Triathlon in three colors
With Jérôme Lê we are planning to swim/bike/run Paris triathlon next July. Before begining the trainning, we want to know where to concentrate efforts. Let us look at some data.
The race distance is known as Intermediate, or Standard, or Olympic distance, with 1.5 km swim, 40 km ride and 10 km run. Data for 2010 Open race (ie not the Elite race) can be found on a site of running races results called Ipitos, after free registration. It consist in 1412 finisher times, for the three parts of the race. Gender is available. Histograms normalized as probabilities are as follows, for time in minutes:
Times for swimming are shorter than the two other parts (resp. 30, 70 and 50 minutes in average). The larger standard deviation is for cycling (resp. 4, 8 and 7 minutes). So larger differences in time are done in this part of the race.
It appears that the skew is positive for the three parts of the race: it sounds usual for that kind of event. It is open to everyone, and most of newcomers enlarge the bulk of the right tail. The cycling histogram is the most skewed (resp. .5, 1.3 and .9). We can see that with boxplots and density estimates. These are done with centered data:
As expected, no outlier is found on the left of the distributions: this is the “no-superman” effect. On the contrary, the otherside of the box outliers are overcrowded, the “nowcomer” effect.
As an aside I have plotted the normalized 3 dimensional data in a square array, with squares of a color defined by data in the RGB model. Sampling 1024 of the 1412 finishers, this provides this (pointless) Richter-like plot:
The following triangle is obtained as in this post:
The fact that the points cloud is on the left illustrates the massive skewness of cycling. The few points outside the cloud correspond to poor performers in the corresponding sport, with swimming at the bottom left, cycling at the bottom right, and running at the top. For example, for the three light green points, loosy bikers, but rather good at swimming and running.