Friday, December 3, 2021

Average Character Finishes by Board - An Analysis

 


Many of you know I'm currently in an educational leadership doctoral program.  This semester I took advanced data analysis, and our final project required us to analyze a data set of our choosing and to write up a report about it.

Many of you know I collect an obnoxious level of data for this-here blog.

You know what I did next.

If you would like to read the paper I submitted, please proceed accordingly.  I warn you, this is the dorkiest thing I've done in quite some time.


Problem of Practice Results Report:

Average Character Finishes by Game Board in Star Wars Epic Duels

Introduction

Star Wars Epic Duels was a board game released in 2002 to coincide with marketing and merchandizing for the second prequel film, Star Wars: Episode II - Attack of the Clones (Star Wars: Epic Duels, n.d.). The game showcases 12 different major characters from the Star Wars movie universe, along with their accompanying minor character or characters. For example, Obi-Wan Kenobi is a major character who comes with two Clone Troopers as minor characters. Boba Fett is a major character who pairs with the minor character Greedo. In the game, each major character features a unique playing deck that includes attack, defense, and special cards that dictate the actions a player can choose as they try to win the game by battling and defeating all of the other players.

The game was originally meant for two to six players, also known as “Duelers.” However, several years ago, I realized there was nothing stopping 12 enterprising Duelers from playing with all of the characters at once (Engblom, 2021). Duels with 12 Duelers became known as “12-way duels,” and I created leagues to play 12-way duels at previous universities where I worked. None were as successful as my current league, where we have been playing since 2014 and have logged more than a 100 duels. Recaps for each match can be found at 12wayduels.blogspot.com, as well as Dueler and character rankings showing the average finishes and victories from past duels.

Problem of Practice

The original game came with four different playing boards: Emperor’s Throne Room, Carbon Freezing Chamber, Kamino Platform, and Geonosis Arena. Each of the 12 major characters has a designated starting spot on each of the boards, and the layouts and character placements are different for each board. However, across all four boards, the six “light side” characters start at one end of the board while the six “dark side” characters start at the other. 

Anecdotally, it seemed the starting positions on some boards favored certain characters more than others. Likewise, it seemed some starting positions for characters made it harder to outlast the other 11 Duelers on the board. Though I already knew the character rankings for best average finish combining all four boards (Jango Fett was ranked first, Obi-Wan Kenobi was ranked last), I did not know if a character’s average on a specific board was statistically significantly different than their overall average finish in a game. 

The Research Question

The research question which guided this problem of practice results report was: Are there statistically significantly different results on individual boards compared to a character’s overall average finish in a 12-way duel?

Research Design and Methodology

The data collection for this problem of practice was simple because I was already tracking the results of the 12-way duels from the league, including the place of finish (first through twelfth) for each character in every duel and the game board used for the duel. That information was transferred from an Excel file to SPSS. Over a 125 different Duelers have played in the league over the years, but their ability level was not factored into the analysis. That is a limitation of the study. The talent level of a Dueler influences how their character finishes in a duel, but for this study, I ignored that element.

I chose a z test for the statistical analysis. Salkind and Frey (2020) noted one-sample z tests were appropriate when comparing a sample mean to the overall population mean. For this analysis, the average finish of all 12 characters was examined for the four different game boards and compared to their overall average finish in 12-way duels. SPSS does not calculate z tests, but the SPSS descriptive statistics function was used to ascertain the overall means of the characters, the board-specific means of the characters, and the standardized deviations of the overall means for hand calculations of the z scores. The Cohen’s d effect size was also calculated for statistically significant results (Cohen, 1992). Those outputs are covered in the next section.

Results

 There were 92 duels in league history in which all of the original 12 characters that came with the board game were used, one of the original four boards were selected, and the 12 characters began the game in their designated starting spot on those four boards. 18 games were played in the Carbon Freezing Chamber, 24 in the Geonosis Arena, 21 on the Kamino Platform, and 29 in the Emperor’s Throne Room. The overall average finish (first place through twelfth), standard deviation of the overall average, average by board, and z score for each character are presented in Table 1.


