What A Perfect Bracket Looks Like, Part 2

As promised in a previous article, I will try to apply a predictive tool that will better guide us in using the Aggregation Model (AM). If this predictive tool is accurate in forecasting which Aggregate Value (AV) to use, then we should be able to approximate which Elite 8 Seed Pairs (E8SP) to use so that they match the expected Aggregate Value. The predictive tool being used to forecast the AM is the Seed Curve. If you are unfamiliar with the Seed Curve, see this article; and if you are unfamiliar with the AM, AVs or E8SPs, then re-read Part 1 of this article linked in the opening sentence.

First, let's take a collective look at things, and then we'll look at the group perspective. Below is the AM from 2003-2015 displaying each of those year's AVs.

What A Perfect Bracket Looks Like, Part 1

In the 90 hours between the complete reveal of the bracket to the tip-off of the first game, bracket pickers throughout the world use a variety of information, methods, and strategies to make their 63 picks. Whether it be points per game, the W-L record, distance traveled, or even the mascot method, bracket history can be a valuable tool in making your picks. The idea is rather simple: If I want my pre-tournament bracket to look exactly like the post-tournament bracket, then I should examine the post-tournament brackets from previous years and conform this year's pre-tournament bracket to them.

Developing the System

When the 2016 Bracket is unveiled, suppose I look back to the final bracket of 2015 and decide to make my 2016 Bracket resemble the Elite 8 of the 2015. If so, the 2016 Bracket would look like the following: 1v3, 1v2, 4v7, and 1v2. Unfortunately, if this approach was used in 2015 with the 2014 results, I would have some major discrepancies, as 2014 produced these final results: 1vs11, 4v7, 1v2, 8v2. Assuming I picked the right regions, I could match two of the four Elite 8 pairings (both 2014 and 2015 produced a 1v2 and 4v7 in the Elite 8), but I would have missed badly with the other two pairings (the 1v11 in 2014 would miss the 1v3 in 2015 and the 8v2 in 2014 would miss the 1v2 in 2015). To take the analysis deeper, I'm actually picking two games incorrectly. If I picked the 8v2 in 2015 based on the 8v2 in 2014, I first have to pick the 8-seed to beat the 1-seed and then pick the 8-seed to beat the winner of the 4-5-12-13 group winner. Since the 1-seed beat both the 8-seed and the group winner, I've incorrectly picked two games with one bad pick.

The question we have to ask ourselves is how do we make this historical data mean something. One answer that I have stumbled upon is Aggregation. If we take the seeds of all four pairs (8 teams) and aggregate them together, that will give us a value to make year-to-year comparisons.

Quality Curve Analysis (January Edition)

I thought I would start Project: Perfect Bracket with a very familiar analytical tool: the Quality Curve (QC).

The Idea Behind Quality Curves

The theory behind the curves goes as follow: the quality of the teams in the tournament can predict the quality of the tournament results. In layman's terms, higher quality teams in the higher seeds will result in a stable, predictable tournament (much like 2007) and lower quality teams in the higher seeds will result in an insane, unpredictable tournament (much like 2014).