Regarding the brackets... there's more to consider here than just the math though... the solution has to tick 3 boxes:
1. It has to work within our tech framework (okay tech can be modified, but remember we had 4 days to work on this)
2. More importantly it must be able to SCALE as the game grows.
3. It has to not devalue the Gems economy as it scales up
So, in the example above, we see a range of 100 Gems for a bracket.
But what happens if we have 100 brackets? Or 200 brackets? What about 1000 brackets?
Obviously in the final case there, the top bracket would have to be earning 100,000 Gems, but even in the smallest case, the top bracket would be earning 10,000 Gems.
And also, as you move down from bracket to bracket, there are going to be thousands if not tens of thousands of players earning WAY too many gems each week, which is just not feasible for the economy.
So, obviously the solution is to base each bracket on smaller (MUCH SMALLER) ranges of Gems, with a sharp dropoff at the top so as not to flood the economy with too many Gems... but it STILL doesn't scale unfortunately, and as more players are added, and more brackets are added, either we have to dynamically alter the ranges, or we have to create new ranges at the top with bigger rewards, OR add more ranges to the lower end with little-to-no rewards.
In fact, when you do the math on that, you'll very quickly find that the amounts of Gems given per bracket vary SO LITTLE (from top to bottom), that it's simply not worth even having a difference for the most part... you may as well make the reward simply moving upwards into higher brackets.
We actually had 3 maths guys spending hours on this last week, and it's simply not as trivial as a contrived example makes it seem... certainly not something to commit to in 4 days, and then be shoe-horned into an existing framework.