More Bell Curve Bollocks

 As will have been long apparent, my preferred approach to this blog is to write any old rubbish and then forget it, on the basis that no one reads it anyway. Occasionally this backfires, such as in the case of my recent post about dominos as a means of determining initiative in Piquet. I have been asked if I can justify my assertion that the result follows a normal distribution. In particular, the question was asked as to what specifically I was referring: the winner's initiative, the loser's initiative or the difference between the two? A reasonable question.

Well, the results of drawing a single domino and adding the pips follow a normal distribution. If both sides did the same then subtracting one from the other would be the difference between two independent normal distributions, which would also be a normal distribution. So far so good. But apart from the initial drawing of the dominos that's not actually how we allocate initiative. Even more importantly, what we do with the results of the draw renders the probabilities of the winner's and loser's respective initiatives non-independent. So, the answer to the question is: no, I can't justify it.

The author Michael Green wrote a series of books called 'The Art of Coarse Acting', 'The Art of Coarse Rugby' etc. He never got round to 'The Art of Coarse Mathematics' for some reason (*), but had he done so then I'm sure that he would have drawn the attention of readers to two cop-out phrases beloved of mathematicians who either can't or don't want to work everything out in detail: 'by inspection' and 'result follows'. Therefore, by inspection I'm going to assert that, under our methodology, both initiatives have a right-skewed distribution with the mean being higher than the mode. As for the net initiative - who knows?

This correspondence is now closed.

* I should point out that in geometry and topology 'coarseness' is a real and important concept