For the website I am working on at the moment I am on doing a lot of of event coverage. Therefore I think it would be awesome to have a section on the tournament page that shows news related to this tournament. Maybe by linking a category or popst tag with the event.
2nd idea - dates for tournament:
There is no option to link a tournament with a specific date at moment to show the user when the event starts and ends. In addition to that, the tournament stages normally have specific dates as well. (maybe these are already features of the pro version? - If so I will buy it today!) The dates should also be in the tournament header in order to display it with the shortcode.
In addition to that I think it would be awesome to have something like a tournament overview page. Since we now have dates linked with tournaments we can have this page sorted by dates with three sections sorted by "ongoing tournaments", "upcoming tournaments" and "completed tournaments". The user expierence for browsing past, current and upcoming events would be improved a lot in my opinion :D With that you could add some options like only displaying the next two upcoming events. Also, since the section with completed tournaments can get quite long, there should an option to only displaying a certain amount of past tournaments, while giving the option to link the user to another page where all past events can be seen. (idea is to have an archive with the events, at the moment I have a page with like 100 shortcodes linking to all the past events. Having this automated would be awesome ;-) )
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