by Jess Behrens
© 2005-2018 Jess Behrens, All Rights Reserved
In order for Evolutionary Game Theory to work as a tool for understanding the NCAA Tournament, a specific game must be chosen and, subsequently, shown to provide insight into tournament results. There are many different types of evolutionary games with corollaries in nature - Prisoner's dilemma, rock/paper/scissors, war of attrition, etc. For a beginner's description, click here.
Each of these evolutionary games posits that a conditioned, behavioral strategy employed by a given species confers certain advantages and disadvantages depending on the strategies employed by the other, competing species. Furthermore, it explicitly states that these strategies are conditioned rather than the result of a conscious, individual choice as is the case in traditional, economic game theory. For example, a dove doesn't consciously 'choose' to run away from a hawk when the two are competing for the same piece of food, it just does that because it's in its 'nature'.
The explicit assumption here is that basketball teams, as a unit separate from, but related to, the individuals who make up that team, exhibit this same conditioned behavior when placed in stressful situations.
The evolutionary game that worked best as a tool for analysis of the NCAA tournament was a variant of the Hawk/Dove game that involves a third (and in the case of the tournament a fourth) strategy known as the Owl (or 'Assessor').
Hawk/Dove is a unique type of game, because in order for its math to provide insight into the tournament, the competition must be for a shared resource. Hawk/Dove is not about a fight to the death, but about competition for a resource that can be shared. But how does one integrate this reality with the fact that the tournament, and all basketball games, result in one winner and one loser?
So, for Hawk/Dove to comment on the tournament, the arbitrary notion of winning/losing that we assign to a basketball game (or any competition) cannot be the only result that affects a team. A second, more mutable resource must also be at stake. From my point of view, that resource is obvious - the experience of having played in the game is what is shared by both teams. Again, it may seem heretical to the average individual or wannabe Vince Lombardi ("Win, or your out of the family.") to suggest that a team can win a game even though the score says otherwise. But to a person, everyone acknowledges the existence of such. Some statements I've heard over the past several months:
"The Celtics will grow from their series with Cleveland in this years playoffs and get better."
"Sure, Scottie Pippen got Jordan his championships, but it was Michael who made Scottie great."
"The consensus player of the year is on the bench with four fouls (Jalen Brunson) and your still beating Michigan by 10 points?"
Experience, whether playing with a great teammate or against great opponents, is central to everyone's argument about what makes an athlete or team 'great'. It's central to everything about sports and competition, so it should be no surprise that it may actually be quantifiable & what is really at stake in any given game. Furthermore, it is something that accumulates over a season independently of its development across seasons or careers.
So, without further ado, here are the different 'types' of species in the tournament as well as a brief description of their evolutionary 'strategy'. I will explain in a later post how the math I used in developing the definitions for these populations relates to each of the strategies described below. However, the math I used to determine 'risk' was taken from the linear quadratic formula first published in Ballester, Calvo-Armengol, & Zenou (2006), which can be found in Econometrica. I modified their basic equation to include betweenness centrality & clustering coefficient because of the roles those two play in both the win & loss networks:
Hawks - These are your traditional 'great' teams. In nature, Hawks compete with other species for shared resources, such as food, by raising their wings and rushing the other competitor in an attempt to intimidate them. This display is costly from an energetic standpoint, meaning that if the food they are competing for is worth less energy than they expend in the process, their extra effort is actually a disadvantage. In terms of my method for modeling the tournament, which is defined mathematically using two different networks that consider a teams tendency toward winning and, separately, losing, a Hawk is a team that has very little risk of a first round loss despite being significantly exposed to a tendency toward losing. Furthermore, a Hawk's 'investment' in both the 'Win' and 'Loss' network is more or less equivalent. What this means is that the the structure of the network, literally how they are attached to it and the other teams that they are attached too, mitigate their risk of a first round loss. Like a Hawk in nature, the extra 'cost' for these teams is the increased exposure to other teams that lose in the first round. I will spell out in further detail how I do the maths, as well as the references for where I got those maths, in a later post. For now, this definition will suffice. This group is the smallest of all the types and was defined based on the fact that it includes many of the most dominant teams over the past 14 seasons.
