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
1. Select starting players for each game
• 162 games per season
• 33 primary players on roster
1. Determine batting position of each
player in starting line-up
• Maximize runs per game
Player Statistics
OBP – On-Base Percentage
SB – Stolen Bases
RBI – Runs Batted In
HR – Homeruns
Singles, Doubles, Triples
Rest Days
Salary
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 Positions
Some players can play multiple
positions
Player only scheduled in secondary
position if higher priority than
primary position
Factors:
Relative importance of each
position
Number 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
Speed is priority
1st hitter should be
“power hitter,” 2nd
should be more
consistent
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
Player Evaluation
Best player
OBP = 1.6×slugging
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
Player Evaluation
Good hitters
OBP becomes less
important; HR
becomes more
important
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
Player Evaluation
Worse hitter; on-base
becomes more
important
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
Player Evaluation
Fast hitters at end of
line-up
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
RESULTS
Line-up Evaluation
Simulated total season
runs for each line-up
Average line-up scored
782 runs throughout
season
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-up
Deviations from line-up result in fewer
runs over season
Our 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