GAMES TO LOSE When NBA teams don’t want to win Team X Stefano Bertani Federico Fabbri Jorge Machado Scott Shapiro MBA 211 Game Theory, Spring 2010 Games to Lose – MBA 211 Game Theory 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 .......................................................................................... 24 2 Games to Lose – MBA 211 Game Theory 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. 3 Games to Lose – MBA 211 Game Theory 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 division records are tied then the team with the best winning percentage against teams in its conference gets the higher seed. This continues with three more levels of tiebreaking potential1. 1.4 NBA Playoff Tournament Once the 1st through 8th seeds are determined for each conference, the first round of the playoffs beings with teams matched in a single elimination bracket. This first round consists of a best-of- seven series such that the first team to win four matches moves on to the next round. In this round, the first seed plays the eighth seed, second plays seventh, third plays sixth and fourth plays fifth. In theory, the first seed, by having the best record in the conference, should enter the first round of the 1 NBA playoff seed tiebreaking rules http://www.cbssports.com/nba/story/7164305 4 Games to Lose – MBA 211 Game Theory playoffs with the highest likelihood of advancing to the second round. By playing the eighth seed, which has the worst record of all teams in the top 8 in that conference, the first seed should breeze through to the second round. 1.5 Home Court Advantage Unlike some other sporting leagues, all NBA games (except for the All-star game and certain exhibition games) are played at one of the participating team’s venues. Games are never played at a neutral 3rd party venue. It has also been shown that the home team is more likely to win a game, all things being equal, than the visiting team. In a particular matchup in the playoffs, the team with the better regular season record receives home court advantage according to NBA rules. Home court advantage is manifested in the number of games played at a specific venue during a best-of-seven series. The team with the better record and thus home court advantage will play in its arena during four of the seven possible games (encounters 1, 2, 5 and 7). This rule is intended to motivate teams to have the best regular season record possible so that they can maximize the amount of games they play at home during the playoffs. 1.6 Structure of the paper In chapter 2, we will analyze the scenarios from the game and the outcomes for Dallas and San Antonio depending on the result of the matches. In chapter 3 we will describe the mental model of San Antonio’s Coach Popovich and why he decided to sit the best players. Finally in chapter 4 we will discuss what the NBA can do to change this negative incentive to lose. 5 Games to Lose – MBA 211 Game Theory 2. Situation analysis 2.1 Scenario analysis On April 13th, before the last day of the regular season, the 8 teams in the western conference heading to the playoffs were already determined. However, the final rankings and thus the resulting playoff bracket were still open to wide swings. As it is shown in Table 1, Dallas, Denver, Utah and Phoenix were all in a 1-point interval (according to regular season wins). Portland and San Antonio were tied for the 6th position. Los Angeles and Oklahoma were the only two teams locked into a position, respectively 1st and 8th. All the other teams could still move in the ranking, depending on the results of the matches being played in the last day of the regular season. Phoenix, for example, could improve its ranking by as much as 3 slots, from 5th to