The state of North Carolina conducts it annual post-season high school football championships over a 5 week period beginning in early November. Schools are classified according to their enrollment, ranging from 4A (the largest classification) down to 1A so that each classification contains roughly the same number of schools. The cutoff for the 4A classification is approximately 1,400 students, while the largest 1A school has an enrollment of approximately 670 students. These enrollment numbers are revisited every 4 years so changes in a school’s classification are dictated by increases or decreases in enrollment during that time period. It is not uncommon for a school to change classifications based on enrollment changes versus those other schools near the cutoff lines.
The state of North Carolina conducts one of the most comprehensive post-season football tournaments in the country. Based on their record, the 64 best teams from each classification qualify for the tournament, with the 32 largest schools being part of the ‘AA’ tournament and the rest being part of the ‘A’ tournament. For example, Riverside High School in Durham was the 25th largest school to qualify for 2013 4A tournament. They compete in the 4AA Football Championships. On the other hand, Hillside High School in Durham was the 56th largest of the same 64 teams to qualify for the 4A tournament and are part of the 32 team 4A Football bracket. As a result, the NCHSAA (North Carolina High School Athletic Association) awards 8 championship trophies.
For each 32-team bracket, the teams are placed into an East and West region, and then seeded 1 through 16 based on record. In the first round, the region’s #1 seed (best record in the region) plays against the #16 seed (lowest qualifying record in the region), the #2 seed (2nd best team in region) plays the #15 (2nd lowest qualifying team in the tournament), #3 vs. #14, etc. for 8 total games with the winners advancing to the next round. The winner of the #1/#16 seed game plays the winner of the #8/#9 seed in the next round, as well as 3 other match-ups between 1st round winners. In the 4th round, the survivor of the games will play in the regional championship culminating in the state championship game pitting the regional champions in the 5th week.
It is common practice for the selection committee to hang a string over a paper map of North Carolina representing a north-south running line (otherwise known as a meridian) so that the 16 teams lying to the right of the string be placed in the East region while the remaining teams are placed in the West region. This can be problematic for teams in the Durham-Chapel Hill area, as they vacillate between regions (East and West), as well as classification (AA or A) on a yearly basis depending upon the sizes and locations of teams qualifying for the postseason tournament. However, it is difficult to prevent this situation without undermining the entire playoff system.
Each region is split into two quadrants of eight teams, with the winner of each quadrant playing in the regional final to determine who advances to the state championship game. One quadrant contains the #1,#4,#5,#8,#9,#12,#13 and #16 seeded teams in the region while the other quadrant contains the #2,#3,#6,#7,#10,#11,#14 and #15 seeded teams. While it appears that some attempts to place teams in the same quadrant (or at least first round game) by location have been made, these attempts seem random and haphazard. For example, of the five teams from the Greensboro/Winston-Salem area qualifying for the 4AA playoffs, three of them (West Forsyth, East Forsyth and Grimsley) appear in one quadrant while the other two (Northwest Guilford and Page) appear in another quadrant. While an argument could be made to separate the two teams from the area with 10-1 records (#1 seed West Forsyth and #3 seed Northwest Guilford), they play in separate conferences and didn’t meet during the regular season. In addition, another 10-1 team (Hough High School) was seeded #5 in the region and placed within West Forsyth’s quadrant.
While there is a method behind it, this configuration disregards existing transportation networks, most notably roads, that may better group teams based on a better metric than just grouping on a map and the predilections of a select few athletic administrators. Distance can be measured different ways. Manhattan, Euclidean [Blanchard and Lyson (2006], or driving distance along a vector road network [Van Hoesen et al. (2013)] are all potential options to create regions based on these types of distances. It is also common in social quantitative research to consider travel time along existing transportation networks as a more accurate quantification of proximity rather than simple geographic proximity. Teams that are located closer to major Interstate highways in the state such as Routes 85, 40 and 95 can travel much further in the same amount of time than a team that may need to travel along state or local roads. This may change quadrant configurations.
This research will explore the notion of creating four quadrants (two for each region) of eight teams for each football bracket based off driving time. Using GIS tools, an O-D (Origin-Destination) Matrix can be created to determine the drive-time between all 16 teams in a region that will be competing against each other for a berth in the state championship game. Using statistical programming techniques, matrix optimization methods will create the two sets of eight teams within each region whose average driving time between each other has been minimized. These eight teams can be seeded into their appropriate brackets or optimized even further to create sub-regions (called pods) in concert with seeding to prevent the best teams from meeting in first round games. This paper focuses on the feasibility of creating theses quadrants and evaluating the efficacy of these methods.
These optimized brackets were compared to the brackets created for the 2013 football post-season to determine which of the eight brackets could have benefited most from this new algorithm design. Preliminary analysis of the 4AA and 2A brackets has shown that each bracket would benefit from this dynamic algorithm. Maps for each tournament, showing the bracket organized by officials versus the optimized bracket make that apparent. However, geostatistical techniques can quantitatively reinforce these configurations. Point pattern metrics such as the Average Nearest Neighbor and the Getis-Ord General G statistics show that the computer-generated quadrants created are in fact statistically better than their counterparts created by the NCHSAA. These metrics will be run for all quadrants within all eight tournaments to determine football brackets that deviate furthest from optimal configuration. From there, officials can explore the qualitative reasons for these deviations, any possible remediations and recommendations for future configurations that take these qualitative reasons into account.
For the 4AA bracket, all but five teams are located within the I-40/85 corridor in the Raleigh / Durham, Greensboro / Winston-Salem and Charlotte areas. For the 2A bracket, teams range from ElizabethCity in the east all of the way to TransylvaniaCounty in the west. Given the sheer size of North Carolina and placement of the qualifying schools that changes from year to year, this dynamic algorithm can be implemented on a yearly basis so schools are competing against teams so that fans, players and participants can save valuable time, money and resources traveling to games.