by Jess Behrens
© 2005-2018 Jess Behrens, All Rights Reserved
In Chapter 17, I posted about how the structure of the tournament effectively chooses who wins the championship & that the tournaments cluster around the competition between Doves & Dove-Owls. Furthermore, I showed that in some of these clusters, Nash Mixed Strategy equilibria exist between the two primary species, Hawks & Owls, in the second round.
But the question remains: are the major upsets which occur during years that fall within these two Nash mixed strategy equilibria also caused by these same structural factors? Is it possible to delineate tight regions within the vector using only 2 indexes? The majority of upsets involving teams seeded from 1 - 3 occur during these years.
The answer seems to be yes. Figure 1 shows where the structural holes fall within the vector & demarcate the extent of the 2 index regions. As you can see, in the years with a Nash mixed strategy
Figure 1. Two Index Continuous Range Queries with Losing Teams, Major First Round Upsets
equilibrium in the second round there are at least 3 highly seeded teams falling within these regions. Figure 2 shows the teams effected by year. As you can see, there are some teams falling within these
Figure 2. Teams Impacted by Structural Holes, Cluster A & C Tournament Years
ranges in years other than the cluster A & C years (from Chapter 17) & I did not include 2009 in Figure 2. There was one significant upset that year, 4 seeded Wake Forest, which you can see falls in with the other upset teams at Index 44 Rank 10.
Some of these teams are able to win a single game, particularly the 2 seeds. Obviously, then, it matters who these teams play in the first round. However, as Figure 2 shows, they definitely cluster in the Cluster A (2010, 2016, 2018) & C (2009, 2012, 2013, 2015, 2005) years that also involve a Nash mixed strategy equilibrium in the second round.