The very Reverend Thomas Bayes, the son of London Presbyterian minister was thought to have been born in Hertfordshire in about 1702. He studied in my own home town of Edinburgh and amongst other things, attempted to prove that the principal purpose of God was to make us despicable human souls happy. What has the good Reverend got to do with birding I hear you ask? Well, allow me to explain in a rather roundabout manner:

Today I was seawatching from Bass Point. Shortly after securing cracking views of my first ever Great Shearwater from the Lizard, I observed a petrel for about 2 mins as it flew past relatively close. Detailed description aside, to all intent and purposes, it looked like a Wilson’s Petrel. In fact, based on its appearance, I was about 99% confident it was one. The trouble is, being 99% confident of ID, doesn't mean there’s a 99% probability it

**actually**was one, simply because the obvious confusion species, European Storm Petrel, heavily outnumbers Wilson’s. I don’t know the true figure, but let's say, for the sake of argument, by about 100 to 1. Well, it so happens that the good old Reverend Thomas Bayes came up with a formula for working out this problem, although I don’t think he was thinking about birds when he did. For the mathematically minded, the formula is as follows:Probability of rare bird = probability of ID x probability of it being one based on numbers / (probability of incorrect ID) x probability of it not being one based on numbers + probability of correct ID x probability of it being one on numbers).

That entire complicated math leads me to the rather unfortunate conclusion that it there was a 49.7% chance it was one. Less than 50%! Indeed if I factor in a bit of false expectation due to the fact I’d just seen a Great Shear and the conditions were spot on (say 95% confidence with ID) and we allow European’s to outnumber Wilson’s by 200 to 1, then the figure drops to a woeful 8.7%.

Of course, all of this doesn’t matter one bit if one is certain of identification, but it does get you thinking. I wonder how often the rarities committees take such probabilities into consideration? I suppose they do qualitatively, as mega rare birds increasingly require mega good evidence, but it’s rather worrying that even if one is 99.9% confident with identification of a bird that is outnumbered 1000 to 1 by its potential confusion species, the chances of it actually being one are only 50:50.