Why one price for everyone fails
In the previous guides of this rung you learned to find the *overall* rate level — to answer, for a whole book of business, the one big question: are we charging enough in aggregate? The overall indication might say the company needs, on average, 5% more next year. But "on average" hides a problem. A book of auto policies is not one risk; it is a crowd of wildly different risks pooled together — a careful retiree who drives 4,000 km a year and a teenager with a sports car both sit in it. If you charge them the identical premium, you have set a single price for two very different expected costs.
Now watch what a competitor does. If your rival charges *less* than you to the safe retiree (whose true expected cost is low) and *more* to the teenager, the retiree leaves you for the rival and the teenager happily stays. You keep the expensive risks and lose the cheap ones — the very adverse selection spiral you met back in the foundations rung, now playing out through price. Charging differentiated rates is not greed; in a competitive market it is *survival*. Classification ratemaking is the craft of sorting risks into groups by their expected cost and pricing each group accordingly.
Base rates and relativities
How do you actually price dozens of groups without writing a separate study for each? The elegant trick is to pick one group as a reference and express every other group *relative* to it. The reference group's price is the base rate; the multiplier for each other group is a relativity. This is the heart of relativities and base rates: instead of a huge table of standalone prices, you carry one base rate and a small set of factors that say how much *more* or *less* than the base each category costs.
Take a concrete example. Suppose the base rate is 800 for the reference class — say, a 40-year-old driver in a quiet suburb. A youthful-driver relativity of 2.5 means young drivers cost two-and-a-half times the base; a low-mileage discount of 0.85 means careful low-mileage drivers cost 85% of it. The relativity for any single group is, in principle, that group's expected pure premium divided by the base group's pure premium — *cost relative to cost*. A relativity above 1 means "more expensive than the reference"; below 1 means "cheaper." Pick a populous, stable group as the base so the reference itself is well estimated.
Two cautions keep this honest. First, the base rate carries the *level*; the relativities only carry the *shape*. If you re-balance the relativities, you must re-balance the base rate so the overall average premium still matches the indicated rate level — relativities redistribute the pie, they do not resize it. Second, naive relativities computed one variable at a time can lie, because variables overlap: young drivers also tend to drive older, cheaper cars, so a raw "young driver" cost partly reflects *the car*, not the age. The next section is the modern fix for exactly that.
Rating variables, territory, and class plans
The pieces of evidence you use to sort risks are the rating variables. A good rating variable does three things: it *correlates with loss cost* (it really predicts cost), it is *practical* to measure and verify, and it is *socially and legally acceptable*. Age, vehicle type, years licensed, prior claims, coverage limits, and location all qualify in most markets. The full set of variables, the categories within each, and the relativity for every category, written down as a coherent rulebook, is the class plan — the class plan that turns a messy population into a tidy grid of priced cells.
Territory deserves a special word because location is one of the strongest predictors of loss yet one of the noisiest. A single postcode rarely has enough claims to trust on its own, so actuaries group nearby areas into territories that share similar risk — dense urban centres with more collisions and theft, quiet rural zones with fewer. The grouping is itself a modelling decision: too few territories and you blur a real city-versus-country difference; too many and each one is statistical noise. Drawing sensible territory boundaries is a craft of its own, and it leans heavily on the credibility ideas we turn to next.
Credibility steadies thin cells
Slice a population finely and many cells end up nearly empty — a single rare vehicle in a single small territory might have only a handful of policies and one stray claim, or none. Its raw average loss cost is then almost pure luck. This is exactly the problem the credibility rung solved: how much should you trust a thin, noisy estimate? The answer is credibility applied to class rates: blend each cell's own experience with a broader, steadier estimate, weighting by how much data the cell actually carries.
The arithmetic is the familiar credibility blend. The cell's credibility-weighted relativity is Z times its own observed relativity plus (1 minus Z) times a complement — usually the relativity of the broader group it belongs to, or the current rate. Here Z is the credibility factor you met before: near 1 when the cell has plenty of exposure, near 0 when it has almost none. A small, brand-new territory might get Z near 0.2 and so move only a fifth of the way toward its own wild-looking experience; a large, mature class gets Z near 0.9 and is trusted almost entirely. The result is a rate that is responsive where the data is strong and stable where the data is thin.
Tiny class, observed relativity = 1.80 (only a few claims) Complement (its parent group) = 1.20 Credibility Z = 0.25 Credibility-weighted relativity = Z * observed + (1 - Z) * complement = 0.25 * 1.80 + 0.75 * 1.20 = 0.450 + 0.900 = 1.35 The noisy 1.80 is pulled most of the way back to a believable 1.35.
Limits, deductibles, and assembling your price
So far the variables described the *risk*. But two policyholders identical in every risk respect can still buy *different coverage* — a different policy limit, a different deductible — and that too changes the expected cost. The relativity for choosing a higher limit is the increased-limits factor. If a base policy caps liability at 100,000 and a customer wants 500,000, the increased-limits factor multiplies the base premium by, say, 1.4. Note it is well *below* five even though the limit is five times higher: most claims are small and never reach the higher layer, so the extra cover for the rare huge claim costs far less than five times the base.
Deductibles run the other way. A higher deductible means the insured absorbs more small losses, so the insurer's cost falls and the premium drops — the deductible relativity is below 1. How far below comes straight from the loss-modification ideas of the loss rung: a deductible removes the small bottom slice of every loss, and the fraction of total losses it eliminates is the deductible's loss-elimination effect. The relativity factor is roughly *one minus that eliminated fraction*. Choose a 500 deductible that eliminates 18% of losses, and the deductible relativity is about 0.82.
Now everything snaps together into the rating algorithm — the recipe a quoting system runs in milliseconds. Start from the base rate; multiply by each rating-variable relativity in turn; multiply by the increased-limits factor and the deductible relativity; apply any loss cost multiplier that loads in expenses and profit; then add fixed fees. Walk it through: base 800, youthful-driver 2.5, urban territory 1.3, a 0.82 deductible factor — 800 times 2.5 times 1.3 times 0.82 lands near 2,132 before fees. That single number is *your* price, and you can now see it was never one number at all but a product of honest, separately-justified pieces.