Tour de France Summary

Another Tour de France is in the books, and Great Britain has its first champion.  Below is a table that summarizes the stages' winning times and our predictions.

Stage	Actual	Predicted	Difference	% Diff.
0	0h 07' 13"	0h 07' 35"	00' 22"	5.08
1	4h 58' 19"	4h 49' 18"	-09' 01"	-3.02
2	4h 56' 59"	4h 48' 45"	-08' 14"	-2.77
3	4h 42' 58"	4h 47' 16"	04' 18"	1.52
4	5h 18' 32"	5h 10' 00"	-08' 32"	-2.68
5	4h 41' 30"	4h 35' 16"	-06' 14"	-2.21
6	4h 37' 00"	4h 57' 12"	20' 12"	7.29
7	4h 58' 35"	5h 13' 07"	14' 32"	4.87
8	3h 56' 10"	3h 57' 04"	00' 54"	0.38
9	0h 51' 24"	0h 51' 06"	-00' 18"	-0.58
10	4h 46' 26"	5h 09' 49"	23' 23"	8.16
11	4h 43' 54"	4h 28' 03"	-15' 51"	-5.58
12	5h 42' 46"	5h 40' 12"	-02' 34"	-0.75
13	4h 57' 59"	5h 02' 23"	04' 24"	1.48
14	4h 50' 29"	5h 03' 27"	12' 58"	4.46
15	3h 40' 15"	3h 50' 46"	10' 31"	4.77
16	5h 35' 02"	5h 34' 01"	-01' 01"	-0.30
17	4h 12' 11"	4h 01' 29"	-10' 42"	-4.24
18	4h 54' 12"	5h 15' 05"	20' 53"	7.10
19	1h 04' 13"	1h 04' 39"	00' 26"	0.67
20	3h 08' 07"	3h 05' 49"	-02' 18"	-1.22
TOTAL	86h 44' 14"	87h 32' 22"	48' 08"	0.92

We predicted five stages to better than 1%, eight stages to better than 1.5% (rounded), and 12 stages to better than 3% (rounded).  I am very pleased with our predictions!  I would obviously liked to have done better on Stages 6, 10, and 18.  My student, Brian Ramsey, and I will sit down this week and go through the Tour de France again and see if can discover how to have modeled the race even better.  The point of all this from a research point of view is to better understand how to model the real world.  When one of our predictions matches an actual time to better than 1%, we think we have a good idea what's going on.  When we are off by more than 7% or so, we need to let the real world teach us how to do better.

Note the last row in the above table gives the sum of the stage-winning times.  Our model cyclist completed the Tour de France in a time 0.92% slower than the sum of all the stage-winning times.  Note that that time is not the total time posted by this year's winner, Bradley Wiggins.  His winning time was 87h 34' 47".  Though that time is a mere 02' 25" seconds off from the sum of our stage-winning times, our goal at the outset was not to predict the overall time for any one cyclist, but the sum of the stage-winning times.  My model could, in fact, be better at predicting the winner's overall time than the sum of stage-winning times.  I use published research to determine power outputs, and I don't use maximum values unless there is a particularly steep climb that must be overcome.  Athletes are getting better every year, and it's clear to me over the past two years that I need to up power outputs on certain portions of stages.  Again, there is more for us to learn, which is what makes all this so much fun!


For anyone wishing for more details on my model, check out Chapter 4 of my book.  Click here for the Amazon link.  Click here for a paper I gave at the most recent ISEA conference in Lowell, Massachusetts.  It describes my 2011 Tour de France work.