by Jess Behrens
© 2005-2018 Jess Behrens, All Rights Reserved
Over the past few chapters, I've illustrated, using tables & graphics, how the tournament structure is based on competition among the four evolutionary game theory species types. These illustrations are based on the evolutionary game theory simulations described in previous chapters & which consider each of the four species' percentage of the total tournament population to be the primary, driving force behind a given tournament. In Chapter 17, I first showed a Seaborn cluster map, shown again here in Figure 1, that results from the fact that the Dove-Owls play like Owls in the second round. Subsequently, in Chapter 18, I showed that the Year/Type clusters shown in Figure 1 have corresponding structural holes in which highly seeded teams fall. The explicit assertion here is that these structural holes and the memorable tournament runs that occur in those years are a direct result of the same structural factors, which themselves have been produced by the season statistics of the teams invited to the tournament.
Figure 1. Seaborn Cluster Map, Linear Regression Slope, All Tournament Year Pairs & Species Types
However, if this is true, it would also have to be true that the teams which make those memorable runs must benefit from these holes in a demonstrable way. If a memorable team's results are tied to a given species distribution, then the locations in the vector where that team falls must vary with that species distribution (as seen in Figure 1). But what is the mechanism by which this occurs within the method described in these posts?
In effect, the way my tournament method works comes down to the fact that teams are competing with one another for a spot in a multi-dimensional space. Furthermore, this means that they bump into each other and push one another around within that multi-dimensional space throughout the season. Once the tournament is announced, a team is either on a spot or it is not. It's kind of like Duck/Duck/Goose. Ore, even better, musical chairs. If you're left without a seat, you're sucking pond water. As I've shown in other posts, many of the dominant teams fall in the same spot(s) across years. However, those teams that make the most memorable & surprising runs often don't fall in these championship spots. Thus, those teams who 'surprise' the pundits and make a long run are most likely located in portions of the vector that are more uncertain. These teams are effectively dependent on the rest of the tournament for their strength; they make that run because the competition in that year allowed them to push into other regions of the vector that reduce their risk of an early exit. If this hypothesis is true, we must be able to identify those regions, the teams affected, and show that they correspond to the years with the structural holes identified in Chapter 18.
For the readers' sake, I have included a snippet of the vector, for tournament year 2016, as Figure 2. My hope is that this snippet will help the reader by providing a picture of what the two term queries are
Figure 2. Snippet of Tournament Vector with Indexes
applied to when the network is generated. As you can see, there are 48 indexes (13 has a mirror in 13a) and each team, whose names have not been included, has a rank for each of the indexes. Index 35 & 39 are effectively identical, except for a few very important exceptions, none of which are shown here.
To identify the regions which correspond to where the 'surprise' teams lie, we need to consider the different types of 'surprise' runs. Effectively, 'surprise' is associated with one of two things: a mid-major team that over performs or a major conference team that has had a sub-par season. Not all of the 'surprise' runs in the tournament are the same. As I said earlier, many of the 'surprise' teams do not fall within the same queries as the most dominant teams. That isn't always the case because some of the 'surprise' teams are actually wayyyyy under seeded. Figure 3 shows the first of these 'surprise' team types, which can and do occur in any of the tournament years shown in Figure 1, regardless of cluster type A, B, C, or D status. These are teams who have earned their spot, regardless of who else was invited to
Figure 3. 'Surprise' Tournament Team Clusters, Clusters with Dominant Seeds
the tournament and how those other teams have done over the course of the season. Pay attention to the exceptions: those teams who didn't make at least the Elite 8. They prove the rule & show just how important seeding really is.
Loyola-Chicago, Nevada, & Cincinnati from last tournament, Butler's 2010 team, Davidson in 2008, & Wichita State 2014 are all teams that cluster primarily with teams typically seeded much higher than they are. You can see there are teams that under performed within those same clusters: Butler in 2008, Purdue in 2010, Wichita State in 2014, Cincinnati from last season, BYU in 2011, & Louisville in 2014. Of these teams, only 2008 Butler, 2010 Purdue, & 2011 BYU lost to a team that isn't also included in Figure 3 or one that is among the teams I will discuss later in this post. Of those three, 2010 Purdue lost to Duke, the eventual champion, which fell on the Index 44, Ranks 3-4 spot that was dominant in 2010 (Chapter 17).
