Mortality and life expectancy in damages calculations

A future loss is only incurred while the plaintiff is alive, so every future year is weighted by the probability of surviving to it. Those survival probabilities come from published mortality tables. The longer and more distant the loss, the more mortality matters.

This article is about mortality alone, which is the one contingency that applies to every future loss. It is not the only one. A loss-of-income claim can also be reduced for the chance of having been disabled or out of work, where the evidence supports it, and those reduce the same payments. See contingencies for how they fit together and where they overlap.

What follows is background on the method, not legal or actuarial advice for a specific file.

Why mortality enters the calculation at all

Future loss of income runs to retirement, and future cost of care can run for life. Neither is certain to be paid in full, because the plaintiff might not survive every year of the projection.

Rather than assume the person lives exactly to their average life expectancy and then stops, the calculation weights each future year by the chance of being alive in it. That survival weighting sits on top of discounting for the time value of money, so a dollar far in the future is reduced twice: once for time, once for the probability of reaching it.

What the numbers actually look like

Take a man aged 45, on the Statistics Canada 2022 to 2024 Ontario table. His remaining life expectancy is 37.1 years, which puts him at 82.1.

Life expectancy is an average, though, and the spread around it is wide:

He is very likely to see 65, a little under even money to see 85, and about one man in ten reaches 95. A calculation that pays out to 82.1 and stops describes none of those people.

Why you cannot just multiply by life expectancy

It is tempting to take the annual amount, multiply by life expectancy, discount the result, and call it done. That gives the wrong answer, and at any positive discount rate it errs in one direction: too high.

Here is $10,000 a year for life from age 45, at a 2.5% discount rate:

The shortcut overstates by 3.2%.

A fixed 37.1-year term treats every one of those payments as guaranteed, and then ends. Reality runs both ways: he might die at 60 and miss twenty-two years of payments, or live to 95 and collect thirteen more. The two do not offset, because the present value of a stream does not rise in proportion to its length: years added at the far end are worth less than years lost near the start.

Figures are from the Ontario 2022 to 2024 table at 2.5%, on the same mid-year convention the calculator uses.

Where the probabilities come from

The survival probabilities are drawn from published mortality tables, such as the Statistics Canada life tables. A life table gives, for each age and sex, the probability of surviving to each later age. DamageIQ records which edition it used, for example Statistics Canada 2022 to 2024, so a figure produced today can be reproduced later even after the tables are updated.

Standard vs. reduced life expectancy

DamageIQ offers three bases in File Details.

Standard means survival follows the published table for the plaintiff's age and sex. This is the usual choice, and the summary shows the resulting life-expectancy age.

Reduced applies a constant multiplicative load to that table's mortality rates, solved so the survival-weighted life expectancy equals a target total age taken from the medical evidence. Nothing is cut off at the target: amounts beyond it are still counted, at the reduced survival probability. The effect falls hardest on long-dated, lifelong losses, because those depend most on survival to distant years.

Custom table replaces the published rates with an expert's own, entered age by age. The reports name it as expert-provided, so a reader knows the table was not ours.

The basis and the underlying table are recorded together in the file summary.

Why it moves the number

Survival probability compounds year over year, so the effect grows with the length of the projection, and the range is wide. Five years of care for a 60-year-old loses about 2% to survival weighting. Income running to 65 for a 45-year-old loses about 4%. Lifetime care for that same 45-year-old loses about 28%, because most of what it is paying for sits in years he may not see.

A calculation, not an opinion

DamageIQ is a calculator. It applies the selected mortality table and basis to the ages and dates you enter, and every input is traceable in the figure it returns. It is not an expert opinion. The choice of basis, and any reduced life expectancy, are yours to set and to support with evidence. Where life expectancy itself is in dispute, that is a matter for expert opinion rather than a calculator.

Try it

The free PV Multiplier calculator shows how survival weighting flows through to present-value factors for any age, sex, jurisdiction, and discount rate. For the wider method, see How present-value damages are calculated in Canada, and for how mortality applies within each module, loss of income and future cost of care.

By Mike Austin, FCIA, FSA. Fellow of the Canadian Institute of Actuaries and the Society of Actuaries.