Fermi estimate, about 120-180 sinkings a year * 30 crewmembers/ship * 0.75 chance of dying (I'm guessing some sink in port or are evacuated?) = 2700 deaths / year.
Whether by luck or not, that's actually not far off one of the better estimates I can find. The paper "Fatalities among the world's merchant seafarers (1990–1994)" [1] ends up with a rough estimate of 2200 fatalities per year worldwide for the early 1990s. This is based on relatively good data from 19 major maritime flags and major insurance underwriters, followed by more shaky extrapolation to the worldwide numbers. Of the 2200/yr, the authors attribute about half to maritime accidents, so the number due to actual sinkings and such is lower, around 1100/yr in their estimate. The other fatalities break down as: 1/4 of the total attributed to occupational accidents (falling off a ladder, etc.), and 1/4 to illness while at sea.
The paper does mention that other estimates have reached both considerably higher and considerably lower totals (they quote one author who estimated 13,000/yr in the 1980s!). It's hard to get good numbers because the worst safety records appear to be among flag-of-convenience nations who also have the worst reporting and insurance practices, so a large portion of total fatalities (probably) come from the places with the highest uncertainties. But even among rich nations they did still find it a comparatively dangerous occupation: it's safer to be a Danish-flagged seafarer than most other flags, but still >10x the fatality rate compared to having a job on land in Denmark.
Good point. I was guessing randomly with justification. If I had guessed that 0.001% or 1000% of all sunk sailors died it wouldn't be a Fermi estimate.
The paper does mention that other estimates have reached both considerably higher and considerably lower totals (they quote one author who estimated 13,000/yr in the 1980s!). It's hard to get good numbers because the worst safety records appear to be among flag-of-convenience nations who also have the worst reporting and insurance practices, so a large portion of total fatalities (probably) come from the places with the highest uncertainties. But even among rich nations they did still find it a comparatively dangerous occupation: it's safer to be a Danish-flagged seafarer than most other flags, but still >10x the fatality rate compared to having a job on land in Denmark.
[1] https://doi.org/10.1016/S0308-597X(98)00017-7