How the Climb Time Models Were Built, Tested and Bounded

Every number this site produces for Alpe du Zwift or Ven-Top comes out of one of two fitted equations. This is how those equations were made, and where they should not be trusted.

I should set expectations first. This is one person with a spreadsheet, a statistics course and a lot of hours on Zwift. It is not a laboratory, it is not peer-reviewed, and the dataset is small enough that I will keep saying so. What I can offer is that every step is described plainly enough for you to disagree with it, and both equations are published in full so you can check any output by hand.

If you want the results rather than the method, they are in the article on what the data actually shows. This one is about how the curves were built.

The data, and what a single record contains

The dataset is roughly 500 Alpe du Zwift results and roughly 300 Ven-Top results, taken from ZwiftPower. Each record is exactly two things: a power-to-weight figure, and a finishing time for the timed segment.

That is worth stating precisely, because it defines what the whole site can honestly claim. There are no timestamps, so nothing here can say anything about time of day. There are no power traces, so nothing here can describe how riders distribute their effort within a climb. There are no repeat attempts linked to individuals, so nothing here can describe improvement over time. Roughly 800 pairs of numbers is the entire evidence base, and any claim on this site that needs more than that is either labelled as reasoning and personal experience or should not be there at all.

I used verified results specifically. ZwiftPower's verification requires a rider to have a recognised power source and applies consistency checks, which filters out a good deal of the obviously impossible. It does not catch everything. A miscalibrated trainer reporting 5% high produces a perfectly plausible record that is simply wrong, and nothing in this method can detect that.

I deliberately kept the full spread of abilities rather than concentrating on fast riders. A curve fitted only to 4.5 W/kg and above would be useless to most of the people who visit this site, and the interesting part of the shape happens lower down.

Why not a straight line

The first thing anyone tries is a straight line: time equals some constant times W/kg, plus another constant. It does not work, and the reason is worth understanding because it is a property of the problem rather than of the data.

Time is the inverse of speed. If you double your speed you halve your time, so equal increases in power do not buy equal savings in time. Going from 2.5 to 3.0 W/kg on the Alpe saves far more than going from 4.5 to 5.0 does, even though both are a 0.5 W/kg improvement. A straight line cannot represent that; it insists every 0.5 W/kg is worth the same number of minutes, which contradicts both the data and the physics.

So the model has to bend. The question is what shape to use, and there is more than one defensible answer.

Two climbs, two different shapes

The two climbs ended up with different functional forms, which was not the original plan.

Alpe du Zwift: a quadratic

A second-order polynomial fitted the Alpe data well across the range where the records actually sit, roughly 2.5 to 5.0 W/kg. The quadratic term is what produces the flattening: each additional 0.1 W/kg saves less time than the one before it.

It also has a known and serious failure mode, which I would rather point out myself. A parabola turns around. This one turns at 1954.08 divided by twice 148.60, which is 6.57 W/kg, and beyond that point the equation claims a stronger rider climbs slower. That is obviously false. It is not a flaw in the fitting, it is what happens when a shape is evaluated far outside the data that produced it.

Ven-Top: an inverse

Ven-Top is longer and slightly shallower, and an inverse relationship described it better than a polynomial did. That form is also closer to what the physics suggests, since on a sustained climb vertical speed is roughly proportional to power per kilogram, and time is distance over speed.

It fails differently and more quietly. An inverse never turns around, so it never produces obvious nonsense. Instead it tends towards its constant, so the equation implies a rider with infinite power would still need 3.2 minutes for 20.9 km and 1,534 m. Long before that it has stopped being credible.

Both failure modes, and the ranges where each curve is worth believing, are worked through in detail in the data article.

Checking the fit against data it had not seen

A curve fitted to a set of points will always describe those points reasonably. The question is whether it describes points it was never shown, so part of the data was held back from the fitting and used only to test the result afterwards.

On that held-out data the mean absolute error came out under 3% within the fitted range. That is the number quoted everywhere on this site, and it is worth being concrete about what it means rather than letting it sound better than it is.

There is a second, cruder check that I find more convincing than the first. Roughly 3.2 W/kg is widely treated among Zwift riders as the sub-hour benchmark for the Alpe, and that consensus formed independently of anything on this site. The equation returns 59:58 at 3.2 W/kg. Agreeing with a number the community arrived at separately is weak evidence, but it is evidence, and it would have been a strong warning sign if the fit had disagreed.

What I did about outliers

Some records sit a long way off the trend. The temptation is to delete them until the curve looks tidy, which is also the fastest way to produce a model that describes your preferences rather than the sport.

The distinction I worked to was between noise and signal. A record that is physically impossible, or that shows a finishing time inconsistent with the segment itself, is an error and was removed. A record that is merely surprising, from a rider who paced it unusually well or unusually badly, is real variation and was kept. Most of the scatter in these plots is genuine: two riders at the same W/kg do finish minutes apart, for reasons the model cannot see.

Keeping legitimate outliers is part of why the error band is as wide as it is. A tighter band would look better and mean less.

What the models assume, and cannot know

Every estimate on this site carries these assumptions, whether or not the page says so.

• Steady power. The riders who post verified times mostly ride near-constant efforts, so that is what the curve describes. Ride the Alpe in bursts and you will be slower than the estimate.
• Ordinary equipment. Frames and wheels carry different in-game weight and drag. The fit reflects whatever the sampled riders were on, which is presumably sensible climbing setups.
• Solo effort. Drafting is worth little on a gradient this steep, but it is not zero, and the model does not represent it.
• Nothing about you specifically. The curve returns one number per W/kg. It has no view on your pacing, your cooling, your trainer's calibration or how the day is going.
• A snapshot of the game. If Zwift changes its physics, the fit describes the old version until the data is rebuilt.

What would actually improve this

In descending order of how much difference it would make:

• More records, especially at the extremes. The thin ends of the range are where both curves are least reliable, and that is a sample size problem rather than a modelling one.
• Rider mass as a separate variable. At the same W/kg a heavier rider pushes slightly more air. On an 8.5% gradient that is minor, but it is not nothing, and a two-variable fit could capture it.
• Split times. These would allow something to be said about pacing, which is currently the largest unexplained source of variation and about which this site can say nothing quantitative.
• A published uncertainty band on the calculator output rather than a single number. This is the change I most want to make, because a single figure invites more confidence than the data supports.

Check it yourself

Both equations are above in full. A 75 kg rider at 250 W is at 3.33 W/kg: 148.60 × 11.09 is about 1,648; 1954.08 × 3.33 is about 6,507; so 1,648 − 6,507 + 8,330 is about 3,471 seconds, or 57:51. That is a phone calculator's worth of arithmetic, and it is the whole model.

If your own verified time disagrees with the estimate by more than the error band, I would genuinely like to know, because reader reports are the main way the fits get better. Send the numbers over, and if a correction is needed it gets made and logged under the editorial policy.