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The World Blackball Pool Championships have been held biennially since 2006 and since 2008 have been administered by Blackball International.
Here are some graphics showing the total number of wins, by nation, in both team and individual events up to and including the 2018 event.

Firstly nations which have won team events in the World Championships.
Doubles team wins are not included in these numbers.

world blackball pool team statistics 2018 by country

The following are nations for which individual players have been successful in the World Championships up to 2018.

world blackball pool individual statistics 2018 by country

Total wins by nation for both team and individual events up to and including 2018 are listed.
Of course many more nations than those listed here participated in the Championships.

World Blackball Championships
Total Wins by Nation of Events up to 2018
N. Ireland11
S. Africa44
Rep. Ireland41

The following tables provide further details of individual and team World Championships results.
For the 2016 and 2018 Championships, the 2nd and 3rd final places are additional to the 1st place honours listed elsewhere.
And for 2014 these are the final group points tables before play-offs and the knock-out match scores on the final day of the Championships.
Many thanks to the European Blackball Association for the provision of this data.