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Usage Based Insurance Loss Probability Calculator

A usage-based insurance loss probability calculator converts an estimated annual loss frequency into the probability of experiencing at least one loss over a chosen time horizon. It is useful when driving exposure, telematics observations, or your own risk model is expressed as expected events per year rather than as a simple percentage.

The calculation uses a Poisson model, a common simplified approach for independent events occurring at an average rate. It helps translate a frequency assumption into an easier-to-read probability for one year or several years. The result is not a personalized actuarial score and does not capture changing driving behavior, clustering of accidents, weather, location, or insurer-specific rating variables, so the rate you enter remains the most important assumption.

Estimate loss probability

events/yr
years
Result
—
Probability of at least one loss event
Probability of no loss—
Expected number of events—
One-year probability—
Horizon probability—

1. Estimate annual event frequency
Enter the average number of modeled loss events expected per year, such as 0.10 events per year.

2. Choose the horizon
Enter how many years of exposure you want to evaluate.

3. Review the main probability
The main result shows the chance of one or more modeled events during the full horizon.

4. Compare with one year
Use the one-year probability to see how the same annual rate translates over a single year.

5. Check expected events
Expected events equals frequency multiplied by years and is not itself a probability.

6. Test another driving profile
Change the annual frequency to explore how a lower or higher exposure assumption changes risk.

Probability of at least one loss = 1 − e^(−λt) Probability of no loss = e^(−λt) Expected events = λ × t

λ (lambda) is the expected number of loss events per year and t is the time horizon in years. The Poisson model assumes a constant average event rate and independent event timing during the modeled period.

What the result means

The main percentage is the modeled chance of one or more loss events over the selected horizon under a constant-rate Poisson assumption.

If your risk changes materially over time, use separate periods or a more detailed model rather than treating one annual frequency as constant.

Given: Expected loss frequency of 0.10 events per year and a 3-year horizon.

Calculation: Expected events = 0.10 × 3 = 0.30. Probability of no loss = e^(-0.30) ≈ 0.7408. Probability of at least one loss = 1 − 0.7408 = 0.2592, or 25.92%. The one-year probability is 1 − e^(-0.10) ≈ 9.52%.

Result: The modeled 3-year probability of at least one loss is about 25.92%.

Interpretation: A 0.10 annual event frequency does not mean a 10% three-year risk; compounding the event process produces a higher multi-year probability.

Why is annual frequency different from annual probability?

Frequency is an expected count of events, while probability is the chance that at least one event occurs. Under the Poisson model, 0.10 expected events per year corresponds to about a 9.52% one-year probability.

Can the event frequency be greater than 1?

Yes. A frequency above 1 means more than one event per year on average is possible. The probability result still remains between 0% and 100%.

Does the model assume my driving behavior stays the same?

Yes. The entered annual frequency is treated as constant throughout the selected horizon. If mileage or risk conditions change, model the periods separately.

Can I enter a telematics score directly?

No. A score must first be translated into an expected annual event frequency using an external model or data source. This calculator does not assume a proprietary insurer conversion.

When is a Poisson assumption less suitable?

It may be less suitable when events strongly cluster, risk changes quickly, or one event changes the chance of another. In those cases a time-varying or dependency-aware model may be more appropriate.