For reality television and competitive cooking enthusiasts the show Ultimate Cakeoff, produced by TLC, is a real tour de force. The premise: top cake artists and decorators are brought together to compete in creating a cake for some high-profile event. The judges evaluate their efforts based on technical difficulty, adherence to the theme, and aesthetic value, then choose a winning team to receive the $10,000 prize.
Each team has nine hours to produce their ultimate cake. In order to keep the competition interesting and generate some much-needed drama, each episode is broken up by one or two smaller challenges designed to test the team leader's technical skill and speed at a particular cake-related task (such as piping, decorating, carving, etc.) The winner of each mini-challenge can choose one of the other two teams to sit out for thirty minutes.
Nine hours is already a short timeframe to create an award-winning cake - many wedding cakes can take up to a week to construct - so it would seem like losing 30 minutes to an hour would be a serious disadvantage. But, after watching two seasons of Ultimate Cakeoff (a dirty job, but someone had to do it) I noticed something strange: teams forced to sit out didn't seem to lose with any greater frequency. In fact, they often went on to win the competition!
This counter-intuitive trend sparked my curiosity, so I decided to put the question to a statistics program. After collecting data on every episode to find the characteristics of each team, who was forced to sit out, and who won each competition, I was able to find some results. The first regression found that being forced to sit out due to a challenge would increase the chance of winning by about 24%, a statistically significant result. After controlling for the individual attributes of of each participant the statistical significance vanished, and being forced to sit out had no measurable impact on the chance of winning at all (Click here to view the regressions performed, in STATA output format).
What might explain these findings? It would seem that less working time would result in a lower-quality cake, that was less likely to take the prize. Discovering the opposite result is somewhat surprising.
Of course, cake artists forced to sit out were not chosen randomly. The most common reason when choosing who to give a penalty was some variation of "(s)he looks way ahead! Take a break and slow down!" Apparently, cake artists are pretty good at judging each others' progress, and the team that is ahead partway through the competition is often the most talented. Trying to stall them with a penalty may even the field slightly, but not enough to overcome superior cake skills and design.
Admittedly, this is a pretty trivial application for a powerful statistics program. But, there may be some broader lessons for social scientists generally. When human choice is involved few events are truly random, which would be the ideal in an experimental setting. Economists can find some clever ways to mimic a true experiment, but perfect success in that regard still remains elusive. Examining how the data are collected and what selection effects are present is crucial to interpreting statistical results... Otherwise one might be inclined to believe that a shorter work-time makes a better wedding cake!