Never Say “Caused By Chance”

Why does everybody blame me?
Why does everybody blame me?
One of the services of this blog is grammatical guidance. In that spirit, here are phrases which should be forbidden, and will be once I am in charge (all highlights mine):

  • “If our actions are caused by chance…” (source)
  • “How can you tell whether this deviation was due to chance?” (source)
  • “A difference among samples that is due to random variation (chance) is called sampling error.” (source)
  • “In normal English, ‘significant’ means important, while in Statistics ‘significant’ means probably true (not due to chance).” (source)
  • “Such alternative explanations may be due to the effects of chance (random error)…” (source
  • “The difference between two groups is statistically significant if it can not be explained by chance alone.” (source)
  • “A significance test will help us decide if the observed difference between two sample proportions is the result of pure chance…” (source)

We needn’t continue; the gist is clear.

Chance is not a cause; it is not a physical thing; it cannot be operative; it is not a measurable property. If you think it is, I challenge you to collect a bucket of it and bring it our way. If that is too much to carry, make it a thimbleful. Or tell us how it can be seen, felt, heard, smelt (yes, smelt), or touched. Or show us just how, by what precise mechanism, the property of chance carries out its nefarious duties.

Saying events are “due to chance” is a holdover from the days when if a cause was unknown it was ascribed to fairies, pixies, or spirits. It’s the same now, except that chance is sort of vague mystical entity, a dangerous creature not to be stared at, nor sought. Its presence can be felt; it is just as real as any vaporous apparition, and as vexing as a poltergeist. Chance is always destructive of knowledge in a demonically playful way, operating always behind a cloak. It never sleeps.

It’s true that the old (and not yet deceased) frequentist view of probability requires chance (or Chance) to be real; probability is (somehow) created in the wake of Chance. Chance is the being, to a frequentist, which fiddles with the coin as it is spinning, causing it to land heads. Busy man, Chance. Think of all those quarks it has to spin.

But even Bayesians who should know better use the same words. A guess is that this is so because Bayesians were first trained as frequentists and that it is difficult to leave behind fully a bad upbringing. If true, the solution is to eschew frequentist training—which should be done in any case.

What is real definition of chance? Since probability (also not real) is just a measure of uncertainty, chance is a synonym for unknown cause. Try it in the sentences above and you’ll see that they usually become tautological or nonsensical.

“How can you tell whether this deviation was caused by something unknown?” Well, it’s when we don’t know what the cause was. “The difference between two groups is statistically significant if it can not be explained by a cause we don’t know about.” Say that three times fast. “A difference among samples that is due to an unknown cause is called sampling error.” This one works, except for the unfortunate word error, which implies a mistake has been made.

Chance always means “I don’t know how that happened.” This does not imply that somebody doesn’t know why it happened, thought that could be true sometimes (e.g. quantum effects). Coin flips are great examples. Most times the initial conditions are of such complexity that predicting the outcome is too difficult, especially for most civilians. But the measurements can be done. The same flip which for one man is “random”, i.e. “caused by chance”, i.e. “caused by he knows not what”, is for the next man perfectly predictable.

Incidentally, my favorite bad example in today’s list is the one which begins “In normal English…” signaling that in statistics we will be using abnormal language. Too true. The unintentional additional hilarity of getting the (frequentist) theory wrong, I leave you to work out for yourself.

Update In comments some expressed a habit of saying “by chance”. Break it. To say a thing comes to be (known) by something is to say it either caused by it, or is part of the cause of it. Webster by: “With, as means, way, process, etc.; through means of; with aid of; through; through the act or agency of” Chance.

If pressed for a cause, admit ignorance up to the point of probability and then say, “But my uncertainty in the thing is expressed by this & such probability.”

Example 1: Something caused the coin to land heads; I don’t enough to say what; but given the evidence we discussed, the probability of a heads is 1/2.

Example 2: Something caused the observed minor differences between patient groups; I don’t know what; but given the evidence of the study, the probability of a difference is only 1/2.


