So I’ve been thinking about this off and on for a while and finally actually like my formula.
Here is my idea for rewards on multiplayer levels:
At the end of each month all multiplayer arenas grant gems to the top ranked players. The formula would give value to everyone in the top 100 positions on either side (though you only collect once). It should be set that the differential between rank 2 and 1 is higher than the differential between rank 100 and 99. You only get gems that are more than you have previously earned.
G® will be the formula for calculating gems for a given rank.
G® could have a variety of forms and should incorporate the world into the calculations. My first thought is:
G® = 0.1 * W * (100 - r + 1) ^ 2 #This would grant a maximum of 1000 gems for being #1 in a dungeon arena, and 5000 in the glacier. It also gives a difference of 19.9 gems for moving from #2 to #1, but only a difference of .3 gems moving from #100 to #99.
G® = 0.001 * W * (100 - r + 1) ^ 3 #This would have the same maximum values, but would be even more strongly pushed toward the top ranks. 29.7 gems from #2 to #1 and .007 from #100 to #99.
These are just 2 examples, it could be created in order to shape the reward line however we wanted.
In any case, the actual rewards would be something like this:
January 31, you are ranked #1, you get G(1) gems. February 29, you are ranked #1, you get nothing because you’ve already earned the top rank.
January 31, you are ranked #90, you get G(90) gems. February 29, you improve to #19 and earn G(19)-G(90) gems.
What do you think?