from Amazon
Monday, August 22, 2011
How to convert an ordered list into a dollar-value list
Someone asked me how I convert the ordered list of ballots into an implied dollar-value list.
I think we’ve discussed this in the past. And perhaps there are better ways to do it. I’ll show you my way, and you can figure out if it works for you, or if you can improve it:
In my league, there are 550 players to draft, the average player is 10$, and the minimum is 1$.
This is the core:
=( 549 / (548+ORDER_ID) -0.5 ) ^ 1.56
The 549 is one less than 550, and the 548 is two less. In this way, if ORDER_ID = 1, then you get 549/549 = 1, and if ORDER_ID = 550, you get 549/998 = 0.5. That sets the extreme range from 1 to 0.5.
I then subtract 0.5 to get the range from 0.5 to 0.
I raise to the power of 1.56 to get a non-linear function that approximates how dollars are spent by ORDER_ID.
The average for all that (ORDER_ID from 1 to 550) is 0.095. So, you do (10-1)/.095 to get the multiplier (which is 95 in my case), and then you add 1$ because that’s the minimum. The “10” above is for an average of 10$ per player. If your average is higher (say 260/23 = 11.3), then use 11.3 instead of 10.
So, you take the core above, and do this:
CORE * 95 + 1
You do that, and, in a league of 550 picks, you get this:
1 $33
50 $25
100 $19
150 $15
200 $11
250 $8
300 $6
350 $4
400 $3
450 $2
500 $1
550 $1
If you have say 300 players in your league drafted, where the average player is 11.3$, you start with this:
=( 299 / (298+ORDER_ID) -0.5 ) ^ 1.56
In this case, you multiply by 109 and add 1. So, now you have this:
1 $38
50 $23
100 $14
150 $8
200 $4
250 $2
300 $1
Of course, this is “on average”. We can’t always assume that the #1 guy is of the same expectation levels each year. This is just a quick way to work this out.