Saturday, January 26, 2013

Position, Velocity, & Acceleration as Web Analytics Metrics

As Isaac Newton was seeking to describe gravity and explain his Laws of Motion, he understood that he needed to do so in terms of position, velocity, and acceleration.[1]  Calculus was born to give us the derivative.  The derivative of position is velocity, and the derivative of velocity is acceleration.  The Fundamental Theorem of Calculus tells us the integral can take us in the other direction, from acceleration to velocity to position.[2]

Before your eyes glaze over I will quit the calculus talk, but a little history and context is always a good thing.  So how do we incorporate history and context into a static metric, like page views?  What if we want a simple dashboard with easily recognizable metrics?  Page views seem like a good candidate.  Imagine our dashboard indicates 357 page views.  Is that good or bad?  “It depends” should be your answer.  It depends on how many we had in the period before.  What if we had 342 before that one?  Well it still depends.  Maybe even on the period before.  Is our increase in page views growing at an increasing rate, or a declining rate?  This can be indicated by velocity.  

If one were to look at the blue line (position could be page views or something similar), it might be interpreted as things are good.  But are they?  If we look at velocity, we can see that our rate of growth has decreased.  This is important to notice and the velocity metric is more responsive to movements trended behavior.  Acceleration increases this responsiveness.  Maybe we made changes to a website, and notice the velocity is flat, but positive.  Our page views would continue to increase and we could mistakenly assume that the changes were good. [3]

My last post was on dashboards.  The next will be on incorporating predictive metrics into the dashboard in order to compare actuals with a trended projection.  This post will serve as the bridge.  Incorporating velocity as a metric on the dashboard serves to identify trends in the movement of variables.  

Looking at a static metric, like page views, would be like using your odometer to drive while ignoring the speedometer.  This seems crazy to us.  We actually use the speedometer, and mostly ignore the odometer.  The speedometer provides an instantaneous velocity.  Of course we are not observing our speedometer in relation to time, we are only glancing at an instant to answer a few questions.  Am I going to be on time?  Am I going too fast?  By measuring velocity over longer time periods ( 12 hrs, day, week,..) we can reduce volatility and find a more meaningful metric that better depicts trending within the underlying data.  

This topic is much broader than web analytics.  ( This philosophy and reason could also apply to sales, losses, employee turnover, and really any metric in which the data results in a number that usually moves around over time.  We use velocity in order to quickly discern trending.  It is not the only way to do this but is a great compliment to important dashboard metrics.

1 Newton, Isaac Principia