Can you help refine my schemas?

Working with Data
#1

Hello there,
I’m creating an application that will allow certain businesses (aka “venues”) to host tournaments for a specific sport.

Here are my schemas (simplified):

Venue
   name: string

Team
   name: string
   players: [type: objectId, ref: User]
   venue: [type: objectId, ref: Venue]
   total_score: number

User
   name: string
   email: string
   venue: [type: objectId, ref: Venue]

League
   name: string
   event_type: string
   game: string
   venue: [type: objectId, ref: Venue]
   teams: [type: objectId, ref: Team]
   players: [type: objectId, ref: User, default undefined]

The idea is that a venue can host multiple leagues. The leagues can be either “team” or “solo” type, and they will have many players. Players can be on different teams but not in the same league. Teams can also join different leagues. Both teams and players can visit different venues, but venues shouldn’t be able to see anything from other venues - as it would get overwhelming for them.

While designing this and implementing it in my app, I didn’t really account for teams participating in different leagues. It works, but as soon as you add or remove a player, it adds/removes them from every league that the team is a part of.

I also haven’t even gotten around to implementing a “solo” mode yet, but I thought just adding players to the player array in League would be enough.

One idea I had was to implement the Team like so:

Team
   name: string
   leagues: [
      id: objectId, ref League
      players: [type: objectId, ref User]
      score: number
   ]
   total_score: number
   venue: [type: objectId, ref: Venue]

What do you think about my design? How would you approach this?

Thanks so much for looking.