| Stage | Actual | Predicted | Difference | % Diff. |
| 1 | 4h 41' 31" | 4h 40' 01" | -01' 30" | -0.53 |
| 2 | 0h 25' 16" | 0h 26' 35" | 01' 19" | 5.21 |
| 3 | 4h 40' 21" | 4h 44' 55" | 04' 34" | 1.63 |
| 4 | 4h 11' 39" | 4h 09' 29" | -02' 10" | -0.86 |
| 5 | 3h 38' 32" | 3h 52' 05" | 13' 33" | 6.20 |
| 6 | 5h 13' 37" | 5h 20' 13" | 06' 36" | 2.10 |
| 7 | 5h 38' 53" | 5h 11' 43" | -27' 10" | -8.02 |
| 8 | 4h 36' 46" | 4h 49' 26" | 12' 40" | 4.58 |
| 9 | 5h 27' 09" | 5h 19' 43" | -07' 26" | -2.27 |
| 10 | 3h 31' 21" | 3h 41' 08" | 09' 47" | 4.63 |
| 11 | 3h 46' 07" | 3h 46' 05" | -00' 02" | -0.01 |
| 12 | 6h 01' 15" | 5h 59' 26" | -01' 49" | -0.50 |
| 13 | 3h 47' 36" | 3h 46' 52" | -00' 44" | -0.32 |
| 14 | 5h 13' 25" | 5h 02' 45" | -10' 40" | -3.40 |
| 15 | 4h 20' 24" | 4h 36' 38" | 16' 14" | 6.23 |
| 16 | 3h 31' 38" | 4h 05' 59" | 34' 21" | 16.23 |
| 17 | 4h 18' 50" | 4h 32' 07" | 13' 17" | 5.13 |
| 18 | 6h 07' 56" | 5h 51' 23" | -16' 33" | -4.50 |
| 19 | 3h 13' 25" | 2h 57' 54" | -15' 31" | -8.02 |
| 20 | 0h 55' 33" | 0h 51' 06" | -04' 27" | -8.01 |
| 21 | 2h 27' 02" | 2h 27' 40" | 00' 38" | 0.43 |
| TOTAL | 85h 48' 16" | 86h 13' 13" | 24' 57" | 0.48 |
Note the last row in the above column gives the sum of the stage-winning times. My model cyclist completed the Tour de France in a time 0.48% 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, Cadel Evans. His winning time was 86h 12' 22". Though that time is just a mere 51 seconds off from the sum of my stage-winning times, my goal at the outset was not to predict the overall time for any one cyclist, but the sum of the stage-winning times.
The overall error of 0.48% is a bit misleading because it comes from a lot of cancellation. For example, I was 27' 10" fast on Stage 5 and 34' 21" slow on Stage 16. Those "fast" and "slow" times tend to cancel at the end. If I add error in quadrature, I wind up with a 1.16% error, which is still not bad!
Modeling the Tour de France is a lot of fun for me, and it enhances my pleasure in following the race. My stats page tells me that people from 21 different countries checked out this blog during the course of the race. I am humbled and flattered by the level of interest in my blog. Please contact me with any questions you may have. If you want more details about Tour de France modeling, check out Chapter 4 in my book, Gold Medal Physics: The Science of Sports.
I plan to add more sports science posts in the future. Feel free to send me suggestions of sporting events and/or athletic feats that might benefit from the eye of a physicist.
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