Where the day was actually won and lost

Your start pen costs you 7 min 59 s

Riders are seeded into 17 pens by expected finish time, the first leaving at 06:30 and each one 7.5 minutes later — a two-hour spread across the field. Comparing raw finish times across pens would just rediscover that seeding, so this doesn’t do that. Instead every one of the 12,165 riders here is matched against others of measured identical climbing ability (their combined time up the 3 timed cols, in 10-minute bands), and then compared only on the parts of the day that were not used to match them.

When the race stops being decidable

At every checkpoint each finisher is ranked against the other finishers who reached it, and compared with where they ended up. The gap between the two is how much of the field they still had left to move through — from 10.09 points at Pied de Col de la Croix de Fer down to 0.36 points by Col de Sarenne. Ranks at a checkpoint count riders who later abandoned, which would credit everyone with the places those riders vacated, so they are re-ranked among finishers only. Done that way the finish line comes out at exactly zero, which is the check that the arithmetic is right.

The line does not fall smoothly, and the bumps are the interesting part: position at the foot of a climb is worth much less than position at its summit. The field arrives at a col in whatever groups the valley assembled, and then the mountain sorts it out again.

the climbs do 83% of the sorting

The obvious way to ask this — take riders within a couple of minutes of each other and see how far apart they finish — turns out to measure the wrong thing. Early on the whole field is packed into a few minutes, so being level on the clock at Pied de Col de la Croix de Fer means something completely different from being level on the clock at the top of a col. So this conditions on position instead: among riders sharing your place in the field at a checkpoint, how widely scattered are their finishes?

At Pied de Col de la Croix de Fer the answer is 43.3 points of the field — knowing someone’s position there tells you very nearly nothing about where they will finish. Every section after it closes that number down.

Read it as a rider and it says something useful: your position at the bottom of a climb is worth far less than your position at the top. Across this course the spread at a summit is 11.87 points against 22.53 points on the approaches. You arrive at a col in whatever group the valley handed you; the climb then throws that away and sorts everyone on their own legs.