Work out deductible effect on expected loss instantly with clear inputs, formula shown and shareable results.
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.
Excess over deductible
E[(X-d)₊] = μ·e^(-d/μ); LER = 1 - e^(-d/μ)
Most claims are small, so a modest deductible removes a large share of claim numbers and the handling expense attached to them.
The proportion of expected losses the deductible removes — the natural basis for the premium discount it earns.