An insurance premium is a prediction about a group, applied to you. Understanding that explains a lot about why the pricing feels arbitrary.
The basic calculation
The insurer estimates the probability of a claim and its likely size, multiplies them to get an expected cost, and adds a margin for expenses and profit.
Everything else is refinement of that estimate.
What they use
Characteristics that correlate with claims in their data. For motor insurance: age, location, vehicle, claims history, mileage, occupation. For home: location, construction, security, claims history.
Some of these feel unfair because they are not about your behaviour. A safe driver in a high-claim postcode pays more because the prediction is about the postcode.
Why quotes differ so much
Different insurers have different data and different appetites. One may have had bad experience with your vehicle type and price accordingly; another may want that market.
This is why shopping around produces large differences for identical cover, and why loyalty is generally penalised rather than rewarded.
What reduces premiums
A higher excess, which shifts small claims to you.
Accurate information – overstating mileage or including unnecessary cover costs money.
Shopping at renewal, every time. Automatic renewal is priced on the assumption you will not check.
And avoiding small claims, since the premium increase over subsequent years frequently exceeds the payout.
What to check in the policy
What is excluded, which is where disputes come from. Read that section rather than the summary.
The caveat
General explanation. Specific products and regulations vary by country.