stochastic programsprobabilityand statistics how often does the better team winthus far we have looked at using statistical methods to help understand possible outcomes of games in which skill is not intended to play role it is also common to apply these methods to situations in which there ispresumablysome skill involved setting odds on football matchchoosing political candidate with chance of winninginvesting in the stock marketand so on almost every october two teams from american major league baseball meet in something called the world series they play each other repeatedly until one of the teams has won four gamesand that team is called (not entirely appropriately"the world champion setting aside the question of whether there is reason to believe that one of the participants in the world series is indeed the best team in the worldhow likely is it that contest that can be at most seven games long will determine which of the two participants is betterclearlyeach year one team will emerge victorious so the question is whether we should attribute that victory to skill or to luck to address that question we can use something called -value -values are used to determine whether or not result is statistically significant to compute -value one needs two thingsa null hypothesis this hypothesis describes the result that one would get if the results were determined entirely by chance in this casethe null hypothesis would be that the teams are equally talentedso if the two teams were to play an infinite number of seven-game serieseach would win half the time an observation data gathered either by observing what happens or by running simulation that one believes provides an accurate model of what would happen the -value gives us the likelihood that the observation is consistent with the null hypothesis the smaller the -valuethe more likely it is that we should reject the hypothesis that the observation is due entirely to chance usuallywe insist that be no larger than before we consider result to be statistically significant we insist that there is no more than chance that the null hypothesis holds getting back to the world seriesshould we consider the results of those sevengame series to be statistically significantthat isshould we conclude that the better team did indeed winfigure contains code that can provide us with some insight into that question the function simseries has one argumentnumseriesa positive integer describing the number of seven-game series to be simulated it plots the probability of the better team winning the series against the probability of that team winning single game it varies the probability of the better team winning single game from to and produces plot