In the dramatized world of Law & Order, the defendant’s lawyer often tries to cast doubt on the evidence. “Is it possible you’ve reached the wrong conclusion?” the lawyer asks. When the expert witness explains that a different conclusion is unlikely, the lawyer retorts, “But is it possible?” The witness concedes that it is possible, but struggles to express the unlikelihood. Is it as unlikely as drawing a full house in poker, giving birth to triplets, or winning the lottery? How unlikely are those events compared to each other?
The Unlikelihood Scale provides a memorable and fun way to consider unlikely events in absolute terms and as compared to other events. Like the Richter Scale, the Unlikelihood Scale is logarithmic.
A logarithmic scale is based on orders of magnitude. For the Unlikelihood Scale, that magnitude is the logarithm of the average chance that the event occurs and is called the improbability factor. A whole number increase in the improbability factor means that the corresponding event is four times as unlikely to occur. For instance, an event that has an improbability factor of 3 is four times as unlikely to occur as an event with an improbability factor of 2. An improbability factor of 0 on the Unlikelihood Scale indicates that an event is not at all unlikely–it’s certain.
Each event on the Unlikelihood Scale also has an improbability tag. This tag labels an event based on where it falls on the scale and puts a name to the chances of that event occurring. Events with an improbability factor between and 0 and 1 are tagged as “Likely,” between 1 and 2 as “Conceivable,” between 2 and 3 as “Uncommon,” and so on.
I hope you find the Unlikelihood Scale enlightening and useful. You can search for unlikely events by name, category, and probability. Find similar events by clicking on their name, category, improbability factor, or improbability tag. You can submit a new event to the list and even buy a t-shirt or mug adorned with your favorite unlikely event. (Want a t-shirt or mug for an event that doesn’t have one listed? Ask for it in the event’s comments section.) Proceeds from the sale of t-shirts and mugs keep the website running, so thank you!
Computing improbability factors
The probability (P) of an event is the number of occurrences divided by the number of chances.
P = occurrences / chances
The improbability factor (F) of an event is the log base 4 of the chances divided by occurrences.
F = log4( chances / occurrences ) = – log4( P )
For example, a fair coin will be heads one time for every two chances. Thus, the probability is ½ and the improbability factor is log4( 2 / 1 ) = ½.
Using logarithms as the basis of the Unlikelihood Scale is a clear choice. Some people have difficulty comprehending large numbers, and logarithms turn large numbers into small ones, while preserving their order.
Since we are measuring unlikelihood, we want to determine the log of the reciprocal of the probability, not the probability itself. This makes the improbability factor increase as the probability gets smaller (starting at zero for an event that is certain).
Keeping the formula as simple as possible leaves one last choice to make: What base should we use for the logarithm? An initial choice might have been 10, in accordance with the Richter Scale and the number of fingers most people have. However, we want improbability factors to be intuitive, and the one probability nearly everyone knows is that of getting heads in a fair coin flip: 50-50 or ½. Thus, we want the improbability factor, -log(½), to be ½ (0.5). This means the base of the logarithm is four.
Contributing to the Unlikelihood Scale
While I’ve collected a wide variety of events, there are hundreds more to be considered. That’s why you can add your own submission to the event list. Simply log in to the website using your existing WordPress login credentials, or create a new login, and fill out the short submission form.
To prevent the ne’er-do-wells of the internet from posting superfluous, inaccurate, or inappropriate events, I review submissions prior to final publication. If you know your probabilities and want to help, become a reviewer. To qualify as a reviewer, email me your CV and links to two of your blog posts or published articles. Reviewers get a free t-shirt or mug of their choice upon reviewing and/or submitting their 10th event. They also get to post full articles on the Unlikelihood Scale website and receive my undying gratitude.
About the Unlikelihood Scale’s creator
My name is Eric Brechner, and though I have a Ph.D. in applied mathematics, I only took one graduate-level course in probability. However, like many people, I’m fascinated by rare events. I’m also frustrated by common misperceptions of risk and improper comparisons of rare, remote, and ridiculous events. Using my experience with websites and blogs, I created UnlikelihoodScale.com in my free time with helpful advice from Beau Lebens (of Automattic, the company behind WordPress) and Scott Berkun (formally of Automattic and Microsoft).
I am a development manager for the Windows Engineering System team at Microsoft and an affiliate professor at the University of Washington. At Microsoft, I’m widely known as my alter ego, I.M. Wright. Prior to my current role, I managed development for Xbox Engineering Services and Xbox.com, was director of engineering learning and development for Microsoft Corporation, and managed development for a shared feature team in Microsoft Office.
Before joining Microsoft in 1995, I was a senior principal scientist at Boeing and a developer for Silicon Graphics, GRAFTEK, and JPL. I’ve published two books on software best practices, hold eight patents, have a BS and MS in mathematics, and have a Ph.D. in applied mathematics. Outside work, I have two adult sons, the younger of whom has autism. I work to develop autism insurance benefits, help run the Microsoft autism alias, and serve on the board of the University of Washington Autism Center.