When NBA teams don’t want to win GAMES TO LOSE Team X Stefano Bertani Federico Fabbri Jorge Machado Scott Shapiro MBA 211 Game Theory, Spring 2010Games to Lose – MBA 211 Game Theory 2 Games to lose – When NBA teams don’t want to win 1. Introduction ................................................................................................................................................. 3 1.1 Situation ................................................................................................................................................ 3 1.2 NBA Structure ........................................................................................................................................ 3 1.3 NBA Playoff Seeding ............................................................................................................................... 4 1.4 NBA Playoff Tournament ........................................................................................................................ 4 1.5 Home Court Advantage .......................................................................................................................... 5 1.6 Structure of the paper ............................................................................................................................ 5 2. Situation analysis ......................................................................................................................................... 6 2.1 Scenario analysis .................................................................................................................................... 6 2.2 Calculating winning probabilities ............................................................................................................ 9 2.3 Payoffs calculation ............................................................................................................................... 10 3. Dissecting Popovich’s move ....................................................................................................................... 12 3.1 Playing to win or playing to lose? ......................................................................................................... 12 3.2 Payoff when both teams play to lose .................................................................................................... 13 3.3 Calculating the equilibrium solution ..................................................................................................... 14 3.4 Signaling by sitting the best players ...................................................................................................... 15 4. Conclusions ................................................................................................................................................ 18 4.1 What can NBA do to change the incentives to lose? ............................................................................. 18 4.2 The next chapter of the story ............................................................................................................... 19 5. Appendix ................................................................................................................................................... 21 5.1 Calculating the winning probabilities .................................................................................................... 21 5.2 Calculating the payoffs of a war of attrition .......................................................................................... 24Games to Lose – MBA 211 Game Theory 3 1. Introduction 1.1 Situation On Wednesday, April 14th, 2010, the San Antonio Spurs were heading to Dallas for the last game of the NBA regular season. While both the Spurs and Dallas Mavericks were guaranteed spots in the playoffs, the outcome of this game would have a far reaching impact on each team’s seed in the playoffs. If San Antonio won, they could become a 6th seed, but if they lost, they would be a 7th seed. San Antonio coach Greg Popovich submitted his team roster earlier that day. As usual, the starting lineup included his two best players: Tim Duncan and Manu Ginobili. Minutes before the 8pm tipoff, coach Popovich publicly instructed the leaders of his team, Duncan and Ginobili, to sit this game out. In fact, they were dressed in business suits throughout the game and were not even given a chance to play. So in this all-important final game of the season, why would a coach bench his two best players? Perhaps he had developed a mental model of his opponent and the entire NBA Western conference and determined that his expected payoff of future winnings would increase by not playing his two stars against Dallas. 1.2 NBA Structure The NBA playoffs are a single elimination tournament consisting of several “Best of 7” series. The playoffs commence following the NBA regular season. In the NBA regular season there are 30 teams who each play 82 games. These teams are split into two 15-team conferences: East and West. Each conference is further divided into three divisions.Games to Lose – MBA 211 Game Theory 4 1.3 NBA Playoff Seeding The top eight teams (by overall winning percentage) in each conference are seeded one through eight at the conclusion of the regular season. The team with the best record in each division is named a division champion and guaranteed a seed of four or better. For example, let’s envision a situation in which four teams in the Western Conference Pacific Division have the top four records in the NBA Western Conference. All of these four teams are guaranteed playoff spots, but only the division champion and the second best record holder will end up in the top 4. The third and fourth seeds are allocated to the champions of the Southwest and Northwest divisions even though Pacific division teams may have better records. So the fifth through eighth seeds are allocated by remaining best records, starting with the teams that finished third and fourth place in the Pacific division. If two teams are tied for the same record, the team with the better regular season record against the opponent gets the higher seed. If they are tied in regular season playing, then the team with the best record against teams within its own division gets the higher seed. If their