# Term for rate of approaching 1.0?

I need to know the accepted term in statistics of a certain concept. What is the term for the following?

When percentages change over some variable like time, it is referred to as a growth rate. But if my percentage is 90%, it will never grow 50% to reach 135%. (If 100% is limiting as if it is infinity.) But if the remainder (like a ones-complement) of 10% is cut in half, then the value can grow from 90% to 95%. What should I call this concept?

## 1 Answer

I don't have a specific answer to your question -- there is no standard way to express changes in percentages. There are several common choices, but none of them is perfect.

Talking about changes in percentages is problematic in a number of ways. The problem you are getting at is fundamentally because probabilities are bounded between 0 and 1, so it is hard to compare changes near 0 and 1 with changes near 0.5.

One option is to express probabilities in terms of log odds (sometimes expressed in decibels). On the log-odds scale, the difference between 0 and 1 is the same as the difference between 10 and 11, which is the same as the difference between 100 and 101 (in the sense that each increment represents the same amount of information).

It takes a while to get comfortable with log odds, and they are not appropriate for all audiences, but they let you avoid some of the awkwardness of working with probabilities.

I wrote more about this topic in a blog post related to interpreting probabilistic predictions: "Why are we so surprised?"