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4 At-Bat Statistics

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When baseball season is upon us, batting averages are a topic of discussion, and data are actively recorded to maintain the most up-to-date statistics. Here we attempt to introduce a few statistical calculations by way of a binomial experiment utilizing the at-bats data garnered from one major league player’s 200 consecutive games spanning across seasons, where we consider only games where the player had exactly four at-bats. Our four at-bats experiment is a binomial experiment because the experiment consists of repeated trails; each trial resulting in just two possible outcomes; with a constant 0.50 probability of success; and where trials are independent of each other (Colorado State University-Global Campus, 2018). In our experiment, …show more content…

This illustration clearly reveals that when our batter has four at-bats, he most often gets one hit. From our frequency distribution, we can easily compute a mean number of hits (Table 1). Here, we calculate a weighted mean, by summing the products of each variable and its associated frequency, and then dividing by the total frequency. McDaniel (2011) asserts that using a weighted average calculation will supply a more meaningful final average number that considers the “relative importance of each number that is being averaged” (p.1). In our four at-bats experiment, the average number of hits is 1.19. With our frequency distribution compiled, we construct a corresponding probability distribution and its associated scatter plot (Figure 2). The probability distribution scatter plot resembles the frequency distribution scatter plot, yet it provides the probability of achieving each variable …show more content…

In our experiment, x = number of hits, n = number of at-bats 4, and p = batting average .297. The probability of the experiment is calculated in Excel by way of the BINOM.DIST function, where results are shown in Table 3. When understanding the number of trials (n) and probability of one successful trial (p), we can calculate the mean of the binomial distribution E(x) = µ = np. In our experiment, n = 4 at-bats, and p = .297 batting average, which results in 1.19 mean number of successes. From our binomial probability distribution we create a scatter plot to further illustrate our binomial probability distribution results (Figure 3). As we review our results, we see similarities in the probabilities of our four at-bats frequency distribution and binomial distribution. This makes sense, because the frequency probability distribution utilizes actual hit results, and the binomial probability distribution utilizes the batting average that is garnered from actual hit results - which lends to similarity in the means as

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