Definition
A per-capita ratio is any quantity divided by population — emissions per person, income per person, doctors per person, deaths per person. It converts a total (which scales with how many people are in the bucket) into a rate (which makes buckets of different size comparable).
It is Rosling's first move whenever a 'huge number' is presented. Most of the time the headline collapses to a rate that is much more or much less alarming than it sounded.
Why it matters
How it works
Pick the denominator that matches the question. To compare countries on environmental footprint, divide by population. To compare hospitals on outcomes, divide by patients treated. To compare road designs on safety, divide by vehicle-miles. The wrong denominator is worse than no denominator because it masquerades as a fair comparison.
Once you have a rate, the next question is whether the rate itself needs normalising further. Deaths per capita is informative; deaths per capita per year is more informative; age-adjusted deaths per capita per year is most informative when comparing populations with very different age structures. Each layer strips out a confounder.
Rosling's practical rule: when shown a total, ask "out of how many?". When shown a per-capita rate, ask "compared with what?". The two questions, applied in series, are most of the work of becoming numerate about news.