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The “Sophomore Slump”

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.

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The “Sophomore Slump”

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  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.

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

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