When do we need an alternative explanation for statistically unlikely events?

I ask because I am interested in miracles: is an extremely unlikely event enough to warrant the claim that something is out of the ordinary and we need a new explanation for it, which seems necessary for miracle claims.

If not, they may be reserved for facts that go against our natural understanding of the world (resurrection of the dead, statues bleeding, etc.), and then even the most unlikely results, being nomologically possible, are never miracles.

I'm guessing (being no sort of scientist) the answer might involve statistical variation, and wether we ever infer scientifically etc. than events with a vanishingly small probability are actually "impossible". Do we? Just two, slightly different, examples

  • is it scientifically possible e.g. for a man to be 30 feet tall?
  • do we need to a new explanation for me winning the lotto 1000 days in a row, beyond me buying tickets?

If so, what is extremely unlikely is not already accounted for, then an extremely low probability may signal something is nomologically impossible and a miracle if it does occur. If not, then its freakish unlikelihood does not make it a candidate for miracle claims.


2 Answers 2


When do we need an alternative explanation for statistically unlikely events?

I ask because I am interested in miracles…

I think of a miracle as an event that violates the laws of physics. The ability to walk on water, for example, is not accurately described as statistically unlikely. The claim, if true, would violate what is known about water and human physiology.

That claim, when assumed to be true, could be used to unravel all of physics, much as one would peel an onion. The unraveling, for example, could start with the density of water, which would require a second look at the bond between hydrogen and oxygen atoms, and so forth. Such a claim would play much the same role in physics as the principle of explosion does in logic.

And so there might be the answer to your question: an alternative explanation is necessary when the event, if it occurred as described, would cause the revision of the laws of physics.

Addtional answer after comment:

Statistics has answered a lot of this question. The short answer is that most natural events that involve living things lie along a bell curve, which describes the chances of the event occurring. This position on the bell curve, in turn, describes the quantum of proof necessary to show that the event actually happened.

An extraordinary event requires an alternative explanation to the extent that it lies outside ordinary experience. So a 6-foot man is well within daily experience and requires no proof. But the chances decrease as taller heights are assumed.

An 8-foot man is unusual. If the chance that a man will grow to 8 feet is 1 in 10,000, then that fraction also describes the level of proof necessary. The explanation must show how this event could occur at all.

Now assume a 30-foot man. Such a height would not be a miracle in the same sense as a direct violation of the laws of physics. But it would lie completely outside human experience.

As in the case of the 8-foot man, the explanation must start at the beginning and show how such a person could exist given the possibilities and limits of the human skeleton, vascular system, and so forth.

If that proof cannot be shown, and it would be physically impossible for a human to grow so large, then we are back to a miracle in the sense of a violation of the laws of physics.

  • well I agree, so I upvoted the question. but I won't accept it, because I am wondering about more than just the laws of physics. unless you want to add: all miracles violate the laws of physics and a 30 foot man probably doesn't
    – user62133
    Aug 11, 2022 at 1:05
  • @not_again. Well, since you are willing to shave 20 feet off the height of the miracle man, I am willing to give this answer additional thought. Aug 11, 2022 at 3:13
  • Thanks! Incidentally, I am not a Christian, but I find Christian skepticism about miracles, which I assume does exist, to be way out there. Clearly if Jesus were God, he could perform miracles (not just easily but "at will"), and there is a lot of reports of him doing so (by people that claim his divinity). Why believe Jesus is God and not in his miracles: how believe it...
    – user62133
    Aug 11, 2022 at 9:31

extraordinary events which, in theory, are highly improbable or even impossible, usually prove, upon closer inspection, to have “probability levers” that raise the odds they will happen: Roy Sullivan was struck seven times by lightning, which would seem fantastical if you didn’t know he was a forest ranger. “The Improbability Principle tells us that events which we regard as highly improbable occur because we got things wrong,” writes Hand. “If we can find out where we went wrong, then the improbable will become probable.”


So it is argued that extremely unlikely events tend to have a simple explanation we missed.

Whether or not all unusual events have these "probability levers" may just be up to your thirst for explanation: at least if they are explicable. As he suggests, even seemingly inexplicable events can be accounted for, even expected, (even supposing that is not always the case).

Defined by Hand as “an inexplicable event (normally a welcome one) attributed to a god: a supernatural event” [p. 27], a miracle turns out to be perhaps less of a surprise than something almost to be expected. Events that seem rare, or at any rate extraordinary, are, Hand convincingly argues, seen on careful thought to be expected... situations ranging from physics to parasensory phenomena in which seemingly inexplicable results are accounted for...



Unlikely events need to be explained, as everything does, but that is not sufficient for a miracle, because miracles cannot be explained with current science.

  • raises the question whether all miracles seem very unusual. I'm guessing so
    – user62133
    Aug 11, 2022 at 10:06

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