  1. I’m OK saying “caused by chance” as a shortcut for “caused by forces outside our concern or knowledge.” But I’ll concede that although I know that when I say the former I mean the latter, I cannot guarantee that the hearer shares this understanding.

  2. Gary

    Yes, it’s all the fault of the pixies.

    Have e’er you seen the Pixies, the fold not blest or banned?
    They walk upon the waters; they sail upon the land,
    They make the green grass greener where’er their footsteps fall,
    The wildest hind in the forest comes at their call.

    They steal from bolted linneys, they milk the key at grass,
    The maids are kissed a-milking, and no one hears them pass.
    They flit from byre to stable and ride unbroken foals,
    They seek out human lovers to win them souls.

    The Pixies know no sorrow, the Pixies feel no fear,
    They take no care for harvest or seedtime of the year;
    Age lays no finger on them, the reaper time goes by
    The Pixies, they who change not, grow old or die.

    The Pixies though they love us, behold us pass away,
    And are not sad for flowers they gathered yesterday,
    To-day has crimson foxglove.
    If purple hose-in-hose withered last night
    To-morrow will have its rose.

    -Nora Chesson

  3. Briggs


    Substitute “caused by chance” to “I don’t know what the cause is, but our uncertainty in X is…”; or even leave out “I don’t know what the cause is” because the clause is implied.

  4. William Sears

    In “plain” English is better than in “normal” English. I think that your complaint is in the disconnect between the plain and technical meanings of chance, not in an inherent problem of the word. But this comes up all the time in physics. Should words like energy, force, work, or heat all be renamed just because they have less rigorous definitions in plain or every day English?

    Also, your quantum mechanical reference comes dangerously close to a belief in hidden variables. You have been warned, Briggs!

    I enjoyed the playful tone of your article, but maybe God does play dice with the universe. Cheers.

  5. Briggs

    William S,

    The comparison to physics not apt. Heat has a technical and colloquial meaning, to pick one example. Using either is harmless, unless one substitutes incorrectly.

    But chance as an entity is always wrong and harmful. It invokes mysticism and causes (!) sloppy thinking.

    No, I claim no hidden variables; I do say that we do not know what caused the phenomena, and do not say there is no cause.

  6. William Sears

    Sorry Briggs, but to claim a cause, known or unknown, in quantum mechanics (e.g. the Heisenberg uncertainty principle) is to state a belief in hidden variables. The Copenhagen interpretation of QM is a theory involving “chance” in all its annoying implications. Of course this applies to local theories and you could always take refuge in a non-local theory, such as Bohm’s pilot wave interpretation.

  7. Briggs

    William S,

    We disagree. There are indeed “annoying” implications to call that which we do not now “chance.” Better to say that something caused a thing and admit that it cannot be known. Not in this life, anyway.

  8. DAV

    No, I claim no hidden variables; I do say that we do not know what caused the phenomena, and do not say there is no cause.

    Not sure I see the difference between “hidden variable” and “cause unknown”.

  9. DAV

    chance is a synonym for unknown cause

    or perhaps “some other cause” (than the one being considered). so “How can you tell whether this deviation was caused by something unknown?” would become “How can you tell whether this deviation was caused by something else?”

    It seems in quantum physics “no cause at all” is on the list of something-elses. Possible, I suppose, but strikes me as counterproductive for a physicist as it effectively claims that physics is ultimately a futile undertaking. Hard to prove at any rate.

  10. William Sears


    Quote “It seems in quantum physics “no cause at all” is on the list of something-elses. Possible, I suppose, but strikes me as counterproductive for a physicist as it effectively claims that physics is ultimately a futile undertaking.”

    If we can’t know everything then we know nothing. A rather brazen conclusion to say the least. Science, and human understanding in general, advances by discovering what can not be done as much as discovering what can be done. In a pre-scientific society where knowledge is limited, everything seems possible. Even if one can not predict when an individual radioactive nucleus will decay, great accuracy can be obtained in the understanding of a mole of such nuclei. It is all statistics and chance. Right, Briggs?

