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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
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
Best playerOBP = 1.6×slugging
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
Good hitters
OBP becomes less important; HR becomes more important
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
Worse hitter; on-base becomes more important
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
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
Order Criteria Position
1 Brett Gardner Center Field
2 Ichiro Suzuki Right Field
3 Robinson Cano Second Base
4 Mark Teixeira First Base
5 Alfonso Soriano Designated Hitter
6 Vernon Wells Left Field
7 Chris Stewart Catcher
8 Eduardo Nunez Third Base
9 Jayson Nix Short Stop
Total Runs Scored 702
*Removing Derek Jeter
Optimality of Line-Up
Order Criteria Position
1 Brett Gardner Center Field
2 Derek Jeter Short Stop
3 Robinson Cano Second Base
4 Mark Teixeira First Base
5 Alfonso Soriano Designated Hitter
6 Alex Rodriguez Third Base
7 Vernon Wells Left Field
8 Zoilo Almonte Right Field
9 Austin Romine Catcher
Total Runs Scored 688
*Removing Lyle Overbay
Optimality of Batting Order
Order Criteria Position
1 Alex Rodriguez Third Base
2 Chris Stewart Catcher
3 Lyle Overbay Designated Hitter
4 Derek Jeter Short Stop
5 Ichiro Suzuki Right Field
6 Brett Gardner Center Field
7 Mark Teixeira First Base
8 Vernon Wells Left Field
9 Robinson Cano Second Base
Total Runs Scored 763
*Random Permutation
Optimality of Batting Order
Order Criteria Position
1 Robinson Cano Second Base
2 Mark Teixeira First Base
3 Alex Rodriguez Third Base
4 Lyle Overbay Designated Hitter
5 Vernon Wells Left Field
6 Ichiro Suzuki Right Field
7 Chris Stewart Catcher
8 Brett Gardner Center Field
9 Derek Jeter Short Stop
Total Runs Scored 771
*Random Permutation
Optimality of Batting Order
Order Criteria Position
1 Derek Jeter Short Stop
2 Brett Gardner Center Field
3 Mark Teixeira First Base
4 Alex Rodriguez Third Base
5 Lyle Overbay Designated Hitter
6 Robinson Cano Second Base
7 Ichiro Suzuki Right Field
8 Chris Stewart Catcher
9 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