What would it take for Google to recognise live scores of a Sports League and display in search results?
Could not find any relevant documentation. An example from here -
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As far as I know, this is not an algorithmic feature. It doesn't depend on any specific standardized structured data, but instead is added by Google employees behind closed doors from specialized data feeds.
If you think about it, to get live scores Google needs a live feed, the HTTP protocol wouldn't cut it unless they're sending a request every 5 seconds. They probably use a special live protocol behind the scenes, something akin to a socket, where they pipe in the data directly from an official data provider.
To the best of my knowledge, there's no process to "apply" for this with Google. I think it's one of those things where when you get big enough, Google applies to you.