Player Speed vs. Wild Pokémon Encounter Frequency in Pokémon SoulSilver Joshua and AP Statistics, pd. 3B

Transcription

1 Player Speed vs. Wild Pokémon Encounter Frequency in Pokémon SoulSilver Joshua and AP Statistics, pd. 3B In the newest iterations of Nintendo s famous Pokémon franchise, Pokémon HeartGold and SoulSilver versions, the player is capable of both running and walking throughout the world. Shortly after beginning the game, a character tells the player that running through tall grass makes more noise than walking, thereby attracting wild pokémon and increasing the number that appear that the player must battle. This claim could, in actuality, be attributed to the fact that the player simply takes more steps in a shorter period of time while running, and so encounters pokémon more often in real time, but not necessarily more pokémon overall when looking at the distance traveled. The hypotheses for this study are straightforward: H 0 : The average number of steps between wild pokémon encounters while walking is the same as the average number of steps between wild pokémon encounters while running. S avg(run) = S avg(walk) H A : The average number of steps between wild pokémon encounters while running is less than the average number of steps between wild encounters while walking. S avg(run) < S avg(walk) The experiment was very simple to set up. The game would be played, having the character walk through the tall grass, counting the number of steps taken through the grass before each wild pokémon appeared, until the player had encountered 0 wild pokémon. The player would then repeat the process; only this time the character would be running through the grass. The chance of encountering a wild pokémon is assumed to be the same for each patch of grass, so no careful planning of the character s route

2 through the grass was necessary- all that was required was that the player accurately count the number of steps in between encounters. The experiment was designed to easily determine and compare the frequencies of wild pokémon encounters by basing both groups on a constant unit of measurement- the number of steps taken before an encounter. We chose this experiment setup because of its simplicity and relatively fast execution. It is pretty easy to count the number of steps because each step covers exactly one tuft of grass, and the individual tufts of grass are very clearly defined within the grassy area. Each encounter took less than seconds to reach, so collecting all of the data as we went was done very quickly. By collecting 0 values for each group, we were able to make calculations and perform tests that were meaningful in a larger context, based on our large sample size. The character running. A grassy area is in the top left of the screen.

3 In order to make any decisions based on the data, we needed to assume or verify several conditions: 1: Each trial was independent, and the groups were independent of each other. 2: The trials were randomized- we assumed that the game engine handles the wild pokémon encounters, and that they are appropriately randomized. 3: Our sample size was less than % of the population- as each step taken has a chance of resulting in a wild pokémon encounter, the population of wild encounters can be considered to be infinitely many because they are constantly happening in games played by people all over the world. : The distribution is nearly normal OR both sample sizes are greater than 0. Having met or assumed all of the necessary conditions, we were able to perform a twosample t-test of means on the data. A two-sample t-test determines the probability that, assuming the null hypothesis (that the population means are the same), the collected data could come up in any given random sample of the population. If the probability of this event, represented by the p- value, is very low, then we can with some level of confidence reject the null hypothesis for the alternative. However, if the p-value isn t all that low, meaning that such a sample could feasibly be expected to be generated randomly and even perhaps consistently based on the null hypothesis, then there is no reason to reject it, and so we fail to do so. The formula for a t-score is given: Substituting our statistics,

4 Using a calculator, the number of degrees of freedom, df, was given to be 1.. With the calculated t-value of 0.01 and the degrees of freedom 1., the p-value was calculated at.3. This is incredibly high for a p-value. It actually means that we cannot reject the null hypothesis at even the 0% significance level, let alone the 0% or % levels that would be considered statistically significant enough to make a valid rejection of the null hypothesis. Because we fell so short of this level, we fail reject the null hypothesis. In the context of Pokémon SoulSilver, this means that the average number of steps between wild pokémon encounters does not seem to be affected by whether the player is walking or running through the grass. In all likelihood, the perceived increase in the encounter rate while running is due to the lesser amount of time that passes between encounters as a result of the faster movement through the grass.

5 Data- Steps Taken Between Encounters: Walking: Running:

6 Statistical Data: Walking: Mean: Std. Dev.: Min: Q 1 : Med: Q 3 : Max: Mode:.0 steps.2 steps 1 step steps steps steps 31 steps steps Running: Mean: Std. Dev.: Min: Q 1 : Med: Q 3 : Max: Mode:.0 steps.20 steps 3 steps steps. steps steps 23 steps steps