyalty the CTR will stay constant, while on websites with a high visitor loyalty it will decrease over time.

Sources and further reading:

  • Study on banner advertisement type and shape effect on click-through-rate and conversion

Click to access 131481.pdf

  • The impact of banner ad styles on interaction and click-through-rates

Click to access S2008_989.pdf

  • Impact of animation and language on banner click-through-rates

http://www.academia.edu/1608289/Impact_of_Animation_and_Language_on_Banner_Click-Through_Rates

How Statistics Turned a Harmless Nurse Into a Vicious Killer

Let’s do a thought experiment. Suppose you have 2 million coins at hand and a machine that will flip them all at the same time. After twenty flips, you evaluate and you come across one particular coin that showed heads twenty times in a row. Suspicious? Alarming? Is there something wrong with this coin? Let’s dig deeper. How likely is it that a coin shows heads twenty times in a row? Luckily, that’s not so hard to compute. For each flip there’s a 0.5 probability that the coin shows heads and the chance of seeing this twenty times in a row is just 0.5^20 = 0.000001 (rounded). So the odds of this happening are incredibly low. Indeed we stumbled across a very suspicious coin. Deep down I always knew there was something up with this coin. He just had this “crazy flip”, you know what I mean? Guilty as charged and end of story.

Not quite, you say? You are right. After all, we flipped 2 million coins. If the odds of twenty heads in a row are 0.000001, we should expect 0.000001 * 2,000,000 = 2 coins to show this unlikely string. It would be much more surprising not to find this string among the large number of trials. Suddenly, the coin with the supposedly “crazy flip” doesn’t seem so guilty anymore.

What’s the point of all this? Recently, I came across the case of Lucia De Berk, a dutch nurse who was accused of murdering patients in 2003. Over the course of one year, seven of her patients had died and a “sharp” medical expert concluded that there was only a 1 in 342 million chance of this happening. This number and some other pieces of “evidence” (among them, her “odd” diary entries and her “obsession” with Tarot cards) led the court in The Hague to conclude that she must be guilty as charged, end of story.

Not quite, you say? You are right. In 2010 came the not guilty verdict. Turns out (funny story), she never commited any murder, she was just a harmless nurse that was transformed into vicious killer by faulty statistics. Let’s go back to the thought experiment for a moment, imperfect for this case though it may be. Imagine that each coin represents a nurse and each flip a month of duty. It is estimated that there are around 300,000 hospitals worldwide, so we are talking about a lot of nurses/coins doing a lot of work/flips. Should we become suspicious when seeing a string of several deaths for a particular nurse? No, of course not. By pure chance, this will occur. It would be much more surprising not to find a nurse with a “suspicious” string of deaths among this large number of nurses. Focusing in on one nurse only blurs the big picture.

And, leaving statistics behind, the case also goes to show that you can always find something “odd” about a person if you want to. Faced with new information, even if not reliable, you interpret the present and past behavior in a “new light”. The “odd” diary entries, the “obsession” with Tarot cards … weren’t the signs always there?

Be careful to judge. Benjamin Franklin once said he should consider himself lucky if he’s right 50 % of the time. And that’s a genius talking, so I don’t even want to know my stats …

Hollywood and Physics

We’ve all seen these kinds of movies. After a fast and dramatic chase, the bad guy jumps out of the car, determined to end the good guy once and for all. His evil plans have been thwarted for the last time! In self-defense, the good guy is forced to take a shot and when the bullet hits, the evildoer is thrown violently backwards as a result of the impact and through the nearest shop window. Once the hero is reunited with the love of his life, the credits roll and we are left to wonder if that’s really how physics work.

