A theory of monetary distribution and captain handicapping. I won’t go into specific drafting strategies.
I’ve never participated in an auction draft before. This is all just theory. Maybe there will be some math/logical problems.
Assumption/simplification #1: Every point of mmr is equal. For example, a 3000 + a 4000 is the same as a 2500 + a 4500. This is another way of saying that, if the mmr average of teams are the same, then the strengths are the same.
Therefore, the goal of a draft is just to acquire the most mmr.
We also assume that, each point of mmr has the same “monetary value.” For now, we ignore that this monetary value may change as the draft progresses.
Assumption #2: The lowest rated player must go for 0 monetary value.
Simplification #3: We ignore for now, that you can only draft 4 players. Since we’re not going into specific draft strategies, it shouldn’t matter.
With the above assumptions, we can assign a monetary value to each player in the pool.
The lowest rated player will be worth 0. His mmr will be our “floor.” For other players, their values will be their mmr in excess of the floor.
Khillasaurus is the lowest player at 1960 mmr. He is worth $0. inkognito at 6600 mmr will be worth $4640.
https://docs.google.com/spreadsheets/d/19z0FSZ0lOI2snixs9AmuufHdUZPrxTpa7Jm5a0ilM90/edit?usp=sharing
The total value in the 56 players in the pool then, is $125727.
Divided equally among 14 captains, each player would have $8980.5 to spend. For now, assume the captains are all equal mmr.
If all players are drafted at their fair value, equal teams will be produced. (This ignores a lot of nuances/strategies that come up in real drafting. I think they’re okay to ignore for the current purposes of assigning monetary value.)
What if captains are not equal?
My idea is to treat the captains as dummy teams who have already drafted themselves at fair value.
Step 1: Add the captains to the player pool, to find the new “total value” of everyone.
Step 2: Divide the new total (169131) equally into 14 teams = ~12081
Step 3: Subtract the value of the captains, having them “draft themselves.” This produces the starting money.
Step 4: Convert to Buck’s Bucks, keeping Mantis at 664 starting money.
Surprise! We end up with the same values….
Conclusion: I currently believe the handicapping format to be fair, inasmuch as mmr is fair.
Maybe we’ll do a follow up looking into draft strategies, edge cases, exploiting inefficiencies, etc.
For captains: I think you need to pay attention to the “Greg’s wonderland” tab on the spreadsheet.
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