Owls - Perhaps smarter, Owls are the 'Assessor' type. That is to say that in nature, they assess the size of their competitor before determining how to behave. They will even go so far as to pretend to be a hawk in an attempt to goad the hawk into its costly display before stopping and saving energy. They then grab half of the food and run away. In this way, when competing with the hawks, on average, they get half of the resource without expending the same energy as the hawk. If their opponent is a smaller 'Dove', the assessor will take 3/4 of the food and leave half for the dove in attempt to bolster the energy of the Dove - the enemy of my enemy is my friend. They also share half of the resource with other Owls. In my tournament model, Owls have the same extremely low risk of a first round loss as the Hawks. The only difference is that they are more heavily invested in one of the two networks. It may seem counter intuitive to suggest that over investment in the loss network wouldn't predispose a team toward a first round loss. However, as long as that team is overall a very low risk for a first round loss, being more heavily attached to one over the other seems to confer only a qualitative difference, which suggests a difference in conditioning rather than strength.
Doves - High anxiety and low effort, in nature, a Doves primary strategy is to run away from Hawks & Owls. However, if faced with another Dove, they share half of the food. They don't risk expending any of the energy of a Hawk, sacrificing all of the food to the Hawk in a competition, and depend on the presence of other Doves & Owls within the population for survival through sharing. Doves are tournament teams that are almost exclusively, or very heavily, invested in the Loss network and almost always lose in the first round. As I will illustrate in future posts, some of the biggest upsets over the past 14 years occur when a high seed has become so exposed to the Loss network that it overwhelms their attachment to the Win network. In fact, as I will show, some of the tournament structures actually predispose highly seeded teams to loss such that they become 'Doves' or 'Dove-Owls'.
Dove-Owls - Not found in the normal Hawk/Owl/Dove game, this is a species type I've identified in the tournament and defined formally for the math involved in understanding the tournament. When facing a Dove, they behave like Owls; a Hawk or Owl, they behave like Doves; & another Dove-Owl, they share half the food, or in this case half the experience of playing in the game. These are the teams who are a little more dominant than Doves, but not strong enough to compete with either the Owls or the Hawks. They are primarily attached to the Win network and are 'better' than the doves, but still are at a much higher risk of a first round loss than their Owl & Hawk counterparts.
I understand that this all may be confusing, and I will clarify all of it in future posts. However, briefly, when one considers how these species and their evolutionary strategies line up, it becomes clear why defining these populations is necessary.
First of all, correctly identifying these populations provides a tool to contend with the issue of tournament seeding. With one team winning and losing every game, how does one make tournament predictions about who will win the championship independent of how teams were seeded? The method I used to develop the network and, subsequently, define these populations is designed to do its best to deal with this formality.
Secondly, once these populations have been identified, individual team nuances can be more fruitfully explored using conditional forests because the populations have been consistently defined as have the impacts of those populations on a given tournaments structure. Evolutionary game theory simulations do not allow for individual variation among members of a species. That doesn't mean these variations don't exist or can't be identified, however.
Thirdly, defining these populations provides a tool for explaining how a given tournament structure can produce surprising results based on the energetic strategies of each species. Consider a population full of Hawk basketball teams, as would be every basketball coaches dream. When Hawks meet, the additional cost associated with their strategy grows, and repeated interactions with only other Hawks could tear down a team. Likewise, a population with enough Doves may allow that population to out compete the Hawks as it would allow the Doves to share their way to success. Sure, they lose every interaction with a Hawk, but as long as there are enough Doves sharing half of all resources, their population would thrive. What I'm hinting at here is that the breakdown of a given tournament, or assemblage of bird species in nature, will effect which species benefits the most and thrives.
As I will show in future posts, evidence from evolutionary game theory simulations suggests that this is exactly what is happening. But before I get to that evidence, it's necessary that I explain a bit about the mechanics behind those simulations, which will be the subject of my next post!