Your favorite sports team acquired a player last season that they thought would improve the roster, but so far the fit has not worked out well. The team's general manager is considering trading the player, either now at the start of the season or at the trade deadline, which is midway through the season. There is a deal on the table now to trade the player for decent players in return, and the coaching staff estimates that this trade would add5wins to the season. However, it may be possible that if the team waits until the trade deadline, the player's skills may improve or may not improve, and the overall trade market could also either worsen or improve.

If the player does not improve, or if the market conditions worsen, a trade will not be possible, and thus the player must stay on the roster for the remainder of the season. If the player does not improve, the coaching staff estimates this will cost5wins. If the player improves but is not traded, the staff estimates this will add5wins. Finally, if the player improves and the market conditions improve, then the team could decide to trade that would add15wins or instead decide to keep the player. However, the trade available at the start of the season will not be available at the trade deadline. They estimate a50%chance the player improves, and, independently, an80%chance the market improves.

a) If at the trade deadline the player improves and the market conditions also improve, should the team trade the player or keep the player?

b) Should the team trade the player now, or keep the player until the trade deadline and reassess then?

c) The coaching staff has determined that they are actually not sure what the chances are that the player improves. What is the lowest chance of the player improvement the team can handle while wanting to keep the player for now?

d) A few games into the season, it is clear that there will be a good trade market. That is, the coaching staff now estimate a 100% probability of the market improving. How does this change the decision from (c)?

The answers were given as follows but need calculations (formulas) to use:

1) Trade, which adds 15 wins instead of 5

2) Trade now, the expected wins of waiting (4) are lower than the wins added by trading now (5).

3) p = 55.556%

4) p = 50%