1. Introduction to the Current Controversy
Nice work with the analysis of swimming data in the last chapter! You are now going to apply some of the same techniques to tackle the so-called Current Controversy of the 2013 World Championships.
2. The Current Controversy
In those championships in Barcelona, there were anecdotal reports of a very slight, swirling current in the pool. So, for example in a 50 meter event, swimmers in lane 8 would be swimming with the current, while those in lane 1 would be swimming against it. Unfortunately, the pool used in the 2013 World Championships was temporary and was deconstructed after the competition. So there is no way of measuring the current after the fact.
Your goal in this chapter is to use your statistical thinking skills to find evidence of a current in the data from the 2013 World Championships.
3. Citation
The approach you will take is inspired by the analysis in this publication.
4. The Current Controversy
Before investigating lane bias, it is important to know how a swirling current might affect each lane. It is strongest in the outer lanes, and slowest in the middle. This is akin to swirling a cup of tea. The outsides flow the fastest and the center is not flowing.
It is also important to know how swimmers are assigned to lanes. For the finals, the swimmer who was fastest in the semifinal is assigned to lane 4. The next fastest is assigned to lane 5. The next to lane 3, and so on. So, in the absence of current, the swimmers in the center two lanes are expected to be the fastest, but there are typically not major differences among swimmers in the outer lanes.
For your first analysis, you will look at the 50 meter events, since the swimmers in those events do not turn around. They only swim with or against the putative current.
It stands to reason that in a fair pool, we would see athletes swimming in lanes one through three in the finals winning as many medals as those swimming in lanes six through eight. Remember, the top three finishers in the final of each event get medals, so with four strokes and two genders, there are a total of 24 medals awarded in 50 meter events.
5. Medal counts
Looking at medals awarded in recent years, there is not a big disparity between high lane numbers and low lane numbers. Except in 2013, when 11 medals were awarded to swimmers in lanes six through eight and only one in lanes one through three.
If there is an equal chance of getting a medal in low lane numbers as in high lane numbers, the number of medals in low-numbered lanes is Binomially distributed with probability 0.5.
6. How probable is it?
Knowing this, we can use hacker stats to compute the probability of getting zero or one medal in lanes one through three. There is about a 0.3 percent chance. Unlikely, but not impossible.
7. Your tasks
With this in mind, we can set up your tasks for the next few exercises. You will investigate improvement of individual swimmers moving from low- to high-numbered lanes. You will compute the size of the effect swimming in low versus high lane number has on speed. Finally, you will test the hypothesis that on average there is no difference between low- and high-numbered lanes.
8. Let's practice!
All right. Go for it!