### Introduction

Back in 2010 I wrote a short article on the **logistic** (‘S’) curve in which I described its theoretical justification, mathematical properties and relationship to the Wilson score interval. This observed two key points.

- We can map any set of independent probabilities
*p*∈ [0, 1] to a flat Cartesian space using the inverse logistic (‘logit’) function, defined as- logit(
*p*) ≡ log(*p*/ 1 –*p*) = log(*p*) – log(1 –*p*), - where ‘log’ is the natural logarithm and logit(
*p*) ∈ [-∞, ∞].

- logit(
- By performing this transformation
- the logistic curve in probability space becomes a
**straight line**in logit space, and - Wilson score intervals for
*p*∈ (0, 1) are**symmetrical**in logit space, i.e. logit(*p*) – logit(*w*⁻) = logit(*w*⁺) – logit(*p*).

- the logistic curve in probability space becomes a