In a previous example we calculated the momentum of a common 9 mm bullet (p = 5.4 kg m/s). Suppose the m = 75 kg evildoer gets hit by just this bullet. Since the bullet practically comes to a halt on impact, this momentum has to be transferred to the unlucky antihero for the conservation of momentum to hold true. Accordingly, this is the speed at which the bad guy is thrown back:

5.4 kg m/s = 75 kg · v’

v’ ≈ 0.07 m/s ≈ 0.26 km/h ≈ 0.16 mph

This is not even enough to topple a person, let alone make him fly dramatically through the air. From a kinematic point of view, the impact is not noticeable. The same is true for more massive and faster bullets as well as for a series of impacts. The only thing that can make a person fall instantly after getting shot is a sudden drop in blood pressure and the resulting loss of consciousness. But in this case, the evildoer would simply drop where he stands instead of being thrown backwards.

This is not the only example of Hollywood bending the laws of physics. You’ve probably heard the weak “fut” sound a Hollywood gun makes when equipped with a silencer. This way the hero can take out an entire army of bad guys without anyone noticing. But that’s not how pistol silencers work. At best, they can reduce the the sound level to about 120 dB, which is equivalent to what you hear standing near a pneumatic hammer or right in front of the speakers at a rock concert. So unless the hero is up against an army of hearing impaired seniors (which wouldn’t make him that much of a hero), his coming will be noticed.

This was an excerpt from my Kindle book: Physics! In Quantities and Examples

For more interesting physics, check out my Best of Physics selection.

Self-Publishing – A Rat Race

The trouble with the rat race is that even if you win, you’re still a rat. (Lily Tomlin)

Self-publishing seems like a cozy thing to do. You are free to choose any topic, free to write any way you like, free to set your own schedule … in short: a fantastic opportunity to express oneself and to share your ideas with the world. But as with anything on God’s green Earth, you gotta read the small print. There’s a good chance that self-publishing sucks you into a rat race filled with uncertainty, stress, anger and sleepless nights.

You chase the Amazon ranks like an addict chasing the drug that will bring his doom. You rush to finish the next book before the previous one drops out of Amazon’s “new releases” list. You are downright angry at an invisible algorithm that doesn’t make your book appear in the “also bought” list. You spend hours and hours of searching new ways to be seen and spend hours and hours frustrated when you can’t achieve the visibility you desire. You are happy about the sudden rise in sales and wonder obsessively about the following drop. You feel fantastic about the praise and are devasted for days about a bad review. If you get sucked in, there’s little left of the original idea: express oneself and share the ideas.

Any book takes a lot of work. The actual writing and researching, the creative process, is only a part of it. Thorough editing takes patience and time. You have to proof-read your book until you can’t stand the sight of it. This is the only way of making it error-free if you don’t intent to hire an editor. You have to format the whole thing for Kindle properly, including making it pass the EPUB validation (which will most likely cause you to scream at your innocent computer screen on more than one occasion), make the right book cover and write a catchy blurb. Then comes the worst part: marketing. Like a desperate and lonely vacuum cleaner salesman you go from virtual door to virtual door, begging for attention and feeling dirty all along. All for this little gain in visibility and rank, the self-published author’s cocaine. Then come the rollercoaster sales and reviews. If you kept your cool up to now, this will get to you. It’s amazing how much a negative review can hurt. But it’s just part of the job.

The rat race is on and you are rat #2,534,287 trying to find your edge. Remember the original idea? The expressing and sharing thing? Rat #2,534,287 doesn’t, all it wants to do is chase ranks.

I’m not making a case against self-publishing. I’m making a case for remembering why you do it or want to do it. The original idea that made writing your first book a joy. The first book! Just pure creative process. No thought wasted on ranks, promos, new releases, also boughts, pricing, … That’s how it should be. And that’s why I’m taking a break from publishing, to get back to this state of mind. I want to be me, not rat #2,534,287.

