It's obvious when you think about it. Artists get paid per stream but users only pay per month. When someone listens to more streams than they have paid for, the money has to be taken from someone who has listened to less streams than they paid for.
I listen to say 1,000 songs a month on Spotify, at $10 a month royalties that’s 1c per song. If I listen to song K 10 times I would think they’d get 10c from me, but they don’t neccersarilly - it might be 1c, it might be $1.
There’s a sad effect - if I listen to 2 hours of Band A and 3 hours of Band B, but Band A has an average track length of 2m and Band B has a length of 4m, Band A would get more than Band B!
You need a per user second rate (Calculated monthly), applied to the streams they actually listened to on a per second basis. Yes, it is a large calculation, but simple compared to most ML problems.
That would be 1 cent per 108 seconds, so listen to an 8m35 version of American Pie and Don McLean gets 4.75c. Listen to Heartbreak Hotel, 2m08, and Elvis gets 1.18c. Listen to a 1 hour podcast of "The Infinite Monkey Cage", and the BBC get 33.3 cents
If you listen 24/7, or 2,592,000 seconds a month, then your $10 means that Elvis gets a mere 0.05c
You calculation are bang on. Elvis getting a mere 0.05c seems fair in the case of this super user when the user needs a flat rate to consume and all the content providers need to be fairly compensated. If this doesn't seem fair then your issue is with the flat pricing per user per month. Which, without this, I'd bet the pie is much smaller.