Thank you for this initiative @khazrakh!

You've done a good job at describing the problem, and your suggested solution looks good to me. 👍

Since I'm a math nerd, I have to poke a little bit into the crown reward structure.

I suggest a change from logarithmic growth to a hyperbolic tangent structure. The reason for this is that unless you scale the crowns given out in a brawl tier depending on the results of all the guilds, its hard to make the logarithmic growth agree with the fixed amount of crowns awarded per tier. If we use a variant of a hyperbolic tangent instead, then that becomes much easier

The key is that this function is symmetric around 50%. If the crowns are based on any function like that, then the total number of crowns given out in a brawl group is simply the value at 50% multiplied by the number of guilds in the group (since the average winrate necessarily becomes 50% when you look at all the guilds). Of course, a flat bonus can be added to that, and the parameters in the function can be adjusted (apart from the number 50, which ensures the symmetry). This gives Splinterlands direct control over the amount of crowns they want to give out per tier.

Edit: I had written merits instead of crowns several places. Also, the claim above that the total number of crowns given out is the value at 50% times the number of guilds, is only correct when there are 2 guilds in the group. For a larger group, the result is not exactly that, but its close because the function is approximately linear around the center.