Distribution of E-Book Sales on Amazon

For e-books on Amazon the relationship between the daily sales rate s and the rank r is approximately given by:

s = 100,000 / r

Such an inverse proportional relationship between a ranked quantity and the rank is called a Zipf distribution. So a book on rank r = 10,000 can be expected to sell s = 100,000 / 10,000 = 10 copies per day. As of November 2013, there are about 2.4 million e-books available on Amazon’s US store (talk about a tough competition). In this post we’ll answer two questions. The first one is: how many e-books are sold on Amazon each day? To answer that, we need to add the daily sales rate from r = 1 to r = 2,400,000.

s = 100,000 · ( 1/1 + 1/2 + … + 1/2,400,000 )

We can evaluate that using the approximation formula for harmonic sums:

1/1 + 1/2 + 1/3 + … + 1/r ≈ ln(r) + 0.58

Thus we get:

s ≈ 100,000 · ( ln(2,400,000) + 0.58 ) ≈ 1.5 million

That’s a lot of e-books! And a lot of saved trees for that matter. The second question: What percentage of the e-book sales come from the top 100 books? Have a guess before reading on. Let’s calculate the total daily sales for the top 100 e-books:

s ≈ 100,000 · ( ln(100) + 0.58 ) ≈ 0.5 million

So the top 100 e-books already make up one-third of all sales while the other 2,399,900 e-books have to share the remaining two-thirds. The cake is very unevenly distributed.

This was a slightly altered excerpt from More Great Formulas Explained, available on Amazon for Kindle. For more posts on the ebook market go to my E-Book Market and Sales Analysis Pool.

E-Book Market & Sales – Analysis Pool

On this page you can find a collection of all my statistical analysis and research regarding the Kindle ebook market and sales. I’ll keep the page updated.

How E-Book Sales Vary at the End / Beginning of a Month

The E-Book Market in Numbers

Computing and Tracking the Amazon Sales Rank

Typical Per-Page-Prices for E-Books

Quantitative Analysis of Top 60 Kindle Romance Novels

Mathematical Model For E-Book Sales

If you have any suggestions on what to analyze next, just let me know. Share if you like the information.

How E-Book Sales Vary at the End / Beginning of a Month

After getting satisfying data and results on ebook sales over the course of a week, I was also interested in finding out what impact the end or beginning of a month has on sales. For that I looked up the sales of 20 ebooks, all taken from the current top 100 Kindle ebooks list, for November and beginning of December on novelrank. Here’s how they performed at the end of November:

  • Strong Increase: 0%
  • Slight Increase: 0 %
  • Unchanged: 20%
  • Slight Decrease: 35 %
  • Strong Decrease: 45 %

80 % showed either a slight or strong decrease, none showed any increase. So there’s a very pronounced downwards trend in ebook sales at the end of the month. It usually begins around the 20th. Onto the performance at the beginning of December:

  • Strong Increase: 50%
  • Slight Increase: 35 %
  • Unchanged: 10%
  • Slight Decrease: 5 %
  • Strong Decrease: 0 %

Here 85 % showed either a slight or strong increase, while only 5 % showed any decrease. This of course doesn’t leave much room for interpretation, there’s a clear upwards trend at the beginning of the month. It usually lasts only a few days (shorter than the decline period) and after that the elevated level is more or less maintained.

The Rise of the Sequels (1980 to 2012)

Did you also have the feeling that more and more of the top movies are sequels? If yes, then you were absolutely right. Starting with the turn of the millenium, Hollywood realized that sequels are cash cows and a wave of sequels flooded the market (with great success). I analyzed the number of sequels in the top 10 highest grossing films (numbers taken from Box Office Mojo, a fantastic data source for movie fans). Here’s the graph:

sequels top ten movies 1980 2012

In the 80s there were on average about 2 sequels in the top ten each year. In the 90s this declined to only 1 sequel, there even were some years (1993, 1994, 1996 and 1998) without any sequels in the top ten. It seemed that Hollywood was turning away from making sequels. But in the 2000s the situation changed noticeably, on average 3 sequels made it into the top ten. In 2003 and 2007 half of the top ten consisted of sequels! And it seems that these peaks are becoming the standard for the 2010s. The year 2011 set a new record with 7 sequels among the top ten. And with so many high quality sequels coming up (see here: http://www.imdb.com/list/-kbo5fy-BCo), we might even see this record broken in the near future.

