Scheduling the Optimal Baseball Line-up Stefanie Molin Christian Morales Sarah Daniels

Scheduling the Optimal Baseball Line-up

Stefanie MolinChristian Morales

Sarah Daniels

OVERVIEW

Objective: Determine optimal starting lineup and batting order for a MLB team for one season

1. Select starting players for each game• 162 games per season• 33 primary players on roster

2. Determine batting position of each player in starting line-up• Maximize runs per game

Player Statistics

OBP – On-Base PercentageSB – Stolen BasesRBI – Runs Batted InHR – HomerunsSingles, Doubles, TriplesRest DaysSalary

SCHEDULING PROBLEM

Scheduling Overview

SPT-FM Algorithm• Batting Position: “Jobs”• Players: “Machines”

Players are available if not resting• Resting days determined with random

number generator

Assumption: Player’s salary directly reflects value in lineup

Assigning Positions

Primary and Secondary PositionsSome players can play multiple positionsPlayer only scheduled in secondary position if higher priority than primary position

Factors:Relative importance of each positionNumber of primary players available to play in each position

Highest salary player available (fastest machine) in each position is scheduled

Order Position

1 Catcher

2 First Base

3 Second Base

4 Short Stop

5 Third Base

6 Center Field

7 Left Field

8 Right Field

9 Designated Hitter

Player Evaluation

Order Criteria

4 (OBP×130)+Doubles+Triples+(3×HR)+(RBI/10)

3 (OBP×160)+Doubles+Triples+HR+(RBI/10)

1 OBP+SB+Triples

2 OBP+(SB/500)+(Triples/10)+(RBI/10)+Singles

5 (OBP×100)+(15×HR)

6 (OBP×115)+(15×HR)+Doubles+Triples

7 HR

8 Doubles+Triples+HR

9 Singles

Speed is priority

1st hitter should be “power hitter,” 2nd should be more consistent

Player Evaluation

Order Criteria



1 OBP+SB+Triples


5 (OBP×100)+(15×HR)


7 HR


9 Singles

Best playerOBP = 1.6×slugging

Player Evaluation

Order Criteria



1 OBP+SB+Triples


5 (OBP×100)+(15×HR)


7 HR


9 Singles

Good hitters

OBP becomes less important; HR becomes more important

Player Evaluation

Order Criteria



1 OBP+SB+Triples


5 (OBP×100)+(15×HR)


7 HR


9 Singles

Worse hitter; on-base becomes more important

Player Evaluation

Order Criteria



1 OBP+SB+Triples


5 (OBP×100)+(15×HR)


7 HR


9 Singles

Fast hitters at end of line-up

RESULTS

Simulated total season runs for each line-upAverage line-up scored 782 runs throughout season

Line-up Evaluation

Average Lineup

Order Criteria Position

1 Brett Gardner Center Field

2 Derek Jeter Short Stop

3 Robinson Cano Second Base

4 Mark Teixeira First Base

5 Alex Rodriguez Third Base

6 Lyle Overbay Designated Hitter

7 Vernon Wells Left Field

8 Ichiro Suzuki Right Field

9 Chris Stewart Catcher

Total Runs Scored 782

Optimality of Line-Up






5 Alfonso Soriano Designated Hitter



8 Eduardo Nunez Third Base

9 Jayson Nix Short Stop


*Removing Derek Jeter

Optimality of Line-Up






5 Alfonso Soriano Designated Hitter



8 Zoilo Almonte Right Field

9 Austin Romine Catcher


*Removing Lyle Overbay

Optimality of Batting Order












*Random Permutation













*Random Permutation













*Random Permutation

Conclusion

Our procedure produces the optimal line-upDeviations from line-up result in fewer

runs over seasonOur 2013 line-up scored 782 runs

vs. 650 runs scored by the Yankees last season

Next Steps…

Create a more robust model that accounts for player injuries

Verify our model by testing on other teams and past seasons

Documents

Scheduling the Optimal Baseball Line-up Stefanie Molin Christian Morales Sarah Daniels