Transcript The “Sophomore Slump” Mike Kalis, Joe Hultzen, James Asimes Regression to Mean in MLB • The “Sophomore Slump” is described as a second-year.

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 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
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
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
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
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
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
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
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
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
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
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
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
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