In-class activity#10: Correlation between Teams Rank and Wins

In 2012 and 2013, there were 10 teams in the MLB playoffs: the six teams that had the most wins in each baseball division, and four “wild card” teams. The playoffs start between the four wild card teams - the two teams that win proceed in the playoffs (8 teams remaining). Then, these teams are paired off and play a series of games. The four teams that win are then paired and play to determine who will play in the World Series. We can assign rankings to the teams as follows:

Rank 1: the team that won the World Series Rank 2: the team that lost the World Series Rank 3: the two teams that lost to the teams in the World Series Rank 4: the four teams that made it past the wild card round, but lost to the above four teams Rank 5: the two teams that lost the wild card round In your R console, create a corresponding rank vector by typing teamRank = c(1,2,3,3,4,4,4,4,5,5) In this quick question, we’ll see how well these rankings correlate with the regular season wins of the teams. In 2012, the ranking of the teams and their regular season wins were as follows: Rank 1: San Francisco Giants (Wins = 94) Rank 2: Detroit Tigers (Wins = 88) Rank 3: New York Yankees (Wins = 95), and St. Louis Cardinals (Wins = 88) Rank 4: Baltimore Orioles (Wins = 93), Oakland A’s (Wins = 94), Washington Nationals (Wins = 98), Cincinnati Reds (Wins = 97) Rank 5: Texas Rangers (Wins = 93), and Atlanta Braves (Wins = 94) Create a vector in R called wins2012, that has the wins of each team in 2012, in order of rank (the vector should have 10 numbers). In 2013, the ranking of the teams and their regular season wins were as follows: Rank 1: Boston Red Sox (Wins = 97) Rank 2: St. Louis Cardinals (Wins = 97) Rank 3: Los Angeles Dodgers (Wins = 92), and Detroit Tigers (Wins = 93) Rank 4: Tampa Bay Rays (Wins = 92), Oakland A’s (Wins = 96), Pittsburgh Pirates (Wins = 94), and Atlanta Braves (Wins = 96) Rank 5: Cleveland Indians (Wins = 92), and Cincinnati Reds (Wins = 90) Create another vector in R called wins2013, that has the wins of each team in 2013, in order of rank (the vector should have 10 numbers). What is the correlation between teamRank and wins2012? Exercise 1 Numerical Response

What is the correlation between teamRank and wins2013? Exercise 2 Numerical Response

# Team ranking based on postseason performance
teamRank <- c(1, 2, 3, 3, 4, 4, 4, 4, 5, 5)

# Exercise 1: 2012 Correlation
# Wins for each team in order of teamRank (2012)
wins2012 <- c(94, 88, 95, 88, 93, 94, 98, 97, 93, 94)

# Calculate correlation between teamRank and wins2012
cor_2012 <- cor(teamRank, wins2012)
print(paste("Correlation between team rank and 2012 wins:", round(cor_2012, 3)))

[1] "Correlation between team rank and 2012 wins: 0.348"

#Exercise 2:
# Wins for each team in order of teamRank (2013)
wins2013 <- c(97, 97, 92, 93, 92, 96, 94, 96, 92, 90)

# Calculate correlation between teamRank and wins2013
cor_2013 <- cor(teamRank, wins2013)
print(paste("Correlation between team rank and 2013 wins:", round(cor_2013, 3)))

[1] "Correlation between team rank and 2013 wins: -0.656"

In 2012, the weak positive correlation (0.348) suggests a slight link between regular season wins and playoff success. In contrast, the stronger negative correlation in 2013 (-0.656) shows that teams with more wins often performed worse in the playoffs, highlighting the unpredictability of postseason outcomes.