Pop chart gravity

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\"The song flew up the chart, before returning rapidly to earth\". Gravity is often used as a metaphor for success, in everything from pop music and sport to business and academia. When things are going well we are \"flying\". When things are going badly we \"crash\". But how literally should we take this metaphor?

Plotted above are the Billboard Hot 100 rankings of ten successful songs taken from the last 60 years. Click on the song names (try here if you have problems with the application ) and see how they climbed the charts. The circles show the songs\' weekly chart positions over a period of 30 weeks. Some of the songs rise and fall rapidly, like the Christmas one hit wonder \"Chipmunk song\", others climb and fall slowly, like Jason Mraz laid back hit, \"I\'m Yours\", from a few years ago.

We used a simple model of gravity to quantify these differences between songs. If you throw a ball up in the air its path is determined by three things: the initial height you throw it from; the initial speed with which you throw it; and the gravitational pull. The same is true for a pop song. The record companies try to throw songs into the chart as high as possible and with as much upward momentum as possible. We, the consumers, then decide the gravity. Using this model we determined the initial entry position, the velocity and gravity for the ten songs above by fitting gravitational curves to the data. The model curves are shown by the animated solid line.

Different songs take different paths. Dancing Queen, Take on Me, Eternal Flame and Like a Prayer are classic examples of hit songs in the 70\'s 80\'s and early 90\'s. They start low, but climb rapidly, with velocity of between 14-17 places per week, before gravity takes them back down again. Since around 2000, with the introduction of ITunes and then streaming, the gravity of big hits has been reduced. They vary greatly, depending on the hype surrounding them, in their entry position but often have very low gravity. It seems the youth of today have a much higher tolerance for hearing the same song over and over again than those of us who grew up in the 70s, 80s and 90s. Jason Mraz and Coldplay have only one tenth of the gravitational pull of Madonna.

These results are part of a study that myself and Henrik Vallgren have done on pop music over the last 60 years. In a future blog post I will give a fuller analysis of how the dynamics of all chart songs has changed over the last decades. In the meantime, if you leave the name of your favourite song and artist in the comments, along with a good motivation, I\'ll make a new version of the above web app including the most popular choices.

Model

Each song has a position p (t ) and a velocity v (t ) . Both are functions of the number of weeks in the chart, or time, t. The position changes as a function of velocity

p(t+1)=p(t)-v(t)

and the velocity changes as a function of gravitational pull

v(t+1)=g

These are a discrete time version of the kinetic equations of motion for a single particle with constant acceleration g.

Each individual song has its own entry position, p (1 ), velocity p (1 ) and gravitational pull g. These are estimated by quadratic regression of the change of the song through time.