Credibility in pricing: how insurers rate small groups and new models

When a group of drivers or cars is too small to price from its own claims, actuaries give that group's experience a weight between 0 and 1, called its credibility, and fill the rest of the price with experience from a larger, similar group. A territory with few drivers is blended with its neighbors, a brand-new model starts from its sticker price and industry data, and a new insurer starts from industry loss costs. As the group's own data grow, its weight rises and the blend shifts toward what the group has actually done.

This article explains the idea in plain terms, works through a small-territory example with invented numbers, shows what happens when one large claim lands in a small group, describes how a rate filing documents the blend, and sets out the main criticism of the practice.

The small-numbers problem

Insurance pricing relies on the law of large numbers: with enough similar, independent exposures, observed results settle close to the true underlying cost. The Casualty Actuarial Society's text Basic Ratemaking (fifth edition, 2016) says exactly that, and then notes that the volume of data used for rates "may not always be fully sufficient to produce accurate and stable rates," so the actuary can supplement it.

Here is the intuition. Suppose a small group is expected to have about 10 claims a year. Claims arrive randomly, so a swing of three claims in either direction, from 7 to 13, is ordinary luck, not a change in risk. That is a 30% swing in the group's loss total from chance alone. If rates followed each year's result, the group's price would bounce up and down with luck. Credibility is the tool that damps the bounce without ignoring real signal.

How partial credibility works

The CAS text gives the standard formula. The estimate for the group equals Z times the group's own observed experience, plus (1 - Z) times related experience, where Z is the credibility. The related experience is called the complement of credibility.

Z must be between 0 and 1, it should rise as the volume of data rises, and it should rise at a decreasing rate. The most common method, classical or limited-fluctuation credibility, sets a standard for full credibility (Z = 1) based on the number of claims. Below that standard, the square root rule applies: Z equals the square root of (claims observed divided by claims needed for full credibility).

The standard depends on how precise you want to be. The CAS text gives an example: to be 90% sure that observed experience is within 5% of its expected value, about 1,082 claims are needed. Other choices change the answer, and the text lists 271 claims for a 10% tolerance at 90% confidence and 2,652 claims for 5% at 99%. These are illustrations of how the standard moves, not an industry rule.

Using the 1,082-claim standard, credibility rises with claim counts like this:

Because of the square root, you need four times the claims to double the weight, which is why small groups stay mostly "complement" for a long time. A second approach, Bühlmann credibility, uses Z equals N divided by (N + K), where K reflects how much risk variance there is within groups relative to between them. It approaches 1 gradually and never quite reaches it.

A worked example: a small territory

These numbers are invented. A territory has 15,000 car-years of exposure. Over the experience period it produced 120 bodily injury liability claims totaling $3,300,000. A car-year is one car insured for one year.

1. The territory's own pure premium (loss cost per car-year) is $3,300,000 / 15,000 = $220.
2. The statewide pure premium for similar drivers is $190. That is the complement.
3. Credibility is the square root of (120 / 1,082), which is about 0.333.
4. The blended estimate is 0.333 x $220 + 0.667 x $190 = about $200.

The territory's own claims say it costs 16% more than the state ($220 against $190). The blend says 5% more ($200). If the territory really is riskier, it will take time for the price to say so. If it just had a bad stretch, the blend protects it from a swing it did not earn. That trade-off is the whole point.

What the group gets blended with

The choice of complement matters at least as much as Z. The CAS text, drawing on a 2004 paper by Boor, lists six common choices for personal auto and other first-dollar lines:

• Loss costs of a larger group that includes the group being rated. An example from the text: using all drivers aged 16 to 19 to supplement the data for 16-year-olds.
• Loss costs of a larger related group.
• The rate change indicated for a larger group, applied to the subject group's present rates.
• A method named for Harwayne that adjusts other states' data for cost-level differences.
• The group's own present rates, trended forward.
• Competitors' rates.

The text lists desirable traits: the complement should be accurate, unbiased, independent of the group's own data, available, easy to compute and logically related to the group. It also warns that when the data are thin, the complement can drive most of the answer.

New vehicle models

A model that has just launched has no claims history. Verisk, which publishes the Vehicle Series Rating symbols many insurers use, explains in an FAQ on ISO symbols how it sets them. For physical damage (collision and comprehensive), it starts with a preliminary "price-new" symbol based solely on the manufacturer's suggested retail price, then adjusts the symbol up or down using actual loss experience for the vehicle's series. For liability and PIP or medical payments, it combines actual loss experience with a predicted relativity from a model that uses factors such as curb weight and chassis type. Symbols are advisory; insurers may use them, modify them or not use them.

In credibility terms, the price of a new model rests almost entirely on its complement, which is the loss experience of vehicles with similar prices and physical traits, and shifts toward its own claims as they accumulate. Verisk explains that two vehicles with similar sticker prices can end up with different symbols because of differences in theft appeal, collision involvement and repair cost. See vehicle symbol and how a redesign changes a car's insurance rating group and your premium for how a redesign resets the process.

New and small insurers

An insurer with no credible history of its own has to start from someone else's. Verisk describes its advisory loss costs as projections of average future claim costs and loss adjustment expenses, built from its database, as a benchmark an insurer can combine with its own data. In its product sheet (2019), the company calls its database the world's largest and most credible set of insurance statistics, which is marketing language, and says the loss costs are submitted to state regulators for review. See Verisk (ISO) advisory loss costs: the data behind many insurers' rates.

California's rules show what regulators accept. Under 10 CCR 2632.9(b), for class plans filed more than three years after the regulation took effect, an insurer may use only one of these for each rating factor: its own data; its own data plus a single alternative source of primary data; a single alternative source such as an advisory organization; the indicated relativity from another insurer's approved plan with a similar book of business; data published by the Department of Insurance; or Department data combined with its own. An earlier subsection let insurers without credible data use several of these sources in a declared order of priority during the regulation's first three years. See California for the state's rating framework.

