Question

Given the following dataset for a single article on my site:

Article 1
2/1/2010 100
2/2/2010 80
2/3/2010 60

Article 2
2/1/2010 20000
2/2/2010 25000
2/3/2010 23000

where column 1 is the date and column 2 is the number of pageviews for an article. What is a basic velocity calculation that can be done to determine if this article is trending upwards or downwards for the most recent 3 days?

Caveats, the articles will not know the total number of pageviews only their own totals. Ideally with a number between 0 and 1. Any pointers to what this class of algorithms is called?

thanks!

Answer 1

update: Your data actually already is a list of velocities (pageviews/day). The following answer simply shows how to find the average velocity over the past three days. See my other answer for how to calculate pageview acceleration, which is the real statistic you are probably looking for.

Velocity is simply the change in a value (delta pageviews) over time:

For article 1 on 2/3/2010:

delta pageviews = 100 + 80 + 60 
                = 240 pageviews
delta time = 3 days

pageview velocity (over last three days) = [delta pageviews] / [delta time]
                                         = 240               / 3
                                         = 80 pageviews/day

For article 2 on 2/3/2010:

delta pageviews = 20000 + 25000 + 23000 
                = 68000 pageviews
delta time = 3 days

pageview velocity (over last three days) = [delta pageviews] / [delta time] 
                                         = 68,000             / 3
                                         = 22,666 + 2/3 pageviews/day

Now that we know the maximum velocity, we can scale all the velocities to get relative velocities between 0 and 1 (or between 0% and 100%):

relative pageview velocity of article 1 = velocity / MAX_VELOCITY
                                        = 240      / (22,666 + 2/3)
                                        ~ 0.0105882353
                                        ~ 1.05882353%

relative pageview velocity of article 2 = velocity      / MAX_VELOCITY
                                        = (22,666 + 2/3)/(22,666 + 2/3)
                                        = 1
                                        = 100%