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

2. 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)

3. 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.

4. 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) 41 0.2841 0.0218 0.0034 MLB Avg 10 0.26460 0.00582 0.0018 Difference = mu (Avg (R)) - mu (MLB Avg) Estimate for difference: 0.01955 95% lower bound for difference: 0.01305 T-Test of difference = 0 (vs >): T-Value = 5.04 P-Value = 0.000 DF = 48

5. 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) 41 0.2751 0.0341 0.0053 MLB Avg 10 0.26460 0.00582 0.0018 Difference = mu (Avg (S)) - mu (MLB Avg) Estimate for difference: 0.01047 95% lower bound for difference: 0.00103 T-Test of difference = 0 (vs >): T-Value = 1.86 P-Value = 0.035 DF = 47

6. 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) 41 0.3534 0.0260 0.0041 MLB OBP 10 0.33360 0.00786 0.0025 Difference = mu (OBP (R)) - mu (MLB OBP) Estimate for difference: 0.01984 95% lower bound for difference: 0.01185 T-Test of difference = 0 (vs >): T-Value = 4.17 P-Value = 0.000 DF = 46

7. 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) 41 0.3498 0.0381 0.0060 MLB OBP 10 0.33360 0.00786 0.0025 Difference = mu (OBP (S)) - mu (MLB OBP) Estimate for difference: 0.01623 95% lower bound for difference: 0.00541 T-Test of difference = 0 (vs >): T-Value = 2.52 P-Value = 0.008 DF = 48

8. 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) 41 0.4541 0.0669 0.010 MLB Slg 10 0.4091 0.0202 0.0064 Difference = mu (SLG (R)) - mu (MLB Slg) Estimate for difference: 0.0450 95% lower bound for difference: 0.0244 T-Test of difference = 0 (vs >): T-Value = 3.67 P-Value = 0.000 DF = 46

9. 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) 41 0.4351 0.0868 0.014 MLB Slg 10 0.4091 0.0202 0.0064 Difference = mu (SLG (S)) - mu (MLB Slg) Estimate for difference: 0.0260 95% lower bound for difference: 0.0009 T-Test of difference = 0 (vs >): T-Value = 1.74 P-Value = 0.045 DF = 48

10. 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% Upper Variable N Mean StDev SE Mean Bound T P Avg (S) 41 0.27507 0.03406 0.00532 0.28403 -1.11 0.136

11. 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% Upper Variable N Mean StDev SE Mean Bound T P Avg (S) 45 0.27524 0.03282 0.00489 0.28347 -1.18 0.123

12. 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% Upper Variable N Mean StDev SE Mean Bound T P OBP (S) 41 0.34983 0.03813 0.00595 0.35986 -1.20 0.118

13. 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% Upper Variable N Mean StDev SE Mean Bound T P OBP (S) 45 0.34944 0.03662 0.00546 0.35862 -1.20 0.118

14. 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% Upper Variable N Mean StDev SE Mean Bound T P SLG (S) 41 0.4351 0.0868 0.0136 0.4579 -1.39 0.085

15. 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% Upper Variable N Mean StDev SE Mean Bound T P SLG (S) 45 0.4324 0.0850 0.0127 0.4537 -1.62 0.056

16. 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.www.baseball-reference.com

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