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STEM I
Creating Fair Horseshoe Tournaments using Programming and Reseeding

Background

Tournaments are a way of matching up teams against each other, to figure out which team is the most skilled in a particular activity. The main goal of a tournament is to reward higher skill with a higher chance of victory, which is defined to be fair. Some sports tournaments achieve this goal through seeding the tournament, which involves ranking the players in terms of skill, with a lower seed number having more skill, and deciding matchups based on that (Baumann, Matheson and Howe, 2010). For example, the standard seeding method consists of matching teams up so that the sums of the team numbers are constant (Schwenk, 2000). Another method ensures fairness by re-assigning seed numbers (which is called reseeding) multiple times throughout the tournament to reevaluate matchups (Baumann et al., 2010). The tournaments that this paper examined is horseshoes tournaments, in particular double elimination tournaments. While some more official horseshoe tournaments use ringer percentage - a form of skill level - to seed, most horseshoe tournaments lack seeding or reseeding (NHPA, 2019). Horseshoe tournaments are set up by deciding teams of two, and these teams will compete until a goal, which varies between types of tournaments, is completed. For example, double elimination requires teams to lose twice to be eliminated, and the goal is to be last team that is not eliminated. The organizer of the tournament decides these teams by a random draw, which does not always lead to the best results. For example, two people that have the most amount of skill can become partners. While the tournament does favor them in terms of skill, it may not favor the 3rd best player who is also very skilled but became partners with someone of low skill level. These types of matchups would not be considered fair, as the tournament only favors those top two, and not any other skill level. The main goal of this project is to develop and automate a seeding method for horseshoes tournaments and decide whether this method is fairer than current random draw methods of determining teams.

Methodology / Process

To determine if seeding would benefit double elimination horseshoe tournaments, a Java program was written using Eclipse IDE to simulate tournaments. The tournaments were simulated mainly because this project was being completed during a global pandemic, so in-person testing was not as readily available. Another reason is that horseshoes tournaments take a long time to complete in-person (an average of 2-4 hours per tournament). By simulating the tournaments, data could be gathered much more quickly and easily.

To simulate the tournaments, data were gathered from an official sanctioned horseshoe league, the Central Connecticut Horseshoe Club (CCHC). The league regularly holds competitions and gathers public access data about said competitions. This data includes ringer percent data, number of points scored, average points per game, etc. (Sluys, n.d.). The data were gathered and put into a CSV file for the Java program to read and simulate tournaments with. To simulate games, the winner was semi-randomly selected, where similarly to real life, a higher seed would have a higher chance of winning than a lower seed in each game.

The seeding method of choice to run double elimination tournaments was equal gap seeding. Although this was not the fairest type of single elimination seeding method available, it was the one that could be translated into double elimination the most effectively. The reason for this is that double elimination tournament was treated as two single elimination tournaments, a winner’s bracket and a loser’s bracket. Although the winner’s bracket was modeled as a basic single elimination tournament, the loser’s bracket was not as simple. The loser’s bracket was a single elimination tournament with the players who lost in the winner’s bracket being added, which the automation for equal gap seeding could handle (Karpov, 2016). This seeding method also functions for team numbers that are not powers of 2, using Hwang’s (1982) method of creating dummy teams that lose to all real teams they face to artificially create a team number that is a power of 2 (Hwang, 1982). To ensure that matches are fair later in the tournament, the tournament is reseeded like the method of Arnone, Cire, and Meyerhofer (2017). After each round, a boost is added to each team’s seeding score, which helps the tournament favor their skill by changing their seed number (Arnone, Cire, and Meyerhofer, 2017).

Once the tournaments were coded in with the equal gap seeding method, 3 sets of 100 tournaments were run. In each set, there was a different number of teams in the tournament to begin, namely 13 teams, 7 teams, and 4 teams. These numbers were randomly chosen between intervals of powers of two to prevent loss of generality. The number of wins for each numbered seed in these sets of 100 tournaments were recorded. The process was repeated, except the seeding method was disabled and random teams were generated to compare random draw to seeding methods. The skill levels of each team were tracked, and were used to record win rate data, although they did not affect the structure of the tournament. The win data was then converted to percentages, accounting for any accidental added tournaments in each set.

Once the win rate data were gathered, Spearman’s Rank Correlation Test was used on both samples to test the correlation between the seed number and the win rate percent.

Figure 1:

Win Rate vs. Seed Graph, for the 4-Team Double Elimination set.

Figure 2:

Win Rate vs. Seed Graph, for the 7-Team Double Elimination set.

Figure 3:

Win Rate vs. Seed Graph, for the 13-Team Double Elimination set.

Table 1:

Results from conducting Spearman's Rank-Order Correlation Test on all 3 sets of tournaments.