If you're a quality player in Silver League, then the next change, a month out; will put you on that leaderboard, and speed your progress toward gold with no extra money in.
NB: I got on top by being patient.
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Above 4700 points, there is no winstreak and minimum is 3pts per win, not 10pts. So playing more does not give advantage. In pessimistic scenario, you can win 10 battles and gain 10x3pts and then lose 1 battle which means -36pts. So after 10 wins / 1 lose, you have 6 points less.
And it would work the same way above each league thresholds. So a bot with a win rate 70% (which is a really good win rate for a bot) won't be able to get top position anyway.
This is valid for Champions, but in the rest of leagues the bots will have definitely a huge advantage and there is a need of fixing this before the league separation.