The Ebook Market in Numbers

Over the years the ebook market has grown from a relatively obscure niche to a thrilling billion-dollar mass market. The total ebook revenues went from 64 million $ in 2008 to about 3 billion $ in 2012. That’s a increase by a factor of close to 50 in just a few years.

ebook market revenues

The number of units sold also increased by the same factor (from 10 million units in 2008 to 457 million in 2012).

ebook market units sold

(Source)

However, many experts believe that the ebook market has reached a plateau and the numbers for the first half of 2013 seem to confirm that.

From the revenues and units sold we can also extract the development of the average price for sold ebooks. It strongly increased from 6.4 $ in 2008 to about 8 $ in 2009. After that, it quickly went back down to 7 $ in 2010 and 6.7 $ in 2012. So ebooks have gotten cheaper in the last few years, but are still more expensive than in 2008.

average price ebook

As of 2012, ebooks make up 20 % of the general book market.

21 % of American adults have read an ebook / magazine / newspaper on an e-reader in 2012. This is up from 17 % in the previous year.

A survey, again from 2012, shows that most e-book consumers prefer Amazon’s Kindle Fire (17 %, up from no use) , followed by Apple’s iPad (10 %, same as previous year) and Barnes & Noble’s Nook (7 %, up from 2 %).

The Emerging World Of Ebooks

As we all know, the Internet changed everything. The Net and the Web have brought the world closer together. Many older means of communication have either been replaced or changed so as to co-exist with, and complement, electronic communication. Email, for example, has replaced almost all business and a lot of personal letter writing, though our mailboxes remain filled with lots of mail, most unwanted. A lot of printed newspapers and magazines still exist, but their content is now also available on websites, and the websites are timelier and often offer more detailed information. Printed media is not dead by any means, as millions of people still prefer to curl up with a good book or grab a paper on their way to work. There have been many efforts to popularize ebooks, downloadable books in digital form, but their acceptance remains in its infancy.

But that won’t stay that way. Ebooks make sense. Since books are almost all text, an ebook download is very fast and hundreds of ebooks can fit onto a small storage card. Ebooks do not contribute to cutting down forests, they do not need to be trucked across the country, they do not produce waste, and they are usually a lot less expensive than printed books. Ebooks also have many other advantages. Depending on your ebook reader software, an ebook can be annotated, bookmarked and searched. The latter is especially useful; I often want to go back to a certain quote or paragraph in a book, and electronic search is so much easier than leafing through a printed book.

One of the problems ebooks face is that people do not know how to use them. They are confused by the many different ebook formats or think they need a particular piece of hardware to read them. In fact, the formats are not really a problem. Most computers can read popular ebook formats and ebook reader software is freely available. Hardware is a bit more of an issue. Hardcovers and paperbacks are awfully convenient and they don’t need batteries, so a lot of people shy away from reading on a computer screen or spending the money for a dedicated ebook reader.

This is really too bad as ebooks are clearly the way of the future. They just make too much sense. Those who dismiss ebooks are missing out on a great and increasingly attractive alternative to the printed page. Those who are willing to give ebooks a chance are rewarded with lower costs and the ability to carry an entire library on a device of their choice, be that a notebook computer, a Tablet PC, a dedicated ebook reader, a PDA or even a smartphone. And they have access to a potentially much larger variety of books. That’s because ebooks make self-publishing easy and lots of authors who don’t have a chance of getting picked up by traditional print publishing houses can distribute their books electronically. Best of all, there is no waste and there will never be unsold books that end up on a bargain table or in a landfill.

My advice is to give ebooks a chance. Download a free ebook. Look for sites dedicated to ebooks, especially those with a website design that is appealing. See what format you prefer, and what device you like to read on. But be warned: you may get hooked. Once you get into them, downloading and reading ebooks can become a passion.

Analysis of Viewers for TV Series

I analysed the number of viewers of all the completed seasons for the following tv shows: Fringe, Lost, Heroes, Gossip Girl, Vampire Diaries, True Blood, The Sopranos, How I met your Mother, Glee and Family Guy. The data was taken from the respective Wikipedia pages.

