The binomial distribution model assumes independence between games and that each team has a constant probability of winning a game throughout the series. Mosteller found both of these assumptions reasonable based on the data in the first half of the century. 

   Hal Stern examines these same questions using the more complete data that we now have. He concludes that the independence assumption is still reasonable but the constant probability is not. One reason for this is that the home team advantage in baseball seems real. 

   Best-of-seven playoffs also occur in professional basketball and hockey. Unlike baseball, in these sports, the teams competing in the playoff have also played against each other a number of times in the regular season. For these sports, Hal Stern applies a logistic regression model to consider how playing at home and the winning ratio for the two teams during the regular-season affect the outcome of the playoff. He finds that, for basketball, both the home team variable and the regular-season win ratio are predictors for the outcome of the playoff series while, for professional hockey, the win ratio is highly significant but the home team advantage is not. 

(1) Hal Stern points out that "one interesting finding in World series data is that there have been many more series lasting the full seven games than six games (33 vs. 21)". He asserts that the best we could expect with a binomial model would be to have an equal number of 6-game and 7-game series. Why is this? 

(2) If you assume a binomial distribution model for a World series between the Yankees and the Dodgers with the Yankees having a probability p=0.55 for winning each game, how likely do you think it is that the Yankees will win the best-of-seven playoff series? 

(3) Consider again a Yankee-Dodger series where the Yankees win each game with probability 0.55. Using EXCEL, find the number of games required to give the Yankees a 95% chance of winning the series. (Hint: As Stern remarks, in a best out of 2n+1 games series, you could require that teams play all 2n+1 games and the winner would not be changed.) 

(4) Evidently, in Bernoulli's time it was the custom in tennis to equalize a game by allowing the weaker player to have a single free point at any time during the game. If you are the weaker player, and assuming a Bernoulli model for the outcome of the points, when should you choose to take your free point? When would you choose to take it?