The logic of the draft is simple. The team with the worst record (the Colts this year) from the last season gets to choose first from the top players coming out of college while the team with the second worst record picks second and goes down the line until it gets to the Super Bowl Champion who picks last in the round. The picks are a reflection of which players are available and what the team's needs (or what the teams believe that their needs) are. The exchange above shows how passionate people's beliefs about a teams needs can be. Steeler's coach Chuck Noll was called a genius for his drafting in the 1970s which built their dynasty in that decade. Later he was heavily criticized for passing on Dan Marino in 1983 (although almost every other team did too except Miami which picked next to last that year). Imagine what problems could be solved if all that energy and talent were trained on the real problems of the world such as cancer and global warming.
This method of picking players for pro sports teams works well in evening out the talent among the teams, along with the salary cap. This kind of purposeful selection does not work for surveys, polls, and clinical trials because the selections made are a reflection of the selectors biases. Such a survey was done in the 1948 Presidential Election where pollsters selected individuals to meet a quota for gender and other variable in order to make the sample representative according to the variables that they thought were important and the picture at the left was the result. Random sampling has been used since 1948 because it is unbiased with respect to all of the other that are not accounted for by the researchers or coaches. Random sampling may not work for the NFL or other pro sports leagues but high school/junior high gym classes could benefit from randomly assigning kids to teams and having them work together. That would encourage kids to cooperate more.
An example of a Monte Carlo experiment would be to have a group of fans pick their fantasy league teams using the draft method and then have a computer select the league by random using a computer and compare how their respective teams perform over the season. Some teams may differ but overall they will be similar.