My aim was to find simple “rule-of-thumb” formulas to estimate key values from the number of premiere viewers and to see if there’s a pattern for the decline of a show. Below you can see the main results from the analysis.

Result 1: Finale vs. Premiere

The number of finale viewers is about 85 % the number of premiere viewers.

Result 2: Average vs. Premiere

The average number of viewers during a season is about 83 % the number of premiere viewers.

finaleaverage

Result 3: Decline Pattern

The average number of viewers during a season is about 93 % the average number of viewers during the previous season.

averageprevious

This last result implies that the decline in popularity is exponential. If the average number of viewers for the first season is N(1), then the expected number of viewers for season n is: N(n) = N(1) * 0.93^(n-1). We can also express this using a table:

Average season two = 93 % of average season one

Average season three = 86 % of average season one

Average season four = 80 % of average season one

Average season five = 75 % of average season one

Average season six = 70 % of average season one

etc …

Of course, this is all just the sum of the behaviour of all the analyzed shows. Individual shows can behave very differently form that.

Setting the order for your wordpress blog posts

Usually your blog entries are ordered according to the date on which they were published. You can however also order them according to your wishes by altering the time tag. It’s a good idea to bump posts which have proven to be popular among readers to the top of the page from time to time. Note that the posts will not appear as newly published in the feed, but they will be the first thing a reader sees when he or she clicks on your blog’s title.

Here’s how to bump a post to the top of the page:

1. Go to the most current blog entry and click on edit. Under the section “Publish” (at the top, on the right) you will find the time tag. Note this time.

2. Go to the post to be bumped and click on edit. Again look for the time tag under the section publish and edit it. For it to appear at the top, the time tag must show a later time than the current number one.

I sometimes put this post (Mach Cone) at the top of the page because readers seem to enjoy the picture in it (and because I love it as well, it is physics and math come to life and in action).

While we’re at it, check out my sidebar for the “Posts I like” widget. Add it to your blog as well if you like to help out bloggers who have created great content.

Keywords: How To Use Them Properly On a Website or Blog

Because keywords help determine the ranking of your website, and therefore how visible your pages are to Internet traffic, it is important to use keywords properly in the creation of your blog or website.

In today’s world of Internet lingo, you may frequently hear the terms “keywords,” “search engine rankings,” and “keyword search results” bandied about. However, not everyone knows what keywords are, and how important they are to the success of a website.

Keywords are essentially words or phrases that summarize the topic of a site. When a Web surfer types a word or phrase into the blank field of a search engine such as MSN or Google, the search engine returns a list of related sites. Each site on this list is determined by the presence of the search terms, or keywords, in the site’s meta tags, image tags, and content.

Keywords and Meta Tags

Meta tags are like a site’s “dog tags.” They identify the site’s title, description, and keywords. Meta tags are invisible to Web surfers, but they are instrumental in a search engine’s recognition of the site’s content.

Title Tags

A title tag gives the title of the Web page. A title should only be around six words long, and the primary keyword – the word or phrase that the site is primarily identified with – should be in this title tag. The closer to the beginning of the title the primary keyword is, the stronger the association with that keyword will be.

Description Tags

A Web page’s description tag provides the search engines with a summary of the content contained on the page. Once again, the primary keywords for this page should be contained in the description, as close to the beginning as possible. Description tags only allow 200 characters of text.

Keyword Tags

The keyword tag lists all of the keywords that can be associated with the Web page. The primary keyword used in the title and description tags should be first, followed by other keywords in order of importance and relevance. Although keywords can be separated by commas, they don’t have to be; however, keywords should not be repeated more than three times, lest the Web page be rejected by the search engines as spam. Between 800 and 1,000 characters are allowed for keyword text.

Keywords and Image Tags

Image tags are the text that shows up in place of an image, if the image fails to load for any reason. However, image tags serve a more important function: they allow the search engines to “read” your images. Without image tags, search engines have no way of interpreting your images. Therefore, image tags can also help boost the visibility and relevancy of your site to search engines.