The second type of 'surprise' run also happens regardless of tournament year and includes teams whose strength is independent of the tournament species' structure. In other words, their strength is independent of their association with teams seeded much better than them. These clusters occur throughout the vector, but rather than overwhelm the reader with graphics, I've only included one example here, Figure 4. I chose this one because these teams cluster together across multiple 2 Index
Figure 4. 'Surprise' Tournament Team Cluster, Lower Seeded Clusters
queries, which adds to the evidence supporting my assertion that they are the result of similar competitive structures. Of the teams included in Figure 4, only Louisville is also included in Figure 3. There are two teams in Figure 4 who did not make at least the Sweet 16. Their inclusion will help prove the points made later in this post. One of them, Xavier in 2007, pushed Ohio State (the national runner-up) to overtime before losing 77-71.
The final type of surprise team, and the real subject of this post, are the teams who have had a questionable season and who could, according to the pundits, go either way in the tournament. These are teams whose success or failure is defined by the structure of the tournament itself. They are primarily located in 8 tournament years, which are not surprisingly the 4 most 'right' & 'left' years as shown in Figure 1 (2016, 2010, 2018, 2017 - 'left' or Owl Dominant; 2014, 2011, 2015, 2005 - 'right' or Hawk Dominant).
There are three different clusters that conform to this pattern. I will use the first, Figure 5, to clearly illustrate the process because the teams to which it applies cross both sets of years ('left' & 'right').
Figure 5. 'Surprise' Tournament Team Cluster, Tournament Structure Dependent Teams
The second two clusters are associated with one or the other groups of 4 years ('left' or 'right'). As you can see from just a cursory glance, these clusters include some memorable runs, including Kansas State from last season!
To illustrate the process of getting to results that bear out the effect of tournament structure on team success, you need to examine Figure 5 from left to right. The cluster is based around Index 10, Ranks 40 & 41, which interact significantly with Index 9. The left most table shows all teams over the past 14 years falling on Index 10, Ranks 40-41. Moving to the right, the second/middle table shows those teams in the first table that also fall between Ranks 14-58 on Index 9. Finally the two tables farthest to the right show a breakdown of teams in the middle table that correspond to the two groupings of years described above - 'left' & 'right' years (top table); middle years (bottom table).
As you can see teams that fall in the structurally dependent ('left' & 'right' years) all at least make it to the Sweet 16. Keep in mind Stanford lost to Dayton in 2014, which are both in the top table, & UCLA lost to Gonzaga, who is in Figure 3. Also, New Mexico State in 2010 very nearly beat Michigan State in the first round (there was a questionable travel call at the end of the game). And Michigan State that year went on to make the Final Four. Conversely, the teams located in the bottom right table in Figure 5, all of which fall in the 'middle' 6 years found in Figure 1, never made it to the Sweet 16.
The last two clusters are shown in Figure 6. The table on the left goes with the 'left' years listed above (2010, 2016, 2018, 2017) & the table on the right with the 'right' years (2005, 2015, 2011, 2014). These two
Figure 6. 'Surprise' Tournament Team Clusters, Owl (Left) & Hawk (Right) Champion Dominant Clusters
clusters cover the same range (Ranks 59-64) in Index 23, but the second index is different depending on the year group ('left' or 'right'). The results in Figure 6 are more uncertain than those in Figure 5. They include some of the most significant runs in the past 14 years (Syracuse 2016, Xavier & Michigan 2017, Syracuse last season, Wisconsin 2005, Kentucky 2014, Michigan State & NC State 2015) but the results are clearly more dependent on seeding. They do include several first round losses, notably Baylor in 2016, Brigham Young in 2014, & UCLA in 2005. Keep in mind that UCLA lost to Texas Tech in the first round, a team which is also located in Figure 6. But the premise is sound: Figure 6, if you were to rank the areas of 'strength' in the tournament, would include the weakest potential Final Four teams.
If you recall from Figure 4, neither LSU in 2015 nor Louisville in 2014 made the Final Four. Both of those two teams lost to teams in Figure 6, (LSU lost to NC State & Louisville lost to Kentucky) which illustrates the point: In every year, there are teams who can make a surprise run to the Final Four, and those teams are located in ranges where success depends on the other structural factors at play in any given tournament. These structural factors correlate at nearly 1 to 1 with the structural holes in a given tournament. Furthermore, of those teams that 'qualify' to make a run, seeding is the primary determinant of which one actually succeeds . Regardless, the strength of the teams in Figures 5 & 6 are ultimately dependent on other, structural factors.