  11. Rich

    In my experience the common usage is not “caused by chance” but simply “by chance”. An example would be, “it occurred by chance” which is not at all the same thing as, “it was caused by chance”. If we paraphrase that as, “it occurred for reasons unknown” I don’t think we have exactly the same thing though it may be close; “occurred by chance” suggests much more unknowable causes rather than simply unknown. “The results of coin-tosses occur by chance” seems unobjectionable to me.

  12. I too hate the phrase “caused by chance” but I am happy to say that an event (such as my winning the lottery) has “occurred by chance” if it happens in a circumstance where I (along with all other potential participants)have been effectively precluded from knowing or changing the specific values of a number of relevant variables.

    But of all the annoying usages out there, my own favourite bugbear is the use of “probability that occurred by chance” as a classic misdefinition of a P-value. Even if one accepts “occurred by chance” (as I do) and agrees (as I also do) that it is sometimes reasonable to talk of the probability of an outcome, it would be an insult to my integrity to assert that the occurrence of an unlikely event such as my winning the lottery was evidence that I probably didn’t win “by chance”.

  13. DAV

    If we can’t know everything then we know nothing

    Bit of a jump. What is the goal of physics? To merely characterize and quantify interactions or to determine why they occur? The answer to the latter is impossible if things ultimately have no cause and simply happen. If the purpose is to determine the why then it is ultimately a futile undertaking.

  14. Doug M

    “Caused by chance” and “caused by something unknown” are not at all the same thing.

    “Caused by something unknown” suggests that if we just studied the problem a little harder we could determine the cause.

    “Caused by chance” suggests that it is not worth the effort to investigate the cause. Or that the cause is well understood, and yet will still not provide much insight into the result. In the case of the flipping coin, the mechanics have been well understood for 300 years, but will still provide little insight into the result of the next flip.

  15. Ye Olde Statistician

    To the extent that a theory results in paradoxes like causeless effects, one might suspect the theory is deficient in some manner. A different metaphysic might be required, since facts never have values outside of a certain way of viewing them.

    Regarding “random” events, a fable excerpted from On the Razor’s Edge can be found here:
    provided one scrolls down to the quote starting:
    An ancient sage once wrote that all things happen by chance or by design, but that chance was only the intersection of two designs. Consider the man who is struck on the head by a hammer while walking to his lunch.
    It is then referenced here:
    scrolling to the section headlined Return of the Quanta.

    “Chance” I think is most often a synonym for “unpredictable,” not for “uncaused.”

  16. William Sears


    Quote: “If the purpose is to determine the why then it is ultimately a futile undertaking.”

    Why is a human emotion and not an explanation, as in: Why did you hit your brother? The question “Why?” has never been answered in all of human history. There is only “How?”. It is only futile if you consider life to be ultimately futile. Of course, you can fall back on the cosmological argument but this is a matter of faith and not a why.

    Quote: “The answer to the latter is impossible if things ultimately have no cause and simply happen.”

    Unsatisfying as this may be, it is the Copenhagen interpretation. Do you have an alternative?

  17. DAV

    Do you have an alternative?

    Outside of “causes unknown”? No.

    it is the Copenhagen interpretation.

    Speaking of “Why?”, why is that? What basis is there for it? There’s a big difference between “No cause” and “Perhaps no cause” or “Unknown (maybe forever) cause”. Jumping to “No cause” sounds like surrender.

  18. Noblesse Oblige

    If you hold to the idea of the multiverse interpretation of the Schrodinger Cat paradox (see for example David Deutsch ), there is not even such a thing as chance or randomness. This is because the laws of physics are deterministic. What we observe as “chance” is just the intersection of universes at the quantum level and only when fungible particles are involved.

    So get the word “chance” out of your vocabulary.

  19. William Sears

    Noblesse Oblige,

    Yes, the many-worlds interpretation of QM is an attempt to get around this problem as is Bohm’s Pilot wave interpretation. There are many others so take your pick from the following list.