Keywords and Web Page Content

The tags that you use on a Web page are important identifiers for search engines. However, in order to maintain a respectable search engine ranking, your Web page must establish relevancy. In other words, the keywords in your tags must pertain to the actual content on the page. Therefore, the same keywords you list in your tags must be used within the text your page displays.

The most important part of the content is the opening paragraph. The primary keyword – the keyword that was used in the title and description, and listed first in the keyword text – should be used several times in the first paragraph, and then occasionally throughout the rest of the page. Other, less important keywords can be used occasionally throughout the content, as well. This will indicate to the search engines that your page really is relevant to the keywords listed in your tags.

Another way to judge keywords is via a concept called “keyword density.” Keyword density shows the frequency at which a keyword is used. The density is calculated by taking the total number of words and dividing it into the number of times keywords appear in the text. The resulting number is multiplied by 100 to create a percentage. Keyword density can be a tricky business, however. Too low a density will fail to be noticed by the search engines, whereas too high a density can cause a Web page to be rejected as spam. Typically, a keyword density of around 5% is sufficient.

The Importance of Keywords

Keywords are a vital part of the creation of Web pages because they directly affect how visible the page will be to search engine traffic. The presence of keywords needs to be a consideration in every aspect of designing a Web page: designing the tags as well as writing the content. Because of the impact keywords can have on the success of your site, it’s important to know how to use them properly.

Find out more on how to optimize your blog here: Increase Views per Visit by Linking Within your Blog.

Computing and Tracking the Amazon Sales Rank

The webpage http://www.novelrank.com/ provides a very neat simple way to track the sales rank of any book on Amazon. This service is completely free.

The sales rank is computed from the sales rate. The more a book sells per day, the lower the rank will be.  Here’s an approximate formula, taken from: http://www.edwardwrobertson.com/2013/02/a-quick-way-to-calculate-amazon-sales.html.

100,000 / rank = sales per day

So if a book is on rank 50,000, it sells about twice a day. As far as I know, a borrow counts as a sale and a free download as one third of a sale.

I use novelrank to track my ebooks. This is what the output looks like (launch of “Great Formulas Explained”):

novelrankgreatformulas

Indeed a neat tool to see how a book is performing. Note that the tracking starts on the day you add it, dates before that are not shown.

As you can see, during the period when no sale is made the sales rank increases more or less linearly at about # 50,000 per day. The average rank during this time can be calculated by the formula: final minus initial rank divided by 2. When a sale is made, the rank makes a discontinuous jump to a lower value.

GeoGuessr – Guess the location from the picture

Here’s an awesome link I found a while ago on SPIEGEL ONLINE. You are displayed a picture and have to guess where it was taken. For that you click on a world map. The closer you are, the more points you get. Pay attention to cars, signs and vegetation.

geoguessr

(Click on banner to visit geoguessr.com)

Quantitative Analysis of Top 60 Kindle Romance Novels

I did a quantitative analysis of the current Top 60 Kindle Romance ebooks. Here are the results. First I’ll take a look at all price related data and conclusions.

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  • Price over rank:

pricerank

There seems to be no relation between price and rank. A linear fit confirmed this. The average price was 3.70 $ with a standard deviation of 2.70 $.

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  • Price frequency count:

pricescount

(Note that prices have been rounded up) About one third of all romance novels in the top 60 are offered for 1 $. Roughly another third for 3 $ or 4 $.

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  • Price per 100 pages over rank:

pricerank

Again, no relation here. The average price per 100 pages was 1.24 $ with a standard deviation of 0.86 $.

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  • Price per 100 pages frequency count:

PPP1

About half of all novels in the top 60 have a price per 100 pages lower than 1.20 $. Another third lies between 1.20 $ and 1.60 $.

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  • Price per 100 pages over number of pages:

PPP2

As I expected, the bigger the novel, the less you pay per page. Romance novels of about 200 pages cost 1.50 $ per 100 pages, while at 400 pages the price drops to about 1 $ per 100 pages. The decline is statistically significant, however there’s a lot of variation.

