Wednesday, October 22, 2014

Tour de France: It Keeps Getting Faster at a Suspiciously Constant Rate

"To generalize," said William Blake, "is to be an idiot"--itself an over-generalization, but you get the point.

1. Estimates of Individual Performance in Excess of 6.2W/KG
Aside from blood tests, confessions, eyewitness accounts and the like, we have a hard time generalizing about the effect of blood doping on pro cycling.  A common method involves a generalization about the limits of what is possible; that is, like Aldo Sassi, assuming anything above 6.2 W/kg is likely a doped performance.

The counter-argument against this kind of generalization concerns outliers.  Tour de France riders are all outliers compared the general population, the 99.999th percentile.  But the GC contenders--the ones whose performance skirt that 6.2 W/kg--are almost beyond outliers.

Generalization about the limits of particular performances has...well...its limits.  These athletes are the 100th percentile, precisely the defining edge of the possible.  Pointing to a particular moment or effort from the edge of what is possible--one can only respond with degrees of credulity.  One can't just say, "nope, what we're witnessing is doping."

This post is about other ways of generalizing about doping's effect.

What if, instead of looking at exceptional individual performances, we look at the peleton or portions of the peleton over time?  Can we find correlations between how cyclists performed during the EPO era and during the pre-and post(?)-EPO eras?

2. Increases in average speed 
EPO came into the peleton in 1991, gradually became widespread and near-universal, and no better metric shows this than increased average speed; that's a common generalization made by TV announces and pundits.  My, how fast they're going!

The problem with that generalization is that the data doesn't exactly show it.

This chart shows two metrics from every Tour de France: average peleton speed and average distance traveled.  I include distance traveled because the chart shows a neat inverse correlation between the two:  as distance declines, particularly in the first 70 years, speed rises.
Maybe we can't see the jump in speed because of the scale of the graph above.  Just looking at in isolation, it's clear there's an increase in speed (from 23 to nearly 26 miles per hour):
The 25.88mph average seen in 2005 is over 4mph faster than the Tour's historical average speed (21.12mph).

In the context of prior decades, however, that increase in speed could have been predicted.  It continues a trend of previous years of ever-increasing speeds.  If we look at averages over previous quarter decades, it looks like this:

  • 1903 - 1930: 16.5mph
  • 1931 - 1963: 20.6mph (20% improvement on previous three decades)
  • 1964 - 1987: 22.3mph (7.5% improvement)
  • 1988 - present: 24.7mph (9.58% improvement)

It's no surprise that the Tour continues to get faster, just as sprinters and swimmers and high jumpers and speed skaters get faster.

Still, there's something funny about the rate of improvement in cycling.  Can you spot it?

3.  Non-decreasing marginal gains
Consider the marathon and our progress toward the two-hour mark.  From 2:55:18 in 1908 to 2:15:17 in 1958, 16 runners shaved 40 minutes off the record time.  From 1959 through 1998, 13 runners cut the record time only 10 minutes (to 2:06:05).  Since then, eight runners have cut that margin by another 3 minutes.

In the marathon the general pattern of gains, given fixed variables (i.e., genetics, equipment, environment) is of decreasing marginal gains.

Still, the marathon pace continues to rise at a surprising rate (i.e., it is surprisingly non-decreasing).  Some have argued that is due to the introduction of new populations and participants--namely, East Africans, who seem to have a knack for insanely fast lost distance running.

Even so, the pattern in marathon running is one of decreasing marginal gains--that is, of improving, but at smaller and smaller rates of improvement.

That is not the case in Tour average speeds since 1992, a trend this chart captures nicely:


Here's another chart showing the difference in linear trend lines.
The much steeper green line indicates the decreasing rate of gains made in marathoning, while the red, nearly horizontal line indicates the steady, non-decreasing gains in TdF average speed.

Here's another way of showing the "EPO bump" (below); in the context of the Tour's 100-year history, the EPO era shows up as heat does in graphs of climate change, with the red all crowded into the past few decades:
Conclusion
The problem with the EPO bump--if that's what we claim it to be--is that it never stops; it's still going on.  The peleton continues to average the same speeds it did in the EPO era, although EPO is (we assume) no longer used.  

In fact, the peleton has averaged 0.5 miles an hour faster since the introduction of the biological passport than they did from 1992-1998, the days of 68% hematocrit, before the introduction of an EPO test!

The biological passport didn't slow down the Tour (although it seems to have slowed down some individual riders).  Of the nine Tours that have averaged over 25mph, four have occurred after Lance's retirement.  

We have a choice here:  either we 
(1) throw out our favorite generalization about Tour speeds (the EPO bump!) or 
(2) conclude, on little other evidence, that the bozos are still jacked on blood boosters.

In either case, the average speed of the Tour has remained suspiciously high.  Those who attribute the continued high speed to blood doping lack an explanation for the continuance of that bump into the biological passport era.

Further examination
In my next post I hope to explore time gaps between GC contenders.  There may be a correlation between use of performance enhancement and the time gaps between the top contenders.  

This is something we sometimes observe, even in local races--the presence of dopers produces unusual gaps between top finishers.  

This chart is a taste of that, showing time gaps between top ten finishers (include those whose results were later asterisked):