Not fashionable, but Gompertz curves: https://en.wikipedia.org/wiki/Gompertz_function https://en.wikipedia.org/wiki/Gompertz_function Originally used to model

Not fashionable, but Gompertz curves: https://en.wikipedia.org/wiki/Gompertz_function https://en.wikipedia.org/wiki/Gompertz_function Originally used to model the growth of stable populations. I found that it is perfect for things like spam/abuse timeouts. The function has a couple of tunable parameters for things like the amplitude and steepness of the curve and the x-offset. Once those are dialed in as you like, you get a really nice function for measuring and responding to abuse.