Deductible Effect On Expected Loss Calculator

Work out deductible effect on expected loss instantly with clear inputs, formula shown and shareable results.

About Deductible Effect On Expected Loss Calculator

A deductible removes the first slice of every claim. With exponentially distributed severities the expected payment per claim above a deductible d is μ·e^(−d/μ), which also equals μ times the probability the claim exceeds d.

Formula

Excess over deductible

E[(X-d)₊] = μ·e^(-d/μ); LER = 1 - e^(-d/μ)

μ: Mean severity
d: Deductible

Worked example

With the default values below, Deductible Effect On Expected Loss Calculator returns Expected Loss Net Of Deductible of $1,557,601.57. Change any input above and every figure here is recalculated in your browser.

Inputs used

Mean Claim Severityminimum 0: 20,000
Deductibleminimum 0: 5,000
Expected Claim Countaccepts 0.1–100,000: 100

Results

Expected Loss Net Of Deductible: $1,557,601.57
Loss Eliminated By The Deductible: $442,398.43
Loss Elimination Ratio: 22.120%
Claims Exceeding The Deductible: 77.88

Step by step

1Values used
2Excess over deductible
3Expected Loss Net Of Deductible= 1,557,601.57
4Loss Eliminated By The Deductible= 442,398.43
5Loss Elimination Ratio= 22.120
6Claims Exceeding The Deductible= 77.88

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation or fees or charges into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why do small deductibles cut costs so much?

Most claims are small, so a modest deductible removes a large share of claim numbers and the handling expense attached to them.

What is the loss elimination ratio?

The proportion of expected losses the deductible removes — the natural basis for the premium discount it earns.