However, there will be double ups. For example, Germany and the Netherlands are through from the World League event, but there's a good chance that one of those two nations, world ranked 3 and 2 respectively, will qualify as European champions, thus opening up a further spot. Ditto the Pan American section.
Should Australia win the Oceania title, the Black Sticks could still make Rio, but they will be entirely dependent on events out of their control, which no one enjoys. World rankings will be adjusted after the second World League event starting in Antwerp this weekend.
If one spot is remaining it will be decided by the world rankings of the two teams who have finished in the final relevant place at the two tournaments. New Zealand are ranked seventh and might stay there at the next ranking reckoning.
But in Buenos Aires, they could have sealed the deal.
They lost a penalty shootout 8-7, after 28 shots, to Canada, ranked eight places lower, after a scoreless draw; then were well beaten by Spain, four places behind them, in their last game yesterday morning, in which Spain deserved their 3-1 win.
If in a few months they have missed out on Rio, New Zealand will have only themselves to blame.
The women's Black Sticks, ranked fourth, start their Rio campaign in Antwerp on Saturday.