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  • Review count:

reviewscount

A little less than one half of the top novels have less than 50 reviews. About 40 % have between 50 and 150 reviews. Note that some of the remaining 10 % more than 600 reviews (not included in the graph).

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  • Rating over rank:

rankreviews

There’s practically no dependence of rank on rating among the top 60 novels. However, all have a rating of 3.5 stars or higher, most of them (95 %) 4 stars or higher.

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  • Pages over ranking:

pagesrank

There’s no relation between number of pages and rank. A linear fit confirmed this. The average number of pages was 316 with a standard deviation of 107.

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  • Pages count:

pagescount

About 70 % of the analyzed novels have between 200 and 400 pages. 12 % are below and 18 % above this range.

Six Typical English Mistakes Germans Make

I’ve been teaching German and English in companies for the last five years. During this time, I noticed that some mistakes repeat over and over. Usually they are a result of people trying to translate their native language one-by-one into the foreign language. It goes without saying that this doesn’t always work. Here are some common mistakes Germans do when speaking English.

  • I become the steak.

This one’s very common and always hilarious. Germans become emails every day. At a restaurant they become the menu card and then become the steak. If a German woman is pregnant she becomes a child. And if a German writer is really good, he might just become a price. What an honor!

I think you noticed what’s going on. When Germans say become, often what they really mean is get. This is because in German we use the word bekommen for get! Talk about confusing. This is what’s called a false friend: words that sound the same in German and English but have a different meaning.

  • My car sucks. I will a new car!

Here’s another false friend. The German word will means want to (have). So despite being written just like the English word will and sounding exactly the same, it means something completely different. Accordingly, if you’re German and your car sucks (for example because you bought an American car – snap!), you will a new car. And everybody will more money.

  • I sit me on the chair, he sits him on the sofa.

Reflexive verbs are verbs, that need refering back to the person. For example you cannot simply say: I wash. You have to refer back to yourself: I wash myself. Such reflexive verbs are very uncommon in English, in German not so much. We use reflexive verbs all the time. For example the word sitze = sit is reflexive in German:

I sit on the chair.

Ich setze mich auf den Stuhl.

Note that I refer back using mich = me, myself. Translate that one-by-one and you got: I sit me on the chair. As a German, I also dress me in the morning and I hurry me to get to work on time. In my free time, I interest me in music.

  • Live you in America? Work you at BMW?

This one I basically hear every day. When you construct a question in the Present Simple, you need to use the auxiliary verbs do or does. In German there are no such auxiliary verbs. When we make a question, we simply switch verb and subject. For example, in English we go from statement to question like this:

You live in America. Do you live in America?

So we need to add the auxiliary verb do. In German it works like this (you = du, live = lebst):

Du lebst in Amerika. → Lebst du in America?

Note that we simply switched you and live. If you translate this sentence structure one-to-one to English (which many do), you’ll end up with such sentences: Live you in America? Work you at BMW? Understand you this?

  • I live not in America. I work not at BMW.

This is another common mistake. You need to use auxiliary verbs when negating a sentence in the Simple Present. These are: don’t and doesn’t. In German however we simply add nicht = not.

I live in America. → I don’t live in America.

Ich lebe in Amerika. → Ich lebe nicht in America.

Again, translate this one-to-one and you’ll end up with: I live not in America. I work not at BMW. I understand this not.

  • It gives a nice Italian restaurant here.

In German cities it gives a lot of nice restaurant. And on the street it gives a lot of nice cars. And despite common belief, it gives a lot of happy and friendly people here. Sounds odd? Well it’s all true, except that you shouldn’t use it gives for there is / are, which is just what a lot of Germans do. Hardly a day goes by that I don’t notice this mistake. How does it happen? The correct German phrase for there is / are is es gibt. And this translates one-to-one into it gives.

Understand you Germans now? I hope this bit helped. And be sure to check out the rest of the blog, it gives a lot of great entries here and I become a lot of nice comments from all over the world. Really!