Rescale a Probability to a Different Chance Level

Converts a probability or accuracy value from one chance-level scale to another while preserving the same chance-relative performance.

Usage

rescale_chance(p, chance.old, chance.new)

Arguments

p

Numeric vector. Observed probability or accuracy values on the original scale. Values must be between 0 and 1.

chance.old

Numeric vector or scalar. Original chance-level probability. Values must be greater than or equal to 0 and strictly less than 1.

chance.new

Numeric vector or scalar. New chance-level probability. Values must be between 0 and 1.

Value

A numeric vector of probabilities rescaled to the new chance level.

Details

The transformation first computes chance-relative performance:

$$ r = \frac{p - chance.old}{1 - chance.old} $$

and then maps it onto the new chance-level scale:

$$ p_{new} = chance.new + r(1 - chance.new) $$

Equivalently:

$$ p_{new} = chance.new + \frac{p - chance.old}{1 - chance.old}(1 - chance.new) $$

This preserves the relative distance between chance and perfect performance.

Examples

rescale_chance(0.60, chance.old = 0.5, chance.new = 0.2)
#> [1] 0.36

p <- c(0.55, 0.60, 0.70)
rescale_chance(p, chance.old = 0.5, chance.new = 0.25)
#> [1] 0.325 0.400 0.550