    At present Copenhagen is the simplest but maybe someday one of the others or a completely new one will win out. There is no experiment to distinguish them at present, that I know of. You can call these whys if you like DAV, but I wouldn’t. There is no why and it is turtles all the way down – an inside joke.

  20. MattL

    This will make playing Monopoly very awkward.

  21. Stephen J.

    Maybe instead of “causes unknown”, say chance means “causes practically unpredictable”, due to quantity of factors and complexity of their interrelationship.

    In theory, if you are capable of measuring all the factors applying to the roll of a die and correctly calculating all their relationships, you can predict what the die will roll every time. In practice, such measurements and calculations are currently impossible to actually achieve (and quite possibly will remain so well into the future). “Chance” is simply the label put on the Schrodinger’s boxes we haven’t figured out how to open yet.

  22. Stephen J.

    Wups. Looks like I got beaten to this thought at 11:57 a.m., above.

  23. William Sears

    Stephen J,

    Precision dice rolling has been done! At least in this story.

    Speaking of Schrodinger’s cat, the purpose of this thought experiment is not as usually presented. It was presented not only as a challenge to the Copenhagen interpretation but as a means of thinking about the transition from the quantum mechanical world to the classical world. See's_cat

    As regards this transition Briggs, we do not disagree about your criticism of the misuse of chance in the classical world – at least not entirely – but we seem to disagree in the quantum mechanical world. As to what the case may be when we get to the last turtle, who can say?

  24. Noblesse Oblige

    William Sears (1:46PM)
    Indeed, the Copenhagen seems simplest perhaps because it is a cop out. I actually prefer the turtles.

  25. Michael Babbitt

    Chance of the Gaps.

  26. Sander van der Wal

    If one is capable of doing the computations in theory, there must be a theory to derive the calculations from. For dice, that’s Classical Mechanics. I would expect the calculations to be chaotic, i.e. a tiny difference in initial conditions will lead to a huge, exponentially huge, difference in possible outcomes. Setting up the initial state to exact conditions is theoretically impossible (there are just too many real numbers), and therefore the outcome cannot be calculated.

  27. Fletcher Christian

    There are several possible meanings to “occurred by chance” (which IMHO is better English than “caused by chance”. One is simply “cause unknown”. Another is “cause known but incalculable due to lack of data”; this might apply to coin flips for example. Another is “cause known but non-determinable because of chaotic factors” which might well apply to such things as whether you are rained on, on a day when showers are occurring. There is “cause known but inherently non-predictable” which applies to events caused by such things as whether you get cancer because a random cosmic ray hits something important, or a spacecraft is hit by a pebble-sized meteorite. And lastly (I think!) there is “no cause at all” which applies to such things as radioactive decay.

    The distinctions might or might not be important. For example, it is theoretically possible that one could predict the next ball to be called in a bingo game; but in practice it’s impossible. If a lottery is called by a machine that uses a quantum process such as radioactive decay (I believe this is the case for Britain’s Premium Bonds” then there is no possibility, even theoretical, of predicting it. There is no real practical difference between the tow, in terms of predictability.

  28. The notion of ‘common cause variation’ created by Shewhart for industrial process analysis, and more widely promoted, and developed, by Deming, helps deal with this difficulty. Observations which are consistent with a ‘business as usual’ state of a process beset by many, and not necessarily understood nor even identified causes are said to be due to ‘common causes’, and such observations by themselves do not justify corrective actions or investigation into individual instances (e.g. a relatively high value which may have recently occurred). Of course, despite the random appearance of data in such circumstances does not mean causality has been abandoned, merely that no sufficient evidence is present for anything unusual having happened. The corresponding term for something unusual having happened is ‘special cause’, and here there is some reasonable hope that it is an identifiable single cause that could be readily tracked down by immediate investigation. So-called ‘chance’ causes on the other hand would typically be tougher to identify. This simple model has proven to be of enormous practical value in industrial process monitoring.

