A Near-Optimal Solution

The students have had a chance to give their perspective on various aspects of the course so far, but now it's time for the professors to chime in.

As with most competitions, the team that wins does so relying on a mixture of skill and luck. Some might argue that when their team wins a game, it is all skill, while when their team loses on a last-second shot, it was just luck. There are some theories as to why upsets occur in sports. One rather good one is that for an underdog to win against a highly-ranked opponent, the underdog must reduce the total number of possessions that the game has. The theory goes that if the better team has more possessions, the better team will have more opportunities to show its natural skill and overcome short bursts of lucky scoring from an over-matched opponent. Whatever opinion you tend to have in these matters, we, the professors, think you will agree that in a one game challenge, such as the Traveling Epcot Tourist Challenge we had Thursday (with a mere 18 possessions), that luck/variability played a significant role in the outcome.

We know what you are thinking. These folks have sour grapes for finishing third behind two groups of students without PhD’s in Mathematics. You’re totally right, but there are some valuable lessons that the students can learn and be mindful of when they feel the need to gloat about this. Since the challenge has been explained well in previous posts, let us lay out the case for the good fortune of some of the teams and at the same time show some of the pitfalls encountered while putting together a good model.

Lack of data increases variability

The teams that beat us lucked into joining “movie” rides just as they started. Many attractions at Disney World have a pre-show movie that entertains guests while waiting for an attraction. These rides (or attractions in Disney-speak) had no posted start times so there was no way to plan ahead for when to show up. As a result, some teams did not occur a penalty for showing up to these rides too early. For instance, our last ride was Ellen’s Energy Adventure. When we showed up for the ride we had to wait 4 minutes to enter the building and then sit through Ellen’s entire pre-ride introduction video, another 8 minutes, before riding the ride. However, one is allowed access to the ride without watching the pre-ride video if the timing works out. Since the ride start time is not posted, there is variability in the length of this experience because riders have no way of knowing when to show up to skip the “non-essential” parts. Some teams lucked into to timing this better.

Coin Flips

Certain processes at amusement parks are naturally random. For instance, on Soarin', an attendant decides whether riders will go to one of two different “glider” pods. While the experience in each of these pods is the same, the exit tunnel for one pod is longer than the other. When we boarded Soarin' for the first ride of the day, we saw other teams go to the pod with the shorter exit tunnel, while we were directed to the other. When we finished, these teams had already moved on to another attraction. We were unlucky here.

Professors quickly move through the tunnels near Soarin' (not even slowing down for pictures that are in focus).

Another example of a random process is when a ride will break down. This is also an example of where having more data is useful in reducing the variability of the queue/ride experience because knowing the frequency in which a ride breaks down can be used in the planning of when to go to this attraction. The third through fifth-place teams all had to wait through malfunctions on different rides, sometimes while on the ride. For instance, we were delayed on Maelstrom (15 extra minutes) and Spaceship Earth (3 extra minutes) due to mechanical problems. These delays more than add up to the difference in our third-place time and the first-place time.

Professors before the Maelstrom delay (we weren't nearly as smily after the extra delay).

Invalid assumptions

One of the things we, the professors, had going against us that perhaps not all of the teams did is that we have collectively been to Epcot a lot. We failed to recognize in our planning how the new FastPass+ system would affect our wait times for certain rides. For instance, collectively we believed that we could walk on to Journey Into Imagination at any time during the day since we had all had this experience in the past numerous times. However, now that the new FastPass+ system has this ride as an option, more people seem to be visiting it. Hence, what we thought would be a five minute wait turned out to be a 25 minute wait. In short, garbage in (bad, no longer valid assumption) equals garbage out (a 20 minute penalty for us). Also, we were slowed here as Dr. Harris stopped to sign numerous autographs due to his uncanny resemblance to Rick Moranis.

So we think you will agree that sometimes superior skill and planning are thwarted due to variability and luck. We just needed more possessions.  

All kidding aside, everyone did a great job putting a lot of thought, energy, and effort into the execution of this task.  We'll give you a deeper look into the winning team's efforts soon, but in the mean time, cheers to all!

Soda samples from around the world at Club Cool.