Breaking the Law of Averages: Real-Life Probability and Statistics in Plain English

It is finally done!

Breaking the Law of Averages

You may order directly from the publisher here1. The book will also be available on Amazon, Barnes and Noble, etc. in about a month. I’ll update this post with the links when the book is in the distribution channels. Order as many copies as humanely possible.

Signed copies
I have had several requests for signed copies. I’ll be happy to do this for people. If you want a signed book, please email me at Please use “SIGNED COPY” as a subject line, and include your address in the body of the email. I’ll buy a few books from the publisher and then re-ship them out to people who want a copy. The charge will be the same as the publisher’s plus the same as they charge for Media Mail shipping and handling ($5.90), plus $1.15 cents (to cover tax). This makes the cost an even US$32.00. Payment will be arranged through PayPal (apparently, you don’t have to have an account to pay this way). I’ll send those who email me a PayPal “Request for Payment”; after that is received, I’ll ship the book (anywhere in the world).

Because I first have to order copies, sign them and then mail them out, it will of course take longer for you to get your book. I will wait a couple of days to see how many people email so I have a rough idea of how many books I should order.

I have two permanent places for news of the book:

  1. My books tab (see upper right of screen): general news and information
  2. Code page: free R code examples, erratum, links to papers, data, etc.


Why is this book different?

Statistics has traditionally been taught decade after decade in a fashion that is long outdated. This book presents a brand new way of understanding probability and statistics at the introductory level. The approach taken does not require mindless memorization. There is very little math, and what there is requires nothing beyond multiplication and division. This book takes busy work out of standard statistics and puts insight back in.

Preface excerpt:

The regular readers of my blog, where parts of this book previewed piece by piece, provided razor sharp editing and keen questioning and kept me from making major blunders. So thanks to (screen names) Mike D, JH, Harvey, Joy, Noahpoah, Harry G, Bernie, Lucia, Luis Dias, Noblesse Oblige, Charlie (Colorado), Dan Hughes, Mr C Physics, Jinnah Mohammed, Ari, Steve Hempell, Wade Michaels, Raphael, TCO, Sylvain, Schnoerkelmanon, and many others (sorry if I left you out!). Any mistakes left are obviously their fault.

What’s next?
I use the book in my own classes, of course, and a few other professors have been either using a draft or have expressed interest in the book for their classes. If, by some miracle, the book becomes popular, I’ll start working on a “Answers to Selected Exercises” or, given that I get substantial comments from actual class use, a Second Edition. But that is all in the far, far future.

If you are a professor of a statistics class and want to chat about the book, send me an email at and we can set up a time to talk. I have had great success with this approach for beginning students and can let you know how I run the class. Some guidelines are also given in the Preface.

1The cover art looks terrible on the publisher’s page. They have scaled it down from an enormous PDF to a small JPEG and it is pixelated. It looks great when printed, however.


  1. Ari

    Sweet. My name is in a preface. Except now I’ll probably be excommunicated by all my liberal friends because you’re a climate change/global warming “denialist” (wasn’t that what the guy at Pharyngula [PZ Meyers?] called you?)

    It’s a risk I’m willing to take. 🙂

  2. Bernie

    I contributed far, far less to this than to some other financially successful publications and never received a word, nevermind such a polite acknowledgement. I appreciate it.

  3. Bernie

    Hey guys, in the acknowledgement he blamed us for all the mistakes!!!

  4. Matt — Big Congrats. Teaching is noble. You are dedicated and have a gift for it.

    Bernie — I’m used to it. Around here everything is my fault. Even when it isn’t.

  5. Joy


    I’m tickled pink, My name is in a real book!

    Thank you. One copy will go to Worcester College For The Blind, (where I went). If they like it they can sort Braille versions, but they have to be ordered in larger numbers, so fingers crossed. I’m sure they will find it very appropriate as many of the boys are into economics and computing.
    This is not to be confused with Essex College for the Blonde, where this book would be of limited use.

    Mike, spot on,
    And Man’s place is in the wrong.
    Joy Clarke

  6. Briggs


    Somebody always has to take the fall.


    How do they render mathematical equations and graphs in Braille? I can easily imagine graphs; simple ones, anyway. I suppose there must be a standard set of Greek letters for equations, but how about subscripts and so forth? I’m shockingly ignorant of this subject.

  7. TCO

    That was nice of you. I don’t really remember commenting on the book at all.

    Actually am mostly worried that your novel, studen-friendly approach will not be so. For instance, you are big into Bayesianism. But for a first timer, frequentist stuff is easier to understand. I’m reminded of chem texts like Oxtaby and Nachtrieb that are loved by chem profs (who already know the subject) and have non-orthodox ordering of material. but for first timer students, the conventional order of Zumdahl is much better way to learn.

