Baloney Detection 101: Probability

Most people have a very poor intuitive grasp of mathematical probability, and this can more often than not lead us to formulate erroneous conclusions regarding how likely some things are to happen. A good example of this is the so-called Birthday Paradox: What do you think is the likelihood of any two people in a gathering of 23 or more sharing the same birthday? The answer is: more than 50%. In this case, though the result seems counterintuitive, it is the math, not our intuition, which is correct. This becomes apparent when you actually do the math, and it then makes much more sense.

There is a thing in statistics called the Law of Truly Large Numbers, and a failure to take this into consideration results in the commission of the Lottery Fallacy, or Argument from Probability, such as the argument that the chances of winning the lottery twice in one’s life have odds of over trillions to one, which when you do the math it actually turns out that the chance of this happening to just anyone is more like 1 in 30, as most lottery players buy more than one ticket per game. The same happening to any specific individual who only bought two lottery tickets, one for each lottery, would be highly unlikely.

Simply put, the Law of truly large numbers states that truly incredible coincidences can and do happen quite often in a large enough sample size. For example, in a city of ten million or so, a 1 in 10 million coincidence is likely to happen every day. One of the numerous reasons that I don’t believe in genuine psychics is the fact that statistically, at least one of them should have been able to predict the horrific events of September 11, 2001 so that lives could have been saved, but not one psychic came forward with a warning. The ‘psychics’ were just as clueless as we mere muggles.

Probability, or rather, misunderstanding of it, is essential for many cold reading techniques used by psychics, as they depend on their marks to misjudge the likelihood of their hitting upon the correct guess during the reading, which they are often, even if sincerely believing in their own ‘powers,’ very successful at. The lottery fallacy is also used by creationists, when they use seemingly impressive figures to ‘prove’ the unlikelihood of life arising and evolving by natural causes, such as stating that the chances are 1.0×10^50,000 to 1, or somesuch. The thing they don’t mention is that this, aside from the fact that the numbers are just made up arbitrarily, only describes the chances of life coming about and evolving as it is now, when the chances of life arising and evolving any way at all are far greater.

Of course I’m not going to let the parapsychologists off the hook either, for they are occasionally prone to using flawed statistical analyses in their studies, often claiming, for example, that the probability of getting such-and-such a score in a study is astronomically unlikely to be due to the vagaries of chance and therefore must be due to a paranormal agency, while themselves not understanding the difference between statistical significance well within what is predicted by the laws of chance, and scientific importance. This is not only the use of lottery fallacy, but the Texas Sharpshooter Fallacy, Affirming the Consequent, and Begging the Question, i.e, assuming what they should be proving. There’s a reason that statistics has its own branch of mathematics: it’s a much-needed tool to help us with what we are inherently bad at, so we don’t remain that way if and when we bother to learn.