The “Sophomore Slump” Mike Kalis, Joe Hultzen, James Asimes

Regression to Mean in MLB The “Sophomore Slump” is described as a second-year player, coming off a productive rookie season, having a second year worse than his rookie season. We looked at the top three in voting for Rookie of the Year in both leagues, excluding pitchers from the list, from Rookie “eligibility” in baseball. – Example: David Price (Tampa Bay)

Data Collection We looked at batting average (AVG), on base percentage (OBP) and slugging percentage (SLG) for the rookie and sophomore seasons and compared the data to their career statistics. We also looked at the MLB data for AVG, OBP, and SLG for the period from 1990 to 1999.

Rookie Batting Average Two-Sample T-Test and CI: Avg (R), MLB Avg Two-sample T for Avg (R) vs MLB Avg N Mean StDev SE Mean Avg (R) MLB Avg Difference = mu (Avg (R)) - mu (MLB Avg) Estimate for difference: % lower bound for difference: T-Test of difference = 0 (vs >): T-Value = 5.04 P-Value = DF = 48

Sophomore Batting Average Two-Sample T-Test and CI: Avg (S), MLB Avg Two-sample T for Avg (S) vs MLB Avg N Mean StDev SE Mean Avg (S) MLB Avg Difference = mu (Avg (S)) - mu (MLB Avg) Estimate for difference: % lower bound for difference: T-Test of difference = 0 (vs >): T-Value = 1.86 P-Value = DF = 47

Rookie On Base Percentage Two-Sample T-Test and CI: OBP (R), MLB OBP Two-sample T for OBP (R) vs MLB OBP N Mean StDev SE Mean OBP (R) MLB OBP Difference = mu (OBP (R)) - mu (MLB OBP) Estimate for difference: % lower bound for difference: T-Test of difference = 0 (vs >): T-Value = 4.17 P-Value = DF = 46

Sophomore Batting Average Two-Sample T-Test and CI: OBP (S), MLB OBP Two-sample T for OBP (S) vs MLB OBP N Mean StDev SE Mean OBP (S) MLB OBP Difference = mu (OBP (S)) - mu (MLB OBP) Estimate for difference: % lower bound for difference: T-Test of difference = 0 (vs >): T-Value = 2.52 P-Value = DF = 48

Rookie Slugging Percentage Two-Sample T-Test and CI: SLG (R), MLB Slg Two-sample T for SLG (R) vs MLB Slg N Mean StDev SE Mean SLG (R) MLB Slg Difference = mu (SLG (R)) - mu (MLB Slg) Estimate for difference: % lower bound for difference: T-Test of difference = 0 (vs >): T-Value = 3.67 P-Value = DF = 46

Sophomore Slugging Percentage Two-Sample T-Test and CI: SLG (S), MLB Slg Two-sample T for SLG (S) vs MLB Slg N Mean StDev SE Mean SLG (S) MLB Slg Difference = mu (SLG (S)) - mu (MLB Slg) Estimate for difference: % lower bound for difference: T-Test of difference = 0 (vs >): T-Value = 1.74 P-Value = DF = 48

Batting Average For all players in our data set, the average career average was One-Sample T: Avg (S) Test of mu = vs < % Upper Variable N Mean StDev SE Mean Bound T P Avg (S)

Batting Average Expanded For all players in our expanded data set, the average career batting average was One-Sample T: Avg (S) Test of mu = vs < % Upper Variable N Mean StDev SE Mean Bound T P Avg (S)

On Base Percentage For our data set, the average on base percentage for the career is One-Sample T: OBP (S) Test of mu = vs < % Upper Variable N Mean StDev SE Mean Bound T P OBP (S)

On Base Percentage Expanded For our expanded data set, the average on base percentage for the career is One-Sample T: OBP (S) Test of mu = vs < % Upper Variable N Mean StDev SE Mean Bound T P OBP (S)

Slugging Percentage For all the players in our data set, the average career slugging percentage is One-Sample T: SLG (S) Test of mu = vs < % Upper Variable N Mean StDev SE Mean Bound T P SLG (S)

Slugging Percentage Expanded For all the players in our expanded data set, the average career slugging percentage is One-Sample T: SLG (S) Test of mu = vs < % Upper Variable N Mean StDev SE Mean Bound T P SLG (S)

Class Activity Go to and look up any player and run the 2-Proportion significance test of their sophomore vs. career batting average and on-base percentage and determine if they had a sophomore slump.

Resources MLB Regression to the Mean –