1. NBA Schedule Graph Theory and Strength of Schedule

2. Background At the beginning of the 1967-68 season, the NBA settled on an 82 game schedule which they still use today Matt Winick-architect of the NBA schedule for more than 20 seasons Winick controls scheduling and game operations and starts in February and 6 months later the final schedule for the 30 teams is completed Complicated system-assigns a point value to each date a team makes available and each team must have at least 50 points

3. Main factors for NBA Schedule Distance between games Home team advantage Strength of Schedule (SOS) West coast/ east coast NBA Scheduling formula requirements Court availability Official break Conflicts Broadcasters

4. Graph Theory Study of graphs which are mathematical structures used to model pairwise relations between objects Made up of vertices and edges Graph theory can be very helpful in determining information systems such as an NBA schedule

5. Graph Theory related to NBA In the NBA there are 2 conferences (eastern and western) Each conference contains 3 divisions, with 5 teams in each division(30 teams total) There are 1140 games total to be played throughout the regular season so forming a schedule is very difficult To start off we can look at a division in the Eastern conference by making it a complete graph with 5 vertices representing the 5 teams

6. Division in the NBA

7. Graph Theory in the NBA We could use colors to represent days and numbers 1-5 to represent each team in the division Day 1 (white): 2 plays at 5, and 3 plays at 4..1 has off Day 2(blue): 1 plays at 4, and 2 plays at 3..5 has off Day 3 (red): 5 plays at 3, and 1 plays at 2..4 has off Day 4 (purple): 4 plays at 2, and 5 plays at 1..3 has off Day 5 (black) 3 plays at 1, and 4 plays at 5..2 has off On days 6-10 the same schedule would apply except home and away teams would switch

8. Graph Theory Cont. 4 games against the other 4 division opponents (4x4=16 games) 4 games against 6 out of the division conference opponents (4x6=24 games) 3 games against the remaining 4 conference teams (3x4=12 games) 2 games against teams in the opposing conference (2x15=30 games)

9. Graph Theory cont. By looking at the graph theory or the complete graph we can see that every team would play each other exactly twice It eliminates most home team advantage bias, distance between games, west coast/east coast and the amount of games played in a certain amount of time Although the graph theory for the division is just a part of the full amount of scheduling we would use the same model to determine the full NBA schedule

10. Strength of schedule A main factor in determining the NBA schedule SOS represents a team’s average schedule difficulty faced by each team in the games that it’s played so far It can be calculated by relative percentage index which includes wins and losses records of opponents and opponents’ opponents SOS= ((2(Opp. Record)+(opp. Opp. Record))/3)

11. Relative Percentage Index If the New York Knicks were currently 3-3 and they were playing the Chicago Bulls who were 3-3, and who’s opponents records were 5-1, 3-2, 3-2, 2-4, 4-2, 1-5 we would first look at the Bulls record (opponent) Bulls record 3-3 which is 3/6 or.5 Next we would look at the Bull’s opponents records which would total 18/36 or.5 as well The Knicks strength of schedule after 6 games would be: (2(.5)+(.5))/3=.5

12. SOS cont. In this case the Knicks strength of schedule would be.5 which would most likely fall In the middle of strength of schedules for the teams in the NBA This formula can be used to determine who they play to evenly balance out games In the future This evens out the league’s difficulty of games played If this aspect of the schedule was random one teams schedule could be extremely more difficult than another NBA team

13. Practice problem The Los Angeles Lakers are currently 9-3 and they are playing the Houston Rockets who are 7-5. The opponents win totals of the Rockets through the first 12 games are 2-10, 8-4, 6-6, 9-3, 1-11, 5-7, 4-8, 3-9, 5-7, 7-5, 7-5, 10-2. What is the Los Angeles Lakers strength of schedule for the season? If the average strength of schedule for NBA teams was.6 how would you predict the difficulty of the Lakers games for the rest of the season?

14. SOS= ((2(Opp. Record)+(opp. Opp. Record))/3) Opponents record (rockets)=7-5 which is 7/12 Rockets opponents record= 67 wins/144 games SOS=((2(7/12)+(67/144))/3)=about.544 This is slightly below average, therefore we would predict the rest of the Lakers games to be slightly more difficult than the league average to balance out

15. Works cited http://webcache.googleusercontent.com/search?q=cache:htt p://kkinder22.files.wordpress.com/2007/06/graph-theory-as- it-relates-to-scheduling.ppt http://webcache.googleusercontent.com/search?q=cache:htt p://kkinder22.files.wordpress.com/2007/06/graph-theory-as- it-relates-to-scheduling.ppt http://www.nbastuffer.com/component/option,com_glossary /Itemid,90/catid,44/func,view/term,How%20the%20NBA%20 Schedule%20is%20Made/ http://www.nbastuffer.com/component/option,com_glossary /Itemid,90/catid,44/func,view/term,How%20the%20NBA%20 Schedule%20is%20Made/ http://www.nationalchamps.net/NCAA/BCS/strength_of_sche dule_explain.htm http://www.nationalchamps.net/NCAA/BCS/strength_of_sche dule_explain.htm