#### Starting the Taper: Prepping for the Portland Marathon

September 22, 2015

# Running and Statistics: A 4th Grade Perspective

As I write this, it’s a sunny, late September Tuesday. I completed a run shortly before picking my son up from school. On the drive home, he asked a few questions about his math homework. The class is learning about estimating and rounding.

One question read, “In the 2010 New York City Marathon, 42,429 people finished the race and received a medal. Before the race, the medals had to be ordered. If you were the person in charge of ordering the medals and estimated how many to order by rounding, would you have ordered enough medals? Explain your thinking.”

My son wanted to know what I thought. Hmm. Tricky question. As it stated, only the finishers are given medals. But how many would actually finish? How could you know that before the race had started? The question didn’t note how many had registered for the race. That would have been helpful, as I’m fairly certain for every paid registration, a medal is ordered for that possible finisher. Again, something not covered in the question.

So I commented that the race organizers would at least know how many people had registered and that would probably be more than the number who actually finished. His answer — and disclaimer that his father is a runner — is priceless. ðŸ™‚

I started thinking about an equation to actually calculate projected medals. There are a few moving parts and uncertainties here, of course. Looking at the past four years of people who registered (r1, r2, r3, r4) and dividing each by the actual finisher counts (f1, f2, f3, f4), summing and diving that by 4 for the average of all four years, then increasing that count by 5%, you just might have a sense for what this year’s numbers could look like (before registrations are all counted), plus a little padding:

`m = (r1/f1) + (r2/f2) + (r3/f3) + (c4/f4))/4 * 1.05`

Other variables are all the last-minute registrations, whether it’s already sold out, if the medals have to be ordered well in advance… and the kinds of beer (and hopefully, cider) that would be served in the beer garden afterwards. You know, the things that matter.

I did say this blog would be about more than just running. ðŸ˜‰

– David