in

The longer it has taken, the longer it will take, Hacker News


Suppose project completion time follows a Pareto (power law) distribution with parameter α. That is, fort>1, the probability that completion time is bigger thantist– α. (We start out time att=1 because that makes the calculations a little simpler.)

Now suppose we know that a project has lasted untilt0so far . Then the expected finish time is αt0/ (α-1) and so the expected additional time ist0/ (α-1). Note that both are proportional tot0. So the longer it has taken, the longer it will take. If the project is running late, you can expect the time remaining to be even more than the expected time before the project started. The finish line is moving away from you!

For example, suppose α=2 (in applications of power laws, α is often between 1 and 3) and you’re measuring time in years. When the project starts att=1, it is expected to take one year, untilt=2. Now suppose you’re starting the second year and the project isn’t done. Now it’s expected to finish att=4, two more years. When you started, the project was supposed to take a year. One year later, it has taken a year, and should be expected to take two more years. I said “should be expected” rather than “is expected” because no one would believe such an estimate. (Ever heard of theBig Dig? Or othermegaprojects?)

Note that we have computed the conditional probability given only the time it has taken so far, andno other information. If you know more, for example maybe you know that some specific pieces have been completed, then you should use that information.

This is related to theLindy effect. The longer a cultural artifact has been around, the longer it is expected to last into the future.

***

For daily posts on probability, follow@ ProbFacton Twitter.

ProbFact twitter icon

Brave Browser
Read More**
Payeer

What do you think?

Leave a Reply

Your email address will not be published. Required fields are marked *

GIPHY App Key not set. Please check settings

What ORMs have taught me: just learn SQL (2014), Hacker News

“Grassroots” anti-Amazon nonprofit turns out to be retailer astroturfing, Ars Technica

“Grassroots” anti-Amazon nonprofit turns out to be retailer astroturfing, Ars Technica