How much slower than a pro are you?

The physics behind ProPace's comparison, what it's calibrated on, and what it deliberately can't tell you.

Everyone who watches a Grand Tour eventually wonders it. You've ridden a climb the race went over. You know your time. You have some vague sense that the gap is enormous. But how enormous, exactly?

Before anything else, one point about which direction this model runs, because it determines what the tool is and isn't good for. ProPace does not look at what a rider did and work backwards to what they must have been producing. It starts from a fixed, published reference profile, a set of numbers decided in advance and identical on every route, then simulates that profile forward over a road to produce a time. Assumption to time, never time to assumption. It never examines a named rider's performance, and it structurally cannot be used to assess one.

What follows is how the forward simulation works.

The gap, in the only unit that means anything

Watts are abstract. Minutes are not.

A strong club rider sits somewhere around 3.5 to 4 watts per kilogram at threshold. The reference profile ProPace uses for a men's Grand Tour GC group is 383 W at 66 kg, or 5.80 W/kg. Call it one and a half times, which sounds survivable right up until it's expressed as time.

Put a rider at 78% of pro pace onto a 158 km mountain stage with 3,600 m of climbing, both riding solo, and the gap is about an hour and a half. Not a sprint finish. Not a few minutes. The pro has showered, eaten and been interviewed before you reach the line. Ride the same road at a level most of us would be delighted with, and you are still most of a working morning behind.

The gap you see on television is real, and it is very close to the size the arithmetic says it should be. There's no mystery in it. There's a large number, and a decade of full-time training behind it.

The equation

The physics is textbook and has been for decades. To move a bike at a given speed you overcome gravity, rolling resistance and air:

P · η = (m·g·sin θ + m·g·Crr·cos θ + ½·ρ·CdA·v_air²) · v_ground

Gravity scales with the gradient. Rolling resistance scales with weight. Aerodynamic drag scales with the square of the speed of the air you're actually moving through, which is why it dominates on the flat and barely matters on a 9% ramp. The η term is drivetrain efficiency, the few percent lost between your pedals and the road.

Note that the drag term uses v_air, not your ground speed. Those are the same number only in still air, which is a condition that essentially never holds outdoors. ProPace resolves the wind into headwind and crosswind components relative to your heading at each point, combines them with your ground speed into an apparent wind vector, and adjusts the drag coefficient for the resulting yaw angle. A 20 km/h crosswind that becomes a headwind at the turnaround costs more time than most riders credit, and a model that collapses the wind into a still-air approximation cannot see that at all.

Solving for time is the awkward part, because speed appears on both sides of the equation. Given a power output you can't rearrange for velocity directly, so the model solves numerically, using Newton-Raphson iterated to convergence on each segment. Every route is cut into short segments, each with its own gradient, altitude and wind, and the times are summed.

The drag and rolling-resistance figures come from published rider profiles and wind-tunnel literature and sit inside the standard ranges. More importantly, they're applied to both riders identically, so much of the uncertainty in them cancels when the two times are compared. That's a deliberate design property, and it's why the comparison is more trustworthy than either time is on its own.

Where the reference numbers come from

Two profiles, one for a men's GC group and one for a women's WorldTour GC group: 383 W at 66 kg, and 288 W at 57 kg.

They describe a group, not a winner. The rider at the front of a Grand Tour on their best day produces considerably more than this. Modelling the leader would make the app both less useful and less honest, because you'd be comparing yourself against an outlier rather than against the level.

There's an independent check available for the men's figure. Horvath and Andersson (2025), modelling Grand Tour time trials in Frontiers in Sports and Active Living, define a GC-contender profile drawn from a database of 144 male World Tour and Pro Continental riders: 63.8 kg, CdA 0.265, and a critical power of 388.6 W with a standard deviation of 24.0.

Worth being precise about what that comparison does and doesn't establish. Critical power and FTP are related but distinct constructs, and for the same athlete CP is normally the higher of the two, so this isn't a like-for-like validation. What it does show is that 383 W is the right order of magnitude for the archetype, arrived at independently by people with no interest in this app existing, and that ProPace's figure sits at or slightly below the literature value rather than above it. The paper is open access if you want to check the working yourself.

The women's model isn't a scaled-down copy of the men's. It has its own mass, its own power, its own drag figures and its own calibration set, because the alternative, taking a men's model and applying a fudge factor, produces numbers that are wrong in ways that are hard to see.

What it's calibrated against, and what it isn't

This is the part that matters most, and the part most likely to be misread.

The power-duration curve, which governs how sustainable output decays as a ride gets longer, is calibrated against efforts that were actually ridden alone against the clock:

That set is small on purpose. It is not calibrated against bunch stage times, and this is the single most important thing to understand about the model.

A stage result is a peloton time. It contains a hundred and fifty riders sharing the work, a neutralised start, tactics, a breakaway that may or may not have been caught, and a finale ridden at a completely different intensity to the four hours before it. Fitting a solo, no-draft model to those times would force the constants upward to compensate, and every number the app produced afterwards would be quietly wrong, inflated to absorb an effect that has nothing to do with the rider.

So the model is fitted only to efforts where a single rider covered a known distance in known conditions with nobody to hide behind. Time trials, and breakaways that stayed away.

The direct consequence, and it's worth stating plainly: the pro times in ProPace will not match published stage results, and they aren't supposed to. They answer a different question. A stage result tells you how fast a bunch got from one town to another. ProPace tells you how long that road would take a rider of a given level, riding it the way you rode it.

This isn't a quirk of one app. The Horvath and Andersson paper reaches the same conclusion from the other direction, noting that for bunch races the predictive ability of this class of model drops without additional handling of drafting and in-race dynamics. Solo physics describes solo efforts. Everyone who does this seriously runs into the same wall.

Rider against rider

Which is the whole design, really.

Sitting in a bunch can be worth around a third of your power on the flat. Any comparison that quietly includes drafting on one side isn't measuring engines, it's measuring group aerodynamics. So both sides get the same treatment. If you rode alone, the pro rides alone. If you rode in a group, the pro gets the same drafting benefit you did. Same road, same wind, same day, same assumption on both sides.

The conditions are real rather than assumