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Scheduling the Optimal Baseball Line-up. Stefanie Molin Christian Morales Sarah Daniels . Overview. Objective: Determine optimal starting lineup and batting order for a MLB team for one season. Select starting players for each game 162 games per season 33 primary players on roster - PowerPoint PPT Presentation
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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 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
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