The randomness of iTunes

In 1998, a rather awkward 25-year-old male walked into a CD store (this was in the day when music was sold on CDs, in stores, to 25 year-olds) and purchased Whitey Ford Sings the Blues by Everlast.  Here’s what the indubitable Wikipedia has to say about said album and artist

Whitey Ford Sings the Blues was both a commercial and critical success (selling more than 3 million copies).  It was hailed for its blend of rap with acoustic and electric guitars, developed by Everlast together with producers Dante Ross and John Gamble (aka SD50).  The album’s genre-crossing lead single “What It’s Like” proved to be his most popular and successful song, although the follow up single, “Ends”, also reached the rock top 10.

Several years later Apple launched iTunes, which also proved to be a commercial and critical success, and the awkward male promptly loaded Whitey Ford Sings the Blues into the song library.  iTunes seemed to take a particular shine to this album, apparently favouring it with many more frequent plays, when iTunes was set to “shuffle”, than any of other 100 or more albums in the collection.  At least that’s how it appeared to the awkward male, who seemed to notice it come up much more often than expected.

In a strange twist of fate I also just happen to have Whitey Ford Sings the Blues in my iTunes collection.  In another strange coincidence, just like that awkward male from a decade ago, I’ve noticed that iTunes tends to favour it over other albums in the song list when iTunes is set to shuffle.

Life is certainly full of strange coincidences, but does iTunes really favour certain songs/ artists/ albums over others?  Let’s test it scientifically…

I set iTunes to shuffle and counted the number of tracks I had to skip before I hit Whitey Ford Sings the Blues.  The results are below:

32, 65, 181, 67, 77, 152, 50, 46, 230, 64

In other words, Whitey Ford Sings the Blues played randomly 10 times in 964 attempts (i.e. 1.037% of the sample).  I have 119 albums in iTunes, so theoretically I should be hearing it 1/119=0.840% of the time.  So the sample is a little bit higher than expected, but statistically significantly higher?

This question can be answered using the probability mass function of the Binomial Distribution.  The probability of exactly 10 “successes” out of 964 “attempts”, given that the probability of a success is 1/119 is, using the very fine SpeedCrunch calculator:

binompmf(10; 964; 1/119) = 0.102 (i.e. 10.2%)

This is well above the standard p=0.05 (5%) significance level.  I have to conclude that Whitey Ford Sings the Blues doesn’t play any more or less frequently than any other album in my iTunes collection when the playlist is set to shuffle.

Humans are very bad a gauging randomness.  Or rather, probably like most predators, we’re very good at detecting patterns, and tend to see patterns when they’re not really there.  Luckily we have statistics to sort it all out for us.

And Whitey Ford Sings the Blues is still an awesome album.