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

2. OVERVIEW

3. 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

4. Player Statistics OBP – On-Base Percentage SB – Stolen Bases RBI – Runs Batted In HR – Homeruns Singles, Doubles, Triples Rest Days Salary

5. SCHEDULING PROBLEM

6. 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

7. 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 OrderPosition 1Catcher 2First Base 3Second Base 4Short Stop 5Third Base 6Center Field 7Left Field 8Right Field 9Designated Hitter

8. Player Evaluation OrderCriteria 4(OBP×130)+Doubles+Triples+(3×HR)+(RBI/10) 3(OBP×160)+Doubles+Triples+HR+(RBI/10) 1OBP+SB+Triples 2OBP+(SB/500)+(Triples/10)+(RBI/10)+Singles 5(OBP×100)+(15×HR) 6(OBP×115)+(15×HR)+Doubles+Triples 7HR 8Doubles+Triples+HR 9Singles Speed is priority 1 st hitter should be “power hitter,” 2 nd should be more consistent

9. Player Evaluation OrderCriteria 4(OBP×130)+Doubles+Triples+(3×HR)+(RBI/10) 3(OBP×160)+Doubles+Triples+HR+(RBI/10) 1OBP+SB+Triples 2OBP+(SB/500)+(Triples/10)+(RBI/10)+Singles 5(OBP×100)+(15×HR) 6(OBP×115)+(15×HR)+Doubles+Triples 7HR 8Doubles+Triples+HR 9Singles Best player OBP = 1.6×slugging

10. Player Evaluation OrderCriteria 4(OBP×130)+Doubles+Triples+(3×HR)+(RBI/10) 3(OBP×160)+Doubles+Triples+HR+(RBI/10) 1OBP+SB+Triples 2OBP+(SB/500)+(Triples/10)+(RBI/10)+Singles 5(OBP×100)+(15×HR) 6(OBP×115)+(15×HR)+Doubles+Triples 7HR 8Doubles+Triples+HR 9Singles Good hitters OBP becomes less important; HR becomes more important

11. Player Evaluation OrderCriteria 4(OBP×130)+Doubles+Triples+(3×HR)+(RBI/10) 3(OBP×160)+Doubles+Triples+HR+(RBI/10) 1OBP+SB+Triples 2OBP+(SB/500)+(Triples/10)+(RBI/10)+Singles 5(OBP×100)+(15×HR) 6(OBP×115)+(15×HR)+Doubles+Triples 7HR 8Doubles+Triples+HR 9Singles Worse hitter; on-base becomes more important

12. Player Evaluation OrderCriteria 4(OBP×130)+Doubles+Triples+(3×HR)+(RBI/10) 3(OBP×160)+Doubles+Triples+HR+(RBI/10) 1OBP+SB+Triples 2OBP+(SB/500)+(Triples/10)+(RBI/10)+Singles 5(OBP×100)+(15×HR) 6(OBP×115)+(15×HR)+Doubles+Triples 7HR 8Doubles+Triples+HR 9Singles Fast hitters at end of line-up

13. RESULTS

14. Simulated total season runs for each line-up Average line-up scored 782 runs throughout season Line-up Evaluation

15. Average Lineup OrderCriteriaPosition 1Brett GardnerCenter Field 2Derek JeterShort Stop 3Robinson CanoSecond Base 4Mark TeixeiraFirst Base 5Alex RodriguezThird Base 6Lyle OverbayDesignated Hitter 7Vernon WellsLeft Field 8Ichiro SuzukiRight Field 9Chris StewartCatcher Total Runs Scored782

16. Optimality of Line-Up OrderCriteriaPosition 1Brett GardnerCenter Field 2Ichiro SuzukiRight Field 3Robinson CanoSecond Base 4Mark TeixeiraFirst Base 5Alfonso SorianoDesignated Hitter 6Vernon WellsLeft Field 7Chris StewartCatcher 8Eduardo NunezThird Base 9Jayson NixShort Stop Total Runs Scored702 *Removing Derek Jeter

17. Optimality of Line-Up OrderCriteriaPosition 1Brett GardnerCenter Field 2Derek JeterShort Stop 3Robinson CanoSecond Base 4Mark TeixeiraFirst Base 5Alfonso SorianoDesignated Hitter 6Alex RodriguezThird Base 7Vernon WellsLeft Field 8Zoilo AlmonteRight Field 9Austin RomineCatcher Total Runs Scored688 *Removing Lyle Overbay

18. Optimality of Batting Order OrderCriteriaPosition 1Alex RodriguezThird Base 2Chris StewartCatcher 3Lyle OverbayDesignated Hitter 4Derek JeterShort Stop 5Ichiro SuzukiRight Field 6Brett GardnerCenter Field 7Mark TeixeiraFirst Base 8Vernon WellsLeft Field 9Robinson CanoSecond Base Total Runs Scored763 *Random Permutation

19. Optimality of Batting Order OrderCriteriaPosition 1Robinson CanoSecond Base 2Mark TeixeiraFirst Base 3Alex RodriguezThird Base 4Lyle OverbayDesignated Hitter 5Vernon WellsLeft Field 6Ichiro SuzukiRight Field 7Chris StewartCatcher 8Brett GardnerCenter Field 9Derek JeterShort Stop Total Runs Scored771 *Random Permutation

20. Optimality of Batting Order OrderCriteriaPosition 1Derek JeterShort Stop 2Brett GardnerCenter Field 3Mark TeixeiraFirst Base 4Alex RodriguezThird Base 5Lyle OverbayDesignated Hitter 6Robinson CanoSecond Base 7Ichiro SuzukiRight Field 8Chris StewartCatcher 9Vernon WellsLeft Field Total Runs Scored775 *Random Permutation

21. 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

22. Next Steps… Create a more robust model that accounts for player injuries Verify our model by testing on other teams and past seasons