  8. Briggs


    I’ll take your word on the chemistry. but I have never found that beginning students understand the frequency approach better. People do not find it natural to think about limits of experiments, for one. It is the extremely rare person who can recall the definition of a p-value, for another. People—even experienced statisticians—almost always give the p-value the Bayesian interpretation. I have had pretty good luck teaching in this style.

    Plus, might as well get it right from the start.

  9. Joy

    You may be sorry you asked.
    The Braille cell is like a domino standing on end. (2 dots horizontally by 3 dots vertically).
    For reference each dot is numbered. So every letter and sign is a combination of these dots and no dots stray outside this cell so will always compare spatially consistently with their neighbouring cells.
    If you typed a full line with all the dots possible it would look like a neat row of dominoes. I can’t show this for technical reasons but found a link:

    Numbers are the same as letters but with a number sign in front so a = 1 up to j =0. In Algebra there are letter indicators. Greek letters, I think but am not sure, have a dot four in front as indicator. ’a’ is alpha with the preceding indicator dot, but theta is a ‘th’ sign with the extra dot. ‘l’ is lambda so most are the same as their corresponding normal letter.

    Upper and lower cases have a dot six or four and six, respectively, to indicate case. In maths of course this is vital. In English Braille, in the main, capitals are not used. As you can imagine, the visual scanning used by sighted people is meaningless and aesthetics is not an issue I guess.
    Different disciplines (maths, computing, music etc) assign different dot indicators so context is important. For example the symbol for ‘st’ in English means the ‘/’ of a fraction in maths but a forward slash in computing.

    As the dots all originate from the Braille cell, one can tell by the position of the dot which dot is intended. When the pattern changes, another dot, or combination there of, will appear in the sequence of characters. These patterns of dots with letters are known as contractions. Combinations of English letters without extra dots are known as abbreviations, much like short hand. If you write the letter ‘b’ on it’s own it means ‘but’, ’abv’ means above and so on. Braille is my favourite medium.

    In music, however, it all goes horribly, horribly wrong!
    The top four dots make up ’A’ to ’G’ and the length of the note is depicted by adding a combination of the lower two dots (3 and 6). To add insult to injury some bright spark decided that ‘a’ really should be b, ‘b’ should be ‘c’, and so on up to ‘g’ should be ‘h’. Before one arrives at the note, there are a selection of three or four other signs, depicting which hand to use and that the music is about to start! It goes on like this until the product resembles hieroglyphics and the pupil has decided to learn by ear or improvise!

    I was lucky enough to study Maths in large print, and so was never an expert on the maths Braille contractions. Graphs were drawn with plastic media called ‘thermaform’ if pre-prepared or plotted by students with drawing pins and elastic bands on a relief grid. I feel sure that computer technology features far more in maths classes now and I’m guessing that the higher level maths students do without seeing the graphs and focus on the method and theory rather than the squiggles. (Like a certain mann that shall remain nameless should learn to do).

    What’s the bet that on learning that the Braille cell has six dots and before reaching the second paragraph, you know how many dot combinations there are!

  10. Bernie

    Matt & Joy:
    The use of Braille to represent mathematical formulae is fascinating: Any chance of some visuals to help those of us who are excessively visually dependent?

  11. Joy

    Matt and Bernie,
    I can’t post proper examples on here so I will mail a sample to Matt and hope he will not mind forwarding the sample if that’s not cheeky. The link only showed the cell and alphabet.

  12. Briggs–
    I think the most confusing thing about frequentisms is tests are generally give answer to questions most people don’t intend to ask. It might be less confusing for students if instructors at least admitted the reason one asks questions that seem “backwards”. It’s that those are the questions that can be tested.

    Unfortunately, some instructors seem to give students the impression these questions are selected because they are somehow, the right question. Well… they are “a” right question. The answer can sometimes tell us something useful. But it would often be nicer to answer a different question.

  13. Larry Sheldon

    I have the book

    I am actually reading it.but I already have two questions that may disqualify me from further study:

    On the back cover, it is written that a book web site has….

    I thought that would be a good place to look for an answer to my second question, but so far I have not identified mthe “book web site”

    Which leave the second question:

    On page 27 it is written “^1Thses are on a sheet in the back of the book.”

    I find no such sheet. What am I missing? (Besides the sheet.)

  14. Larry Sheldon

    Never mind, kinda sorta, about the web page–the incomplete quotation promised code, and I’ve found that.

  15. Briggs

    Larry, if you have questions, please feel free to email me directly and I’ll try and help you out.

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