  29. Ye Olde Statistician

    “no cause at all”… applies to such things as radioactive decay.
    I thought radioactive decay was caused by the emission of particles [e.g., α, β, or γ rays] and that this emission is in turn caused by the atom’s unstable structure [formal cause]. But what most people seem to think is that because the formal calculations of quantum mechanics do not include a term for “time” and they cannot calculate precisely which particle will be emitted at which time, that there is therefore “no cause.” But to have a cause is not necessarily to be predictable. Newton’s equations do not predict which apple will fall on which head, either. For that matter, the cue ball moves because it was struck by the cue stick, but as to when the cue stick will strike is not predicted by the laws of mechanics.
    But it might also be that α, β, or γ radiation have three [or more] different causes and we are at a loss because we are trying to come up with one cause for three different effects!
    Or it might be that we are wondering what the “cause” is of an “event” like “typing this response while an empty soda can sits beside the computer.” We may define as an “event” something which is really a concatenation or coincidence. Such “events” do not have “causes” even in the macro world, as the previously linked example of the man beaned by the falling hammer illustrates.

  30. JH

    Considering how some people would attribute it to God when coming across an unknown cause, chance can be a nickname for God. ^_^

    I, an average person who speaks normal chinenglish, happen to like the explanation given here.

    by chance
    accidentally; randomly; without planning.

  31. Hans Erren

    Would you prefer “Act of God” instead?

  32. “I don’t know” is a skill we must all embrace. The problem though is that few around us comprehend the difference between “I don’t know” and “Experts have said”.

    My neighbor is trying to convince me that the two large ass tornadoes in the Oklahoma in succeeding weeks is a great indicator that something is wrong in the atmosphere. Never has something like that happened before. Well, except for that time, 40 years ago, but it hasn’t happened exactly like this before.

    I look at the data and say, hmmm, “I can’t say what is happening.” Apparently “experts” can say though. I suppose I am not qualified to say that “experts” aren’t really “experts”, but when experts start seeing things in jumbled data using words like “this has never happened before” when it has, I start not believing anything experts say.

    Not believing experts though is a sign of being a conspiracy theorist. Apparently this is a high p-value tied to conspiracy theorists NOT believing experts. Since conspiracy theorists don’t believe experts, and I don’t believe in experts, I must definitely be a conspiracy theorist.

    DO NOT TRY and point out that there is no conspiracy, that just proves that you do believe that there is one.

  33. Nice discussion.

    Thought: chance is a cause in the same way evolution or progress are causes – not at all.

  34. My first thought was “chance caused evolution” so chance is a cause. Or that is the theory put forth. It has always bothered me that a “theory” based on “that happened by chance” can be called a theory at all. You can argue natural selection, but in the end, natural selection is nothing more than chance–the animal in the right place (which is totally by chance) survives while another animal in the wrong place dies. It’s just chance. And chance as a cause does not work……

  35. PJ

    IANAS (I am not a statistician). In the plain English I have always spoken and understood the expression that something happened by chance doesn’t involve the ascription of agency to what is implicitly random, or apparently so. A chance occurrence is one without agency. Pick enough scrabble letters from a large enough bag and you’ll eventually get the word CHANCE. It still happened by chance. In plain English.

    As for the argument that chance “caused evolution” (above), that is a misunderstanding. Random variation, a result of sexual reproduction, simply provides opportunities for differential survival rates. Melanistic moths survive in larger numbers when the tree barks are darker as result of pollution. The agent is the predator that eats the conspicuous moths, not chance. Characteristics that have greater survival value will be be preferentially selected for.

  36. I understand that “random variation” provides opportunities for different survival rates. Those survival rates are based on predators, etc. However, moth A survives because “by chance” he is in an area where the trees are close to the color of his wings. However, if moth A is in an area where the trees burn down and he has no way to hide, he probably will not survive. It is chance that moth A is in an area in which he can survive. If humans come in and destroy his habitat, he does not survive. Humans coming in is by chance–the humans may have found something valuable in the area. In the end, it is by chance that something evolves and survives. Evolution describes how it happens, but not why per se. Evolution describes responses to change, but not why the changes occur in the first place. The driving force still seems to me to be chance.

Leave a Reply

Your email address will not be published. Required fields are marked *