[kq76]

EDIT: Skip this post, unless you really like math and/or want to make this spreadsheet even better.

My math skills aren't what I wish they were so I wonder if someone might be able to assist in something.

The way I made the spread in methods B and C is to calculate the midpoint (not counting any set top %), assign it a value, and then each spot above or below it would be greater or lower by a user-adjustable % (say 25%). That works rather well. The problem comes when you don't have a single midpoint, but a shared midpoint (like with an even # of teams and no odd # of set top %). What I did in that case was to simply give the midpoints the same value, but obviously that's not ideal. If you have say an 8 team draft, you probably wouldn't want the odds of picks 4 and 5 to be equal (some top # of teams sharing the same odds to disincentivize tanking, sure, but there's no reason for the midpoints sharing the same odds). So what to do? Well, you can just go to method A and set the exact # of balls you want to use, but surely I can improve methods B & C when it comes to this scenario.

So in v2 (not yet shared), I tried creating a higher midpoint and a lower midpoint and then separate them by half of that same user-adjustable %. And that's better, but it's not quite perfect either. To explain, say the midpoint is assigned a value of 1. If we're using a user-adjustable % of 25, the next higher pick would normally be assigned a value of 1.25 (and the next lower pick .75). If there were 2 midpoints, we would assign the higher midpoint 1.125 (1*(1+.25/2)) and the lower midpoint .875. But the problem is 1.125 isn't exactly 25% greater than .875 (it's 28.6%), like the rest of the odds would be. For 25% exactly, you'd give the higher midpoint a value of 1.11111 and the lower .88889 (that might be a clue as to how to solve this, 1/9=.11111). But what if the % you're using isn't 25%, but 23%, how do I figure it's ".11111", not through trial and error, but via a formula?

There must be some math that can easily solve it, but I don't know it.

EDIT: Silly me, I just realized 1 isn't 25% greater than .75 like 1.25 is to 1. So I guess my v2 solution isn't as bad as I thought since v1 wasn't as good as I thought. I'll think some more on it.