Kittel wins his third stage!

German Marcel Kittel won his third stage of this year's Tour de France (recall he won Stages 1 and 10) by just barely beating out Mark Cavendish at the finish line.  Chris Froome still holds the yellow jersey.  Below is how Kittel's time compared to our prediction.

• Stage 12:  4h 49' 49" (actual), 5h 02' 54" (prediction), 13' 05" slow (4.51% error)

There is a clear theme with our modeling this year.  We simply do not have quite enough power output to match the winning times we are seeing.  All 182 cyclists beat our prediction today, and that was despite 20 kph (12 mph) crosswinds with predominately headwind components.  Check out the average speed below for Kittel's win.

• Stage 12:  12.54 m/s (45.13 kph or 28.04 mph)

You see the average speed above for today's 218-km (135-mi) flat stage.  Below is a table of last year's (2012 Tour de France) flat stages and the average speeds for the winners of those stages.

Stage	Length (km)	vave (kph)
1	198.0	39.82
2	207.5	41.92
4	214.5	40.40
5	196.5	41.88
6	207.5	44.95
13	217.0	43.69
15	158.5	43.18
18	222.5	45.38

I left out the ceremonial last stage.  Only Mark Cavendish's phenomenal ride in last year's Stage 18, a stage on which we were 7.10% slow, has an average speed in excess of today's average speed.  What is all the more remarkable about Cavendish's win in last year's Stage 18 is that that stage was 4.5 km (2.8 mi) longer than today's Stage 12.  Whether last year's flat stages were longer or shorter than today's stage, only last year's Stage 18 exceeds today's speed.

It should be obvious from the above table why we have been surprised by this year's race.  The technology that goes into the bikes and apparel, the teams' strategies, and the athletes' performances must have improved considerably since last year's race.  Every Tour de France is different and every stage is different.  Still, we are impressed with this year's speeds.

Tomorrow's Stage 13 is also flat.  It picks up where today's left off, in Tours, and sends riders 173 km (107 mi) southeast to the commune of Saint-Amand-Montrond, which is located right in the center of France.  Below is our prediction.

• Stage 13:  4h 01' 57" (prediction)

Will riders save a little for the daunting mountain stages in the Alps?  Or will they go all out to secure the best time position before the climbing begins?  There is a short category-4 climb in tomorrow's stage, but the route is mostly flat.  Given how fast cyclists have been this year, I won't be surprised to see a winning time closer to 3h 45' 00", but I'll stick with the prediction above.