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 1990-1999.

• 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 AverageTwo-Sample T-Test and CI: Avg (R), MLB Avg

Two-sample T for Avg (R) vs MLB Avg

N Mean StDev SE MeanAvg (R) 41 0.2841 0.0218 0.0034MLB Avg 10 0.26460 0.00582 0.0018

Difference = mu (Avg (R)) - mu (MLB Avg)Estimate for difference: 0.0195595% lower bound for difference: 0.01305T-Test of difference = 0 (vs >): T-Value = 5.04 P-Value = 0.000 DF = 48

Sophomore Batting AverageTwo-Sample T-Test and CI: Avg (S), MLB Avg

Two-sample T for Avg (S) vs MLB Avg

N Mean StDev SE MeanAvg (S) 41 0.2751 0.0341 0.0053MLB Avg 10 0.26460 0.00582 0.0018

Difference = mu (Avg (S)) - mu (MLB Avg)Estimate for difference: 0.0104795% lower bound for difference: 0.00103T-Test of difference = 0 (vs >): T-Value = 1.86 P-Value = 0.035 DF = 47

Rookie On Base PercentageTwo-Sample T-Test and CI: OBP (R), MLB OBP

Two-sample T for OBP (R) vs MLB OBP

N Mean StDev SE MeanOBP (R) 41 0.3534 0.0260 0.0041MLB OBP 10 0.33360 0.00786 0.0025

Difference = mu (OBP (R)) - mu (MLB OBP)Estimate for difference: 0.0198495% lower bound for difference: 0.01185T-Test of difference = 0 (vs >): T-Value = 4.17 P-Value = 0.000 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 MeanOBP (S) 41 0.3498 0.0381 0.0060MLB OBP 10 0.33360 0.00786 0.0025

Difference = mu (OBP (S)) - mu (MLB OBP)Estimate for difference: 0.0162395% lower bound for difference: 0.00541T-Test of difference = 0 (vs >): T-Value = 2.52 P-Value = 0.008 DF = 48

Rookie Slugging PercentageTwo-Sample T-Test and CI: SLG (R), MLB Slg

Two-sample T for SLG (R) vs MLB Slg

N Mean StDev SE MeanSLG (R) 41 0.4541 0.0669 0.010MLB Slg 10 0.4091 0.0202 0.0064

Difference = mu (SLG (R)) - mu (MLB Slg)Estimate for difference: 0.045095% lower bound for difference: 0.0244T-Test of difference = 0 (vs >): T-Value = 3.67 P-Value = 0.000 DF = 46

Sophomore Slugging PercentageTwo-Sample T-Test and CI: SLG (S), MLB Slg

Two-sample T for SLG (S) vs MLB Slg

N Mean StDev SE MeanSLG (S) 41 0.4351 0.0868 0.014MLB Slg 10 0.4091 0.0202 0.0064

Difference = mu (SLG (S)) - mu (MLB Slg)Estimate for difference: 0.026095% lower bound for difference: 0.0009T-Test of difference = 0 (vs >): T-Value = 1.74 P-Value = 0.045 DF = 48

Batting Average• For all players in our data set, the average career average was

0.281• One-Sample T: Avg (S)

Test of mu = 0.281 vs < 0.281 95% UpperVariable N Mean StDev SE Mean Bound T PAvg (S) 41 0.27507 0.03406 0.00532 0.28403 -1.11 0.136

Batting Average Expanded

• For all players in our expanded data set, the average career batting average was 0.281

• One-Sample T: Avg (S) Test of mu = 0.281 vs < 0.281

95% UpperVariable N Mean StDev SE Mean Bound T PAvg (S) 45 0.27524 0.03282 0.00489 0.28347 -1.18 0.123

On Base Percentage• For our data set, the average on base percentage for the career is

0.356805• One-Sample T: OBP (S) Test of mu = 0.357 vs < 0.357

95% UpperVariable N Mean StDev SE Mean Bound T POBP (S) 41 0.34983 0.03813 0.00595 0.35986 -1.20 0.118

On Base Percentage Expanded• For our expanded data set, the average on base percentage for the

career is 0.355822• One-Sample T: OBP (S) Test of mu = 0.356 vs < 0.356

95% UpperVariable N Mean StDev SE Mean Bound T POBP (S) 45 0.34944 0.03662 0.00546 0.35862 -1.20 0.118

Slugging Percentage• For all the players in our data set, the average career slugging

percentage is 0.453585• One-Sample T: SLG (S)

Test of mu = 0.454 vs < 0.454

95% UpperVariable N Mean StDev SE Mean Bound T PSLG (S) 41 0.4351 0.0868 0.0136 0.4579 -1.39 0.085

Slugging Percentage Expanded• For all the players in our expanded data set, the average career

slugging percentage is 0.452511• One-Sample T: SLG (S)

Test of mu = 0.453 vs < 0.453 95% UpperVariable N Mean StDev SE Mean Bound T PSLG (S) 45 0.4324 0.0850 0.0127 0.4537 -1.62 0.056

Class Activity

• Go to www.baseball-reference.com 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

• www.baseball-reference.com• MLB Regression to the Mean– http://www.jstor.org/stable/2685772