In Class Activity 10 - Rank Correlations

Overview and Background 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. To evaluate whether regular season success predicts post season performance, we assign ordinal ranks to teams based on their playoff finishes:

Rank 1: World Series Winner (Champion) Rank 2: World Series Runner Up Rank 3: League Championship Series Losers (2 Teams) Rank 4: Division Series Losers (4 Teams) Rank 5: Wildcard Game Losers (2 Teams)

R Code Implementation Chunk 1: Vector Definitions We first construct the rank vector and win vector for both seasons ordered by playoff finish:

# Define Team Ranks Vector (1 = Champion, 5 = Early Elimination)
teamRank <- c( 1, 2, 3, 3, 4, 4, 4, 4, 5, 5)

# 2012 Regular Season Wins (ordered by teamRank)
# Rank 1: SF (94) | Rank 2: DET (88)
# Rank 3: NYY (95), STL (88)
# Rank 4: BAL (93), OAK (94), WSH(98), CIN (97)
# Rank 5: TEX (93), ATL (94)
wins2012 <- c(94, 88, 95, 88, 93, 94, 98, 97, 93, 94)


# 2013 Regular Season Wins (ordered by teamRank)
# Rank 1: BOS (97) | Rank 2: STL (97)
# Rank 3: LAD (92), DET (93)
# Rank 4: TB (92), OAK (96), PIT(94), ATL (96)
# Rank 5: CLE (92), CIN (90)
wins2013 <- c(97, 97, 92, 93, 92, 96, 94, 96, 92, 90)

Chunk 2: Exercises & Correlation Analysis We calculate Pearson’s correlation coefficient \(r\) for both seasons using R’s cor() function:

# Exercise 1: Correlation for 2012 Season
cor_2012 <- cor(teamRank, wins2012)
cor_2012

[1] 0.3477129

# Exercise 2: Correlation for 2013 Season
cor_2013 <- cor(teamRank, wins2013)
cor_2013

[1] -0.6556945