Thursday, July 23, 2009

SVD Analysis of the 2006 Tour

As promised, here is more of this dorky, generally pointless stuff – Part 3 of a series on using singular value decomposition to study grand tour results. In this post, I will look at the 2006 Tour de France, a year (in)famous for the Floyd Landis doping spectacle and Oscar Pereiro being declared winner in part due to gaining 30 minutes in a flat-stage breakaway that was not chased. Despite these odd circumstances, the overall complexity of this Tour was less than most grand tours, containing only 3.1 effective stages.

As I discussed in the post on the 2007 tour, SVD basically rearranges all of the results from all of the stages into a series of composite stages, the modes, that appear in the data with decreasing weights. Here are the modes and weights for the 2006 Tour:

The SVD modes are read as columns in the raster plot, with red and green corresponding to greater and lesser times for each stage. Only riders who finished the race are included in the results, and among those excluded is Floyd Landis since his results have been removed from the CQ record.

The first striking feature of the mode patterns is how uneventful the first nine stages were. None of the large SVD modes has a large signal for these stages, meaning very few time gaps occurred. The major climbing stages were Stages 11, 15, 16, and 17, and sure enough these are the primary contributors to Mode 1. Stages 7 and 19 were individual time trials, the first of which had minor effects on the GC. Mode 2 primarily encodes large time losses on Stage 13 – the stage in which Voigt, Pereiro, Chavanel, Quinziato, and Grivko gained enormous time in the peloton. Mode 3 mostly encodes time gains on the Stage 17 to Morzine, which saw the peloton shatter in the wake of Landis’s shady escapade. Modes 4 and 5 are more corrections to mountain stage placings, and the latter modes are minor time gaps on flat stages and time trials.

Each riders’ individual results can be recomputed by summing up these patterns, with each pattern separately weighted according to the individual rider. Looking at the weights for the first two modes for each rider, we see something quite unique in this Tour. This plot shows the extent to which each rider’s results (dot) exhibited Mode 1 (x-axis) and Mode 2 (y-axis), with final GC placing running from red to blue:

Comparing this with the results from the 2007 Tour we see a major rotation such that the results tend to spread from upper left to lower right rather than simply left to right. This, of course, is due to the Stage 13 breakaway. The four points isolate below are Pereiro, Voigt, Chavanel, and Quinziato (Grivko is not included since he did not finish the Tour). Their special status as breakaway survivors is clearly shown in their isolation on the plot. Note that Pererio is to the upper left of his breakaway companions, meaning that his Tour did have the makings for GC success even without the break. Looking at the top 10, we see how he compares to the others:

What are you doing all the way down there, Oscar? Winning the Tour de France, apparently.

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