Small territories and their neighbors

Geography is a particularly sparse kind of data. The CAS text says companies typically define territories as groups of small units such as postal codes, counties or census blocks, and that because those units are small, the data in each is thin, a problem that calls for special multivariate techniques. It describes spatial smoothing, which improves the estimate for one unit by weighting in nearby units. Distance-based smoothing, it notes, ignores whether a river or highway separates two areas and treats a mile as the same everywhere regardless of urban or rural setting, and it says the approach suits weather-related perils best.

California's rule is more concrete. Under 10 CCR 2632.5, the optional claims frequency and severity factors, each limited to 20 categories, group ZIP codes or census tracts with similar average claims, and where ZIP or tract data are not fully credible the insurer follows the adjustment process in section 2632.9(d). That section sets a fallback ladder: use census tract data if credible, otherwise ZIP code data; if the insurer's own ZIP code data are not fully credible, use the frequency and severity published in a Department manual directly or to credibility-adjust the insurer's own data; and if the combination is still not credible, use as the complement either the rate for the territory of the state's assigned-risk plan that contains the ZIP code, or the experience of a larger, fully credible group of contiguous ZIP codes that contains it. For how ZIP code affects your own price, see Why your ZIP code changes your car insurance price and territory rating.

When a small group has a large claim

A single large claim can swamp a small group's year. The CAS text calls these shock losses and says that if they are included as-is, indicated rates may jump right after a year with a shock loss and fall when there is none, especially for smaller portfolios. The typical remedy is to cap each claim at a threshold, such as the basic limit or a high percentile, and spread the excess across all policies as a loading based on a long-term average.

Continue the territory example, still with invented numbers. In the next period the territory has the same 120 claims, but one of them is a $400,000 injury claim in place of a typical $27,500 claim. Total losses rise to $3,672,500.

Without credibility the territory's price would have jumped 11%, from $220 to $245. Credibility holds it to about 4% uncapped and about 1% capped. The $300,000 above the cap does not disappear. In a real plan it would be pooled into a loading across the whole state.

How a rate filing documents credibility

In many states rate filings are public records, and the CAS text notes that the actuary must be able to justify methods to a third party such as a regulator. When you read an actuarial memorandum or exhibit, you can look for these typical elements, though format varies by state and insurer:

1. The credibility standard. Is it stated in claims or exposures, and at what confidence and tolerance?
2. The credibility values used. Does Z appear by coverage, territory or class?
3. The complement. What is the source: a countrywide average, industry loss costs, prior rates, a larger region?
4. Treatment of large and catastrophe losses. Are claims capped and loaded back?
5. The time period. How many years of data back each number?

See How to read a car insurance rate filing on SERFF for how to open a filing and where these exhibits sit. Whether and how a state requires this disclosure differs, and your state insurance department can tell you what is public.

The criticism that blending hides differences

Credibility blending is standard practice, but it has real costs.

The complement is biased by design. The CAS text observes that the actuary split the subject group out of a larger group because the group was believed to be different, so the larger group's experience is likely a biased stand-in. A very safe neighborhood is priced closer to the average than its real risk justifies until its own data catch up; a very risky one is under-priced until then. The text suggests adjusting the complement to reduce bias, but that adds complexity.

Smoothing makes assumptions. As noted above, distance-based smoothing may ignore barriers and urban-rural differences.

Territory is contested. In an April 2017 analysis, ProPublica and Consumer Reports compared liability premiums with average payouts by ZIP code in four states and found that many insurers charged more in majority-minority ZIP codes than in comparably risky majority-white ones. California's insurance department called the method flawed and Illinois's called it incomplete, and some insurers said their rates reflect local conditions such as congestion, crime and theft and are approved by regulators. See ZIP-code pricing and racial disparities: what investigations found. The dispute is about territorial rating in general, not credibility specifically, but any blending method sits inside it.

Data access. ProPublica noted that insurers do not publicly release ZIP-level loss data, and that only four states provided it when asked. Outsiders therefore find it hard to test whether a blend is fair.

States respond in different ways. California limits the number of geographic categories and prescribes the fallback described above. South Carolina's statute on physical damage rates bars using location of residence, among other things, but allows a territorial plan approved by the state's insurance director.

Common questions

Does a bad year in my neighborhood raise my rate right away?

Usually not fully. Unless the area has enough claims for full credibility, most of the territory's price comes from the complement, and a rate change must go through the insurer's filing and approval cycle first.

Why did my premium rise when I have no claims?

Your own record is only one rating factor. If the group you belong to, such as a territory, vehicle series or age class, has seen higher losses, the group's relativity can rise without any change in your own history. See how car insurance rates are calculated.

Do big insurers have an advantage because of credibility?

An insurer with more data reaches full credibility in more categories and can often price finer segments. Smaller insurers can use industry loss costs and statewide data as complements, so the gap is narrower on broad factors than on fine ones.

Is credibility the same as the "small numbers" problem in complaint ratios?

They share a cause: a small group's results are noisy. Complaint indexes for small insurers face a similar noise problem; see the small-numbers problem in insurer complaint ratios.

Key takeaways

• Credibility is a weight between 0 and 1 that decides how much a small group's own claims count against broader experience.
• Under the classic square-root rule, doubling the weight takes four times the claims, so small groups stay close to the average for a long time.
• A brand-new model starts from its sticker price and similar vehicles, and moves toward its own losses as claims accumulate.
• A single large claim is usually capped and spread across all policies, so it moves a small group's price far less than its raw effect.
• Blending protects against noise but can hide real differences until data accumulate, which is the core of the criticism.