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Solo queue champion diversity too low

You can have your players prioritize 3 champions in solo queue. However, he will only play the first two. If you do not prioritize champions, there are still only 2 champions in his position he will play relatively frequently. I think this isn't enough diversity.

Right now I try to use the ratings from solo queue to determine which champions my players are better at, as opposed to just copying the pick/ban of the top ELO team. However this lack of diversity forces me to switch the prioritized champions every few days for all my players, which is tedious and slow (it takes almost a season to get enough information on the more popular champions)

The importance of a more diverse champion pool increases with my next suggestions:
1) Player main champions: It would add a lot of personality (not the stat) to players if they had a champion they just performed better on. This would also increase the challenge in both building the right team for the champions you want to pick, and picking the right champions for the team you have. This could be a hidden variable, although it would be fairly easy to see who their favorite champion is by looking at their solo queue stats.
2) Champion training. Right now, it doesn't feel like players become better at a champion by practicing him in solo queue. Adding this feature would again increase tactical depth. Not only for building your own team strategy by training your players to use the 'meta' champions, but also by planning around your opponents team. Does he have players with a small champion pool? If so, you can try to target them in pick and ban. Depending on how deciding champion experience becomes and if the first suggestion is implemented as well, you could even train you player to acquire a new main champion (although this would be a very long process)
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Your second point is already a thing. Games played on a champion in SoloQ increases the performance on that champ for every gamemode.
Most people call it the "champion mastery"