Base rates and relativities: how a premium is multiplied together

Auto premiums are usually built by multiplication. An insurer starts with a base rate for a pre-defined "base" driver and coverage, then multiplies it by a relativity for each fact about you: where the car is garaged, who drives it, what it is, your record. Because the factors multiply instead of add, several small ones compound into a large difference, and a change to one factor lands on top of all the others.

This article builds a premium for a fictional driver, shows why a "10% factor" can cost more than 10% of what you expected, and explains how an insurer can lower one factor and raise your bill in the same filing. Every dollar figure in the walkthrough is invented for illustration. The structure comes from the Casualty Actuarial Society's textbook Basic Ratemaking (fifth edition, 2016), the rating-manual rules in state filings, and the statutory text cited below.

What a base rate is, and what it is not

The base rate is the price for a base risk, a profile the insurer defines in advance. Basic Ratemaking defines it as the rate that applies to that base risk, and notes that it is not usually the average rate. The base risk often represents the most common characteristics, though the insurer may choose it for marketing reasons. For personal auto the text says there is typically a separate base risk, base rate and set of rating tables for each coverage. Liability, collision and comprehensive are each priced on their own.

So there is no single "base rate for my insurer." There is a base rate for bodily injury liability, another for property damage liability, another for collision and so on, each tied to its own base profile, for example a driver of a certain age with a certain vehicle, deductible and limit. If you do not look like the base profile, and nobody exactly does, the rate is adjusted by relativities.

A relativity is a multiplier relative to the base. The same text calls these variations relativities, factors or multipliers when they are applied multiplicatively, and adds that they can instead be additive or follow another formula. The rating algorithm, which the insurer files, specifies the order in which factors apply, whether they multiply or add, any minimum or maximum premium, and rounding. Many private passenger auto rating plans lean heavily on the multiplicative structure.

A worked premium for a fictional driver

Meet Priya, a made-up 34-year-old with a 2021 midsize sedan, a garaging address in a mid-density territory and one at-fault accident two years ago. Her insurer, hypothetical Harbor Mutual, charges these base rates and relativities. All numbers are invented.

Add the four coverages and her annual premium is $1,568. Take collision as an example, multiplying down the column:

1. $340.00 base rate
2. × 1.25 territory = $425.00
3. × 0.92 age and experience = $391.00
4. × 1.20 accident surcharge = $469.20
5. × 1.15 vehicle = $539.58
6. × 1.00 deductible (the base deductible) = $539.58
7. × 1.10 tier = $593.54
8. × 0.93 discount = $551.99

The product of all the collision factors is about 1.62, so her collision premium is 62% above the base rate even though no single factor adds more than 25%. A tier that looks like "just 10%" is applied to a number that already carries the territory, the accident and the vehicle, so its dollars are larger than 10% of the base.

Notice what is different from coverage to coverage. The accident surcharge is a factor on three coverages and none on comprehensive, because an at-fault accident is not evidence about hail or theft. The limits factor matters most on bodily injury, where higher limits cost more. A vehicle factor in collision reflects repair costs; in liability coverages it reflects the injury and damage claims that kind of vehicle has produced for other people. State rules decide which factors may be used at all. That is why two quotes with the same profile can differ: see our article on why two insurers quote the same driver different prices.

How small factors compound

Compounding is the reason premiums feel disproportionate. Suppose six factors each add 5%. Added together, you would expect 30%. Multiplied, you get 1.05 to the sixth power, about 1.34, a 34% increase. The gap grows with more and larger factors: three factors of 8%, 10% and 12% multiply to roughly 1.33, a 33% total rather than the 30% sum.

Two consequences follow.

• A surcharge on a higher-priced profile costs more dollars. If Priya's accident surcharge is 20%, the dollars depend on what the premium already is before the surcharge is applied. In an expensive territory with a high tier, 20% is a larger dollar amount than the same 20% in a cheap territory.
• Removing a surcharge is worth more than it looks. When the accident drops off the rating plan, her collision premium falls by the whole 20% of the pre-surcharge amount and everything multiplied after it. Our article on how violations and accidents stack on a rating plan shows how several surcharges combine and expire.

What is allowed to be a factor

Which factors an insurer may use is set by state law, and it varies. Michigan's Insurance Code section 2111 (read as of the version current through 2026 Public Act 114) is a useful example because it lists the allowed factors for Michigan auto insurance. Classifications must be based only on factors such as the driver's age, length of driving experience or years licensed; driver primacy; miles driven; type of use; vehicle characteristics; commuting mileage; number of cars or licensed operators in the household; and the amount of insurance. For collision and comprehensive it adds anticipated repair or replacement cost, make and model, damageability and anti-theft features. The statute also requires each insurer to set up a merit rating plan with surcharges for substantially at-fault accidents and certain moving violations, and it bars rates based on sex, marital status, home ownership, education, occupation, the postal zone and credit score. Territory grouping is allowed.

That is one state's rule. Another state may allow credit-based factors and bar a different set, so the relativity table in a Michigan filing and a Texas filing will not contain the same columns. Our article on rating factors some states have banned compares more states, and the car insurance quote comparison worksheet helps you line up quotes that were built from different factors.

Tiers and company placement: factors above the factors

Two rating features sit outside the simple factor chain.

