Number of Unique Song Choices on Desert Island Discs

Desert Island Discs celebrates its 75th birthday today, and today’s guest is David Beckham. Beckham will pick 8 song choices to take away with him on a desert island. What I wondered was, will all of his song choices have been picked by guests previously? With over 3,000 episodes there are going to be a lot of repetitions.

Obviously the very first guest, Vic Oliver had to pick 8 unique song choices. There was no one before him! The second guest, James Agate also picked 8 unique choices (they were all different to Vic Oliver’s). This continued until the 8th guest, Joan Jay, who only had 7 unique choices (she picked Ave Maria by Charles‐François Gounod the same as Pat Kirkwood). A quick scrape of the BBC 4 webpage gives us all of the song choices of each of the guests. Plotting the data as a histogram of ‘unique’ choices leads to a not unsurprising result:

On average a castaway picks 3 unique choices, but really anything between 2 and 5 unique choices is quite probable. Picking 0 unique choices (~100 out of 3096 castaways) and all (8) unique choices (~50 out of 3096 castaways) is not very likely. The thing that is rather interesting though is if you look at the number of unique choices as a time series:

The data is obviously very noisy, with 0 and 8 unique choices scattered throughout the time series. But there is a clear trend. I’ve fitted a curve (least-squares) to the data and the results hopefully become clear. There was a decrease in the number of unique choices from the start of the show down until the mid 1980s, and since then there has been an increase again! I would guess that this has something to do with the explosion of popular music, the early choices are dominated by “famous” classical music pieces, but this has decreased over time.