                1.96 and -1.96 are the critical values that make a one-sample z-test score statistically significant (Salkind & Frey, 2020). There were three results which indicated there were statistically significant differences in a character’s performance on a specific duel board compared to their overall average performance in 12-way duels. Emperor Palpatine, when played on the Carbon Freezing Chamber board (M = 8.11, SD = 3.22), had statistically significantly lower finishes than his overall average finishes (m = 6.32, s = 3.31), z = 2.29, p < .05, d = .54. The effect size for this difference was medium, according to Cohen’s (1992) cutoffs. Jango Fett, when played on the Kamino Platform board (M = 6.67, SD = 4.09), also had statistically significantly lower finishes than his overall average finishes (m = 5.25, s = 3.25), z = 2.00, p < .05, d = 0.44. The effect size for this difference was small approaching medium, according to Cohen’s (1992) cutoffs.

            Emperor Palpatine, when played in the Emperor’s Throne Room (M = 4.55, SD = 2.65), had statistically significantly higher finishes than his overall average finishes (m = 6.32, s = 3.31), z = -2.90, p < .05, d = 0.53. The effect size for this difference was medium, according to Cohen’s (1992) cutoffs. Luke Skywalker, when played on the Kamino Platform board (M = 5.33, SD = 2.69), approached statistically significantly higher finishes than his overall average finishes (m = 6.84, s = 3.62), with a z-score of -1.91, just short of matching or exceeding the -1.96 critical value.

Implications

            The results of the statistical analysis confirmed that, in three instances, a character’s performance in a 12-way duel on a specific board was not representative of their overall average finish. Furthermore, the effect sizes for each were substantial. Emperor Palpatine accounted for two of those instances. He performed significantly worse in the Carbon Freezing Chamber. This made sense in that his starting position leaves him exposed to potential attacks from many different characters on that board. However, Palpatine was significantly better when playing in the Emperor’s Throne Room. Not only is that board named after him, but his starting position is on a far edge of the board and shielded from all but one other character at the start of a game.  Luke Skywalker, who nearly accounted for a fourth difference from overall average finish on the Kamino Platform, has a similar advantage like Palpatine in the Throne Room.  He starts on a far edge of the board and very few characters are initially in range to attack him.

            Jango Fett represented the other instance. He performed significantly worse on the Kamino Platform. That was ironic given the board is specific to a scene of his from Star Wars: Episode II - Attack of the Clones when he escaped Obi-Wan Kenobi (you even see his spaceship, Slave One, on the board), and an attack card in his playing deck is more powerful when used on that board compared to the other three. However, similar to Emperor Palpatine in the Carbon Freezing Chamber, his starting spot is not ideal. He is somewhat exposed and surrounded by other characters whose playing decks are more powerful than his own. Furthermore, the “dark side” characters are spread out on Kamino, leaving him vulnerable to “light side” character alliances who are close enough to charge into his starting area.

            Repeating this analysis in the future, with more duels to incorporate into the original dataset, might reveal additional trends. A cursory overview of the current overall average finishes and individual board finishes for each character suggests opportunities for new statistically significant differences, like Luke Skywalker on Kamino. Conversely, additional duel results added to future analyses might normalize individual board averages, reducing or eliminating statistically significant differences. Either outcome is plausible. As Yoda said in The Empire Strikes Back, “Difficult to see, always in motion is the future” (Kershner, 1980).


References

Cohen, J. (1992). Quantitative methods in psychology: A power primer. Psychological Bulletin, 112(1), 155159.

Engblom, R. B. (2021, March 23). 100 memories from the first 100 duels. 12wayduels.blogspot.com. http://12wayduels.blogspot.com/2021/03/100-memories-from-first-100-duels.html#more

KershnerI. (Director)(1980). Star Wars: Episode V - The Empire Strikes Back [Film]Lucasfilm Ltd.

Salkind, N. J., & Frey, B. B. (2020). Statistics for people who (think they) hate statistics. (7th ed.). Sage.

Star Wars: Epic Duels. (n.d.). Board Game Geek. https://boardgamegeek.com/boardgame/3284/star-wars-epic-duels

 

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