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), 155–159.
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
Kershner, I. (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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