The Carolina Cougars is a major league baseball expansion teambeginning its third year of operation. The team had losing recordsin each of its first 2 years and finished near the bottom of itsdivision. However, the team was young and generally competitive.The team’s general manager, Frank Lane, and manager, Biff Diamond,believe that with a few additional good players, the Cougars canbecome a contender for the division title and perhaps even for thepennant. They have prepared several proposals for free- agentacquisitions to present to the team’s owner, Bruce Wayne.
Under one proposal the team would sign several good availablefree agents, including two pitchers, a good fielding shortstop, andtwo power-hitting outfielders for $52 million in bonuses and annualsalary. The second proposal is less ambitious, costing $20 millionto sign a relief pitcher, a solid, good-hitting infielder, and onepower-hitting out- fielder. The final proposal would be to standpat with the current team and continue to develop.
General Manager Lane wants to lay out a possible season scenariofor the owner so he can assess the long-run ramifications of eachdecision strategy. Because the only thing the owner understands ismoney, Frank wants this analysis to be quantitative, indicating themoney to be made or lost from each strategy. To help develop thisanalysis, Frank has hired his kids, Penny and Nathan, bothmanagement science graduates from Tech.
Penny and Nathan analyzed league data for the previous fiveseasons for attendance trends, logo sales (i.e., clothing,souvenirs, hats, etc.), player sales and trades, and revenues. Inaddition, they interviewed several other owners, general managers,and league officials. They also analyzed the free agents that theteam was considering signing.
Based on their analysis, Penny and Nathan feel that if theCougars do not invest in any free agents, the team will have a 25%chance of contending for the division title and a 75% chance ofbeing out of contention most of the sea- son. If the team is acontender, there is a .70 probability that attendance will increaseas the season progresses and the team will have high attendancelevels (between 1.5 million and 2.0 million) with profits of $170million from ticket sales, concessions, advertising sales, TV andradio sales, and logo sales. They estimate a .25 probability thatthe team’s attendance will be mediocre (between 1.0 million and 1.5million) with profits of $115 million and a .05 prob- ability thatthe team will suffer low attendance (less than 1.0 million) withprofit of $90 million. If the team is not a contender, Penny andNathan estimate that there is .05 probability of high attendancewith profits of $95 mil- lion, a .20 probability of mediumattendance with profits of $55 million, and a .75 probability oflow attendance with profits of $30 million.
If the team marginally invests in free agents at a cost of $20million, there is a 50–50 chance it will be a contender. If it is acontender, then later in the season it can either stand pat withits existing roster or buy or trade for players that could improvethe team’s chances of winning the division. If the team stands pat,there is a .75 probability that attendance will be high and profitswill be $195 million. There is a .20 probability that attendancewill be mediocre with profits of $160 million and a .05 probabilityof low attendance and profits of $120 million. Alternatively, ifthe team decides to buy or trade for players, it will cost $8million, and the probability of high attendance with profits of$200 million will be .80. The probability of mediocre attendancewith $170 million in profits will be .15, and there will be a .05probability of low attendance, with profits of $125 million.
If the team is not in contention, then it will either stand pator sell some of its players, earning approximately $8 million inprofit. If the team stands pat, there is a .12 probability of highattendance, with profits of $110 million; a .28 probability ofmediocre attendance, with profits of $65 million; and a .60probability of low attendance, with profits of $40 million. If theteam sells players, the fans will likely lose interest at an evenfaster rate, and the probability of high attendance with profits of$100 million will drop to .08, the probability of mediocreattendance with profits of $60 million will be .22, and theprobability of low attendance with profits of $35 million will be.70.
The most ambitious free-agent strategy will increase the team’schances of being a contender to 65%. This strategy will also excitethe fans most during the off-season and boost ticket sales andadvertising and logo sales early in the year. If the team doescontend for the division title, then later in the season it willhave to decide whether to invest in more players. If the Cougarsstand pat, the probability of high attendance with profits of $210million will be .80, the probability of mediocre attendance withprofits of $170 million will be .15, and the probability of lowattendance with profits of $125 million will be .05. If the teambuys players at a cost of $10 million, then the probability ofhaving high attendance with profits of $220 million will increaseto .83, the probability of mediocre attendance with profits of $175million will be .12, and the probability of low attendance withprofits of $130 million will be .05.
If the team is not in contention, it will either sell someplayers’ contracts later in the season for profits of around $12million or stand pat. If it stays with its roster, the prob-ability of high attendance with profits of $110 million will be.15, the probability of mediocre attendance with profits of $70million will be .30, and the probability of low attendance withprofits of $50 million will be .55. If the team sells players latein the season, there will be a .10 probability of high attendancewith profits of $105 million, a .30 probability of mediocreattendance with profits of $65 mil- lion, and a .60 probability oflow attendance with profits of $45 million.
Assist Penny and Nathan in determining the best strategy tofollow and its expected value.
