Bayes' Theorem and the VMA's Were Outrageous (Again)

The VMA's were outrageous?!?

Well, if the media is to be believed, the news of the day was that it was an outrageous Video Music Award show.

Not true and true. Yes - the show was outrageous, no – it wasn’t news. 

Let me explain. News is noteworthy, significant, and new. It changes your perspective, it is unusual. 

If a fish swims in a fish tank all day and doesn’t drown it isn’t news because it happens all the time. But, if that same fish were to send text messages on a waterproof smartphone that would be news because that is something you don’t see every day. 

The VMA's were outrageous and the VMA's were always outrageous. The only way for them to be newsworthy anymore is if they were NOT outrageous.

The math behind this is pretty simple, it is called Bayes’ Theorem and it goes like this:

VMA.1VMA.2Now to estimate the probabilities let’s devise a model of MTV's programming. For our model we will say that MTV has three different types of shows (represented as circles in the figure below), videos (represented as triangles), reality TV shows, and award shows (represented as squares), and that some of the programming is outrageous (shaded in red) and some of the programming is not outrageous (not shaded).

 VMA.3We are now in a position to calculate the probability that show was going to be outrageous (Event A) given that it was an awards show (Event B). By inspection we can see:

VMA.4That is, based on our assumptions there was a 100% chance that the VMAs were going to be outrageous. Now admittedly the assumptions in our model are wildly off the mark, and Bayes’ Theorem is generally used for much more challenging calculations like what is the probability that someone actually has a disease given that they have tested positive for it, or how should an assessment of risk change based on the number accidents observed, but these applications can wait for another day and another blog post. 

Today, it is enough to simply observe that the VMAs were outrageous, and that is not news.