In many sports competitions, such as men's tennis grand slam and NBA basketball finals, we often see the competition system of three wins in five sets and four wins in seven sets. The snooker billiards world championship is a 10 win system in 19 sets. Why should we implement this multi game system?
This is because every game is a random event. There is a great chance that the outcome of a game will be determined. The strong party does not necessarily win the game. In general, people still want the strong party to win the game. Multi game system can improve the probability of the strong Party winning. So to what extent can multi game games reduce chance?
Take the NBA basketball finals as an example. Suppose there is a strong and weak team game, and the strong team has a 55% chance of winning each game against the weak team. If the system of four wins in seven innings is adopted, what is the probability of the strong team winning in the end? We need Pascal's method, which is to multiply each possibility by the probability of victory of the two teams and add them. The final answer is 60%. That is, the probability of strong teams winning has increased by 5%. Of course, even so, the weak team still has a 40% chance of winning, and the weak team is still very hopeful of winning.
Under this competition system, the team that wins the league title may not be the strongest team. This is why some sports should increase the number of finals as much as possible. The qualification match of snooker billiards World Championship adopts the "long game system" of 19 sets of 10 wins. In the final stage, it adopts the system of 35 sets of 18 wins, which can be played in two days.
35 innings are not long enough. The calculation results show that under the situation of 55% to 45%, 269 sets are needed in the final to ensure that the strong team has at least 95% confidence to win the championship!
So why don't many competitions adopt the competition system of playing hundreds of innings to determine the outcome, so as to ensure that the strong win? On the one hand, both contestants and spectators have limited energy; On the other hand, the existence of contingency will increase the appreciation of sports competitions.