When will the b-day be?

Like other first-time parents entering week 40, I am getting increasingly anxious to meet my little man. Our son is "due" on April 25 — one week from today — but the reality is that his birth is not something for which you can plan. As convenient as it would be, I won't receive a calendar invite from the womb (with a 0-minute reminder, of course) with detailed instructions on how to get to the hospital sans police. The fact of the matter is, we just aren't that great at predicting birth days yet (every birthday celebration after that is pretty straightforward).

Despite the difficulty in making precise predictions, my wife and I are really interested in knowing when our baby will be born. Will it be tomorrow? What about the day after that? Fortunately, there is some data out there that can shed some light on these questions.

Considering that there are significant physiological differences between first-time and repeat mothers, I restricted my analysis to only those mothers that had zero previous births. To properly account for the fact that we also know that our baby has not been born yet, I further restricted my analysis to all births that happen beyond the start of week 40. I then calculated the probability that our baby will be born on any particular day:

Although this doesn't tell us the precise date during which our baby will be born, it definitely gives us more information about when we can expect to be parents. For the next few days, for instance, we're flipping a weighted coin with a 4% chance of landing heads (baby born) and a 96% chance of landing tails. Eventually, given enough chances, we are bound to see a head (pun intended).

For those that find this interesting and/or useful, I've been toying around with creating an interactive version of this for others to use — perhaps as a paternity leave project? — so if anyone else is interested in using something along these lines, leave us a comment or suggestion below.