• Tier placement. In states that permit it, an insurer can charge different rates within a single company to customers with different underwriting characteristics. Basic Ratemaking says the underwriting guidelines specify the rules for assigning the insured to a tier, while the rating algorithm and rate pages specify how the tier affects the premium. In Priya's table, the 1.10 tier factor is that effect.
• Company placement. Some insurance groups use distinct companies to sell similar products at different prices. The text's example is one company in the group serving preferred drivers and another serving nonstandard or high-risk drivers, with underwriting guidelines deciding where an applicant goes. It attributes the structure to regulatory reasons, because the full range of desired rates may not be approvable in one company, or to different distribution systems.

The consequence for a shopper is that "the same insurer" can quote different prices to two similar drivers because the drivers were placed in different companies or tiers. A sister company's rates are filed separately and may use different base rates and different relativities. If a quote seems out of line with the brand's reputation, ask which company and tier is writing the policy.

Why one change can move your price more than it seems it should

Three mechanisms produce surprises.

1. Factors that touch several coverages at once. A change in the territory relativity applies to every coverage in Priya's table. A 4% territory change shows up four times.
2. Reclassification. A move from one tier to another or a vehicle's new rating group changes the multiplier on every coverage that uses it, and the change applies at the next renewal, not when you notice it.
3. The off-balance adjustment. When an insurer changes relativities, the average premium shifts, so the base rate is adjusted to keep the intended overall result. Basic Ratemaking gives the adjustment a name, the off-balance factor: the reciprocal of one plus the change in the average rate differential, which is the amount the base rate must shift to balance the changed relativities.

How a "rate decrease" can come with an increase for you

Here is the off-balance idea with invented numbers. Harbor Mutual files a collision change designed to leave its average collision premium unchanged. It lowers the age-and-experience relativity for drivers in Priya's group from 0.92 to 0.88, which would cut its collected premium by an assumed 2% on average. To stay revenue-neutral, it raises the collision base rate by about 2.04% (1 divided by 0.98). It also raises the surcharge for one at-fault accident from 1.20 to 1.30.

• Priya (one accident): $340.00 base becomes $346.94; her collision premium moves from $551.99 to about $583.66, a rise of about 5.7%.
• Her neighbor with a clean record: the same changes apply but no surcharge, so the neighbor's collision premium falls from about $459.99 to about $448.97, a drop of about 2.4%.

Both are customers of the same insurer in the same territory under one filing whose average change is zero. A press release saying "no overall increase" is true, and so is Priya's higher bill. The place to check is the filing's rate pages, not the headline average. Our guide on reading a filing on SERFF explains where the factor tables sit.

Why relativities are filed with regulators

In many states an insurer must file its rating plan with the insurance department, including the factors, not just the headline rate. The Texas Department of Insurance's SERFF filing instructions describe the combined rate/rule filing type as covering rates, fees, rules and supplementary rating information, including tiering, classifications and territory codes and definitions. So the base rate and the relativity tables are filed together. The same instructions say insurers may use rates and rules for lines under Insurance Code Chapter 2251 on or after the date they are filed.

Other states require approval first. The purpose of the filing is to let the regulator test whether rates are excessive, inadequate or unfairly discriminatory and whether the classification uses only permitted factors. Our guide on how rate approval works compares prior approval with file-and-use. States differ in how deeply they review factors, so check your state's insurance department.

How to use this when you shop or renew

• Ask which factors are driving your quote. An agent or a company representative can name the territory, tier, vehicle rating and surcharges.
• Compare coverage by coverage, not just totals. A quote that is cheaper in collision and costlier in liability is not directly comparable to one that is the reverse.
• Test one factor at a time. Change the deductible or the limit and watch which coverage moves; that isolates one relativity.
• Check every surcharge's expiry. If an accident is due to leave the rating plan, ask the insurer when and whether the next renewal will reflect it.
• Use the filing, if your state posts it. Look for the relativity table that matches your characteristic, such as the factor for your territory.

Common questions

Is my premium really a single base rate times a few factors?

Roughly, yes, but the number of factors can be dozens, and some are additive, capped or applied by tables rather than formulas. Basic Ratemaking notes the algorithm can specify multiplicative, additive or other treatment, maximum and minimum premiums, and rounding.

Why does my price differ from a friend's when we have the same car?

Territory, age and experience, record, limits, tier and company placement all differ. The vehicle factor is only one of the multipliers, so identical cars can produce quite different totals.

Can an insurer use any factor it wants?

No. State law limits permitted factors, and some states ban specific ones. Michigan's statute lists permitted classifications and prohibits several, which is a stricter model than many states. Ask your state insurance department which factors apply.

If a factor changes, when does it affect me?

At your next renewal in most cases, after any notice your state requires. See our timeline in from filing to your bill.

Key takeaways

• A premium is a base rate for each coverage multiplied by relativities for territory, driver, record, vehicle, limits or deductible, tier and discounts.
• Multiplication makes factors compound: six factors of 5% add up to about 34%, not 30%.
• Tier and company placement can change your price before any individual factor is applied.
• A filing can lower one factor and raise another; the average change for the book may differ from yours, so read the factor tables.
• Which factors are allowed is a state decision, so identical profiles can price differently across state lines.