relativities and base rates

Picture a price list built like a recipe: one starting amount, then a series of multipliers for who you are and what you have. The starting amount is the base rate — the price for a reference 'plain vanilla' risk. The multipliers are the relativities — numbers above or below 1 that scale the base up for riskier characteristics and down for safer ones. Together they let one compact table price thousands of different customers.

The base rate is the rate for the base class, the chosen reference level of every rating variable (for example, a middle-aged driver, average territory, standard vehicle). A relativity of 1.00 means 'same cost as the base'; 1.30 means '30 percent more expensive'; 0.85 means '15 percent cheaper'. A customer's premium is the base rate times all the relativities that apply to them (in a multiplicative plan), so base rate 500 with relativities 1.30 and 0.90 gives 500 × 1.30 × 0.90 = 585. Relativities are usually estimated from data — historically by simple one-way loss-ratio or pure-premium comparisons, now more often jointly by a generalized linear model — and then often tempered by credibility before being adopted.

Separating the base rate from the relativities is a tidy and powerful idea: you can change the overall price level by moving one base rate, and change the fairness between groups by moving relativities, without rebuilding everything. But two cautions. First, the base rate and the relativities are entangled — change which class is the 'base' and the relativities all rescale, even though every customer's final price is unchanged (an off-balance correction keeps the average premium on target). Second, relativities estimated one variable at a time can double-count correlated effects, which is why joint estimation matters.