Investigating the Aggregation Model

You may have seen the term Aggregation Model (AM) used throughout PPB (Examples: Link #1 and Link #2). I was even going to do a full write-up about it in Mar 2016, but the article disappeared from my hard-drive and I had to leave you with only the hard data. I have re-written the whole article, and hopefully I didn't forget anything from the first one. Enjoy!

The Aggregation Model

The AM is a predictive bracket tool that displays the sum of all seeds for each and every round of the NCAA Tournament. Peter Tiernan from Bracket Science used a metric known as the Mad-o-meter® (not sure if it was trademarked, but giving credit to be safe), and it is an aggregation of the tournament as a whole. The AM breaks down the M-o-M aggregation to the round-level (R32, S16, E8, F4, CG, NC), and its predictive ability works best for some rounds more than others. Up to this point, PPB has focused primarily on the AM for the Elite 8 (E8AM) for this reason, but in this article, I will look at it for all rounds with a greater emphasis on the rounds for which the AM works better.

Quality Curve Analysis: Final Edition

It is that time of the year. The brackets have been released, and it's time to see what this year has in store for us. If you are not familiar with Quality Curve Analysis, here are some articles you should read first (Jan Edition, Feb Edition, Mar Edition). Let's start with a consolidation of all four QCs from each analysis this season.

The Time Line, Part 3: A Macro-Analysis of the Tournament

This is the 3rd part in my series chronicling the Modern-Era (1985-present) NCAA Tournament via a macro-perspective of the game, a perspective often ignored -- accidentally and intentionally -- in most tournament analysis. It is my belief that these macro-factors have played a role in the outcomes of modern-era tournaments, especially the surprises. If you haven't read Part 1 of this series, it details many of the macro-factors in a year-by-year style that will be discussed in this article. My goal for this article is to explain the patterns of trend in the NCAA tournament from 1985 to 1992. (NOTE: 1993 and 1994 could also be included in this analysis since they share many similarities with these years. However, they are probably best viewed as transitory years between this era and the Straight-Outta-High-School (SOHS) Era, which is why I grouped them with 1995 and 1996 in Part 2.)

To start things off, let's look at the Elite 8 Aggregation Model for the years in question. As stated in Part 2 of The Time Line series, the 1985-1992 era of the tournament was mostly calm, as most Elite 8s featured an Aggregate Value between 20 and 25. There were two outlier years in 1986 and 1990 with Aggregate Values (AVs) of 37 and 40, respectively.

The Time Line, Part 2: A Macro-Analyis of the Tournament

In Part 1 of The Time Line, I detailed changes to college basketball and the NCAA tournament, primarily from the Modern Era (1985-present). I then classified the changes into two categories: structural changes to the tournament and technical changes to the game. One change did not fit into
either category, and in my opinion, it could be in a class on its own.

2007: First tournament featuring the "One-and-Done" rule. Implemented by the NBA, all draft prospects must be 1-year removed from high school (or 19 years old) in order to be draft-eligible. It does not mean that draft prospects have to attend college. As the previous NBA drafts (2003-05) began reaching critical mass with "Straight-Outta-High-School" prospects, the NBA implemented this rule to rein in scouting and recruiting operations that had become over-extended as franchises (especially those with lottery picks) had to scour the entire nation at both the high school and college level in order to get the pick right.

For those of you thinking this is going to be an definitive analysis of the one-and-done (OAD) rule, you will be sorely disappointed! Instead, I intend to address a point I made in Part 1 about the relationship between the OAD rule and tournament results. So, I'll start this examination with a familiar data piece, the E8 Aggregation Model (E8AM). The most unusual stretch of games in the E8AM takes place from 2007-2009, which many regard as the calmest years of the tournament in an otherwise volatile era. Producing both a 13 and a 14 in the AM (and there's only one possible way of doing each of these) during this stretch, I think it is no coincidence that it started at the exact same time in which the OAD rule was implemented. So, what happened?

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.