Scheduling the Optimal Baseball Line-up

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 generatorAssumption: Player’s salary directly reflects value in lineup

Assigning PositionsPrimary and Secondary Positions

Some 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 Position1 Catcher2 First Base3 Second Base4 Short Stop5 Third Base6 Center Field7 Left Field8 Right Field9 Designated

Hitter

Player Evaluation

Order Criteria4 (OBP×130)+Doubles+Triples+(3×HR)+

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

10)1 OBP+SB+Triples2 OBP+(SB/500)+(Triples/10)+(RBI/

10)+Singles5 (OBP×100)+(15×HR)6 (OBP×115)+(15×HR)+Doubles+Triples7 HR8 Doubles+Triples+HR9 Singles

Speed is priority

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

Player Evaluation

Order Criteria4 (OBP×130)+Doubles+Triples+(3×HR)+

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

10)1 OBP+SB+Triples2 OBP+(SB/500)+(Triples/10)+(RBI/

10)+Singles5 (OBP×100)+(15×HR)6 (OBP×115)+(15×HR)+Doubles+Triples7 HR8 Doubles+Triples+HR9 Singles

Best playerOBP = 1.6×slugging

Player Evaluation

Order Criteria4 (OBP×130)+Doubles+Triples+(3×HR)+

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

10)1 OBP+SB+Triples2 OBP+(SB/500)+(Triples/10)+(RBI/

10)+Singles5 (OBP×100)+(15×HR)6 (OBP×115)+(15×HR)+Doubles+Triples7 HR8 Doubles+Triples+HR9 Singles

Good hitters

OBP becomes less important; HR becomes more important

Player Evaluation

Order Criteria4 (OBP×130)+Doubles+Triples+(3×HR)+

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

10)1 OBP+SB+Triples2 OBP+(SB/500)+(Triples/10)+(RBI/

10)+Singles5 (OBP×100)+(15×HR)6 (OBP×115)+(15×HR)+Doubles+Triples7 HR8 Doubles+Triples+HR9 Singles

Worse hitter; on-base becomes more important

Player Evaluation

Order Criteria4 (OBP×130)+Doubles+Triples+(3×HR)+

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

10)1 OBP+SB+Triples2 OBP+(SB/500)+(Triples/10)+(RBI/

10)+Singles5 (OBP×100)+(15×HR)6 (OBP×115)+(15×HR)+Doubles+Triples7 HR8 Doubles+Triples+HR9 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 LineupOrder Criteria Position

1 Brett Gardner Center Field2 Derek Jeter Short Stop3 Robinson Cano Second Base4 Mark Teixeira First Base5 Alex Rodriguez Third Base6 Lyle Overbay Designated

Hitter7 Vernon Wells Left Field8 Ichiro Suzuki Right Field9 Chris Stewart Catcher

Total Runs Scored 782

Optimality of Line-UpOrder Criteria Position

1 Brett Gardner Center Field2 Ichiro Suzuki Right Field3 Robinson Cano Second Base4 Mark Teixeira First Base5 Alfonso Soriano Designated

Hitter6 Vernon Wells Left Field7 Chris Stewart Catcher8 Eduardo Nunez Third Base9 Jayson Nix Short Stop

Total Runs Scored 702

*Removing Derek Jeter

Optimality of Line-UpOrder Criteria Position

1 Brett Gardner Center Field2 Derek Jeter Short Stop3 Robinson Cano Second Base4 Mark Teixeira First Base5 Alfonso Soriano Designated

Hitter6 Alex Rodriguez Third Base7 Vernon Wells Left Field8 Zoilo Almonte Right Field9 Austin Romine Catcher

Total Runs Scored 688

*Removing Lyle Overbay

Optimality of Batting OrderOrder Criteria Position

1 Alex Rodriguez Third Base2 Chris Stewart Catcher3 Lyle Overbay Designated

Hitter4 Derek Jeter Short Stop5 Ichiro Suzuki Right Field6 Brett Gardner Center Field7 Mark Teixeira First Base8 Vernon Wells Left Field9 Robinson Cano Second Base

Total Runs Scored 763

*Random Permutation

Optimality of Batting OrderOrder Criteria Position

1 Robinson Cano Second Base2 Mark Teixeira First Base3 Alex Rodriguez Third Base4 Lyle Overbay Designated

Hitter5 Vernon Wells Left Field6 Ichiro Suzuki Right Field7 Chris Stewart Catcher8 Brett Gardner Center Field9 Derek Jeter Short Stop

Total Runs Scored 771

*Random Permutation

Optimality of Batting OrderOrder Criteria Position

1 Derek Jeter Short Stop2 Brett Gardner Center Field3 Mark Teixeira First Base4 Alex Rodriguez Third Base5 Lyle Overbay Designated

Hitter6 Robinson Cano Second Base7 Ichiro Suzuki Right Field8 Chris Stewart Catcher9 Vernon Wells Left Field

Total Runs Scored 775

*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