13 May 2015

Spotty Maths #1: Freemium

My friend Mark owns 50 CDs. He's gone totally digital now, and is a bit short on cash, so he has decided to sell his CDs in order to buy a new phone. Ten of his CDs are really good and somewhat rare, so he wants to sell those for £12 each. The other 40 CDs are less valuable, so he thinks he will only be able to get £2 for each of those.

Q: Should he only sell the somewhat-rare ones, or should he sell them all?

If he were to only sell the somewhat-rare CDs, he would make 10 x £12 = £120. That's an average of £12 per CD.

If he were to sell them all, he would make an additional 40 x £2 = £80, bringing the total up to £200. But adding these cheaper ones to the mix, results in much lower average of only £4 per CD (£200 / 50).

I would advise Mark to sell them all, because he would end up with more money to spend on his new phone.

But if somebody were to ignore the quantities, actual prices, and total amounts, and only look at the per-CD price, then that person would incorrectly conclude that it's better to only sell the rarer ones, because "that results in a higher per-CD price". But that is simply a bad application of maths.


To apply these maths to streaming services, replace the rare CDs with "premium subscribers", and the others with "free tier users" (1). Offering a premium service results in a certain amount of revenue at a certain per-stream rate. Adding a free tier to that, increases the total revenue, but reduces the average per-stream rate.

The anti-freemium lobby seems to look mostly at the average per-unit revenue. They argue that freemium is bad because freemium services tend to have lower per-stream rates than services without a free tier. But that is not all that matters.

What really matters in this debate is: What would those free tier users have done if there hadn't been a free tier? Nobody knows for sure, because there has always been a free tier. A small group of them would just subscribe to the premium service. But most of them would simply opt for other free services such as YouTube and piracy, which pay even less, or nothing at all, reducing the total income for the music industry.

If the music industry wants to see growth again, they will need to allow freemium models. Those arguing against it are either bad at maths, or may have some hidden agenda.


(1) Freemium users don't pay anything, but they do generate revenue through the advertising they get thrown at them.

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