Two conventions, one set of results
The medal table most of the world sees is ordered by gold medals first, then silver, then bronze — a lexicographic sort in which one gold outranks any number of silvers. A large part of the American media instead orders by total medals won, treating breadth as the better measure. Neither is wrong, and neither is an official ranking of countries: the Olympic movement awards medals to athletes and teams, not to nations.
The practical result is that the same fortnight produces two credible tables with different countries on top, and each is quoted as though it settled the argument. Whenever you see a bold claim about who won a Games, the first question is which ordering it used.
What the count hides
A medal table adds together events that are not remotely comparable. Some disciplines award several medals to a single squad of specialists across related events; others award one medal to the winner of a global knockout. A nation with a deep programme in a sport that happens to contain many medal events will climb a table without being broader than a rival concentrated in sports with fewer.
Team events compound this. One team title is one medal in the table, even though it required a squad to beat every other nation in the world, while an individual sport can deliver a cluster of medals to a handful of athletes at one venue. Reading the table as an index of sporting strength therefore rewards programme design and event structure as much as performance.
Ties are common and are usually left as ties, with countries sharing a rank. Shared medals also occur, most familiarly when a jump-off is declined or a bout is stopped, and they are simply counted twice rather than resolved.
Better questions than 'who won'
The useful readings of a medal table are comparative and specific. Did a nation convert its qualified athletes into finals at the expected rate? Did results improve in the sports where funding increased? Did a small delegation medal at all, which is a different achievement from a large one finishing fourth in the count?
Population-adjusted and funding-adjusted versions of the table circulate every Games, and they are interesting as long as they are labelled as constructions rather than results. What none of them can do is make the count into a measurement, because the underlying events were never designed to be weighed against each other.
Arena publishes no live medal table, because we hold no source we are licensed to publish for it. When that changes we will say where the numbers come from; until then this guide explains the table rather than inventing one.