Hitachi Baseball is a major league baseball team beginning its fifth year of operation. The team had losing records in each of its first 4 years and finished near the bottom of its division. However, the team was young and generally competitive. The team's general manager, Wales Takashi, believes that with a few additional good players, the team can become a contender for the division title and perhaps even for the pennant. They have prepared several proposals for free-agent acquisitions to present to the team's owner, Hitachi Sports Nagoya.

Under one proposal, the team would sign several good available free agent players, including two pitchers, a good fielding shortstop, and two power-hitting outfielders for $42 million in bonuses and annual salary. The second proposal is less ambitious, costing $25 million to sign a relief pitcher, a solid, good-hitting infielder, and one power-hitting out-fielder. The final proposal would be to maintain the current team and continue to develop.

The general manager, Wales Takashi, wants to lay out a possible season scenario for the owner so he can assess the long-run ramifications of each decision strategy. Because the only thing the owner understands is money. Wales Takashi wants this analysis to be quantitative, indicating the money to be made or lost from each strategy. To help develop this analysis, he has hired two new staff, Jenna and Philips, to undertake the task.

Jenna and Philips analysed the league data for the previous eight seasons for attendance trends, logo sales (i.e. clothing, souvenirs, hats, etc.), player sales and trades, and revenues. In addition,they interviewed several other owners, general managers, and league officials. They also analysed the free agent players that the team was considering signing.

Based on their analysis, Jenna and Philips feel that if Hitachi Baseball does not invest in any free agent players, the team will have a 20% chance of contending for the division title and an 80% chance of being out of contention most of the season. If the team is a contender, there is a 0.70 probability that attendance will increase as the season progresses and the team will have high attendance levels (between 1.7 million and 2.0 million) with profits of $160 million from ticket sales, concessions, advertising sales, TV and radio sales, and logo sales. They estimate a 0.20 probability that the team's attendance will be mediocre (between 1.2 million and 1.4 million) with profits of $105 million and a 0.10 probability that the team will suffer low attendance (less than 1.0 million) with profit of $90 million. If the team is not a contender, Jenna and Philips estimate that there is 0.05 probability of high attendance with profits of $85 million, a 0.35 probability of medium attendance with profits of $55 million, and a 0.60 probability of low attendance with profits of $35 million.If the team marginally invests in free agent players at a cost of $25 million, there is a 55% chance it will be a contender. If it is a contender, then later in the season it can either stand pat with its existing roster or buy or trade for players that could improve the team's chances of winning the division. If the team stands pat, there is a 0.70 probability that attendance will be high and profits will be $190 million. There is a 0.20 probability that attendance will be mediocre with profits of $140 million and a 0.10 probability of low attendance and profits of $110 million. Alternatively, if the team decides to buy or trade for players, it will cost $8 million, and the probability of high attendance with profits of $190 million will be 0.80. The probability of mediocre attendance with $155 million in profits will be 0.10, and there will be a 0.10 probability of low attendance, with profits of $115 million.

If the team is not in contention, then it will either stand pat or sell some of its players, earning approximately $10 million in profit. If the team stands pat, there is a 0.20 probability of high attendance, with profits of $125 million; a 0.35 probability of mediocre attendance, with profits of $60 million; and a 0.45 probability of low attendance, with profits of $40 million. If the team sells players, the fans will likely lose interest at an even faster rate, and the probability of high attendance with profits of $100 million will drop to 0.15, the probability of mediocre attendance with profits of $50 million will be 0.25, and the probability of low attendance with profits of $35 million will be 0.60.

The most ambitious free-agent player strategy will increase the team's chances of being a contender to 65%. This strategy will also excite the fans most during the off-season and boost ticket sales and advertising and logo sales early in the year. If the team does contend for the division title, then later in the season it will have to decide whether to invest in more players. If the team stands pat, the probability of high attendance with profits of $210 million will be 0.80, the probability of mediocre attendance with profits of $170 million will be 0.15, and the probability of low attendance with profits of $125 million will be 0.05. If the team buys players at a cost of $10 million, then the probability of having high attendance with profits of $220 million will increase to 0.83, the probability of mediocre attendance with profits of $180 million will be 0.12, and the probability of low attendance with profits of $130 million will be 0.05.

If the team is not in contention, it will either sell some players' contracts later in the season for profits of around $15 million or stand pat. If it stays with its roster, the probability of high attendance with profits of $115 million will be 0.15, the probability of mediocre attendance with profits of $85 million will be 0.25, and the probability of low attendance with profits of $65 million will be 0.60. If the team sells players late in the season, there will be a 0.10 probability of high attendance with profits of $100 million, a 0.30 probability of mediocre attendance with profits of $65 million, and a 0.60 probability of low attendance with profits of $50 million.

Tasks:

1) Articulate the problem using a flow diagram or pay-off table to show the process.

(7.5 marks)

2) Develop a decision tree and show all expected values and probabilities associated with.

(7.5 marks)

3) Interpret your decision to the team owner and assist Jenna and Philips in determining the best strategy to follow.