The Dirkmaat Constant

Having spent time here in Disney World, I have learned two absolutes:

1)It doesn’t matter when you come, there is no “down” season.  It’s always going to be packed

2) There will be lines for everything, but nothing will make you wait longer than the bus

The Poisson Distribution is an important tool to describe the discrete probability of events when the average occurrence rate is known.  In other words, if you know the average occurrence of an event over a period of time, Poisson posited that one could also know the probability of each number of occurrences of that event.

So, if we know that, on average, 2.5 people will try to board a bus every second here in Disney World, then the probability that zero people will try to board a bus in the next second would look like this:

e^(-2.5) × 2.5^0 / 0!

= 0.082 × 1 / 1 (2.5^0 = 1 and 0! = 1)

= 0.082

Alternatively, the probability that four people will board a bus:

e^(-2.5) × 2.5^4 / 4!

= 0.082 × 39.063 / 24

= 0.134

So, the Poisson Distribution is able to effectively predict the probability of someone boarding a bus in the next second at Disney World.  An equally important tool in understanding behavior here at Disney is the Dirkmaat Constant, which posits, for every person that boards a bus here in Disney World, the probability that it will take too long and Paul will mutter something sarcastic is constant at 1.0.