NBA Schedule Graph Theory and Strength of Schedule

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

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

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

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

Division in the NBA

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

Graph Theory Cont. • 4 games against the other 4 division opponents (4 x 4=16 games) • 4 games against 6 out of the division conference opponents (4 x 6=24 games) • 3 games against the remaining 4 conference teams (3 x 4=12 games) • 2 games against teams in the opposing conference (2 x 15=30 games)

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

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)

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, 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

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

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, 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?

• • • 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

Works cited • http: //webcache. googleusercontent. com/search? q=cache: htt p: //kkinder 22. files. wordpress. com/2007/06/graph-theory-asit-relates-to-scheduling. ppt • http: //www. nbastuffer. com/component/option, com_glossary /Itemid, 90/catid, 44/func, view/term, How%20 the%20 NBA%20 Schedule%20 is%20 Made/ • http: //www. nationalchamps. net/NCAA/BCS/strength_of_sche dule_explain. htm