In Class Activity 10

Overview & Background In 2012 and 2013, 10 teams made the Major League Baseball (MLB) playoffs: the six division winners and four wild card teams. To evaluate whether regular season success predicts postseason 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: Wild Card Game Losers (2 teams)

R Code Implementation Chunk 1: Vector Definitions We first construct the rank vector and win vectors 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 AnalysisWe 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