ADV Draft Baseball League Other

Introduction

The wheel pick in a snake draft format, also known as the "bend" and the "snake", consists of the picks at the end of a round of drafting and the beginning of the next round. By virtue of the snaking draft order, these picks both belong to the same person. It makes no functional difference to a drafter whether they select a Pokemon 8th or 9th, since both land on their team and they do not have to worry about another player taking their second pick.

However, where this does make a difference is the stats that I collect. The first pick in a wheel is classified as being chosen within the first round of the wheel, and the second pick the second. This does not affect continuous stats such as Average Draft Position, where it can be divided by eight for an approximate placement within a round and the perceived value of a Pokemon is important (this is how fantasy football drafts, which I've modeled a lot of this database after, handles things). This does, however, affect discrete stats and how they are interpreted.

The Problem

The problem of the wheel first arose when I added a new functionality to the individual Pokemon search tool on the site that displayed a plot of a Pokemon's picks by round. This seemed fine to use at first, but it was brought to my attention by ADV draft player Seeker that there's a bias within the data and that the discrete nature of wheel picks were making the plots inaccurate, to a degree. I knew this issue existed but thought that it came out in the wash and that whether a player would choose something first on the wheel was effectively random. This is true for most of the wheel picks in the game -- however, there are some Pokemon which had a large skew that necessitated some change.

The biggest example of this is Skarmory. At the time of writing, Skarmory has been chosen on the round one wheel consisting of picks 8 and 9 a total of 19 times. 16 of these times were as the 8th pick, leaving 3 on the 9th pick. This skewed the distribution of picks by round very heavily in Round 1's favor for Skarmory, making its perceived value on the draft board higher than it actually is. The opposite example comes for Starmie and Swampert, whom had a distribution of 9/18 and 8/15 on the 8th and 9th pick, respectively, making their value look lower than reality. Wheel picks of Skarmory + Starmie and Starmie + Skarmory are functionally identical yet swing this new graph I had on the website.

The Solution

The solution to this problem had two parts: deciding a border at which the wheel picks become effectively random, and then ‘smoothing the wheel'. After discussion and combing through the data, I decided to apply smoothing to the first two wheels (picks 8 and 9, and picks 16 and 17). Past this, the data became effectively random without any real outliers worth smoothing, like was necessary for Skarmory and Starmie. Next, we take the amount of total picks in the wheel (for example: Skarmory has a distribution of 16/3, or 19 total picks) and spread them evenly across the eighth and ninth pick with the extra pick for an odd number going to the latter of the two picks (so Skarmory's 16/3 becomes 8/9). As mentioned earlier, there is no functional difference between an eighth and a ninth pick except in discrete stats such as pick by round -- this solves the problem of perceived value versus actual value being misrepresented.

As of now, this is only used on the above chart on individual Pokemon lookup, as ADP is calculated using the "true" unsmoothed set of overall draft positions. However, I have the method in place in case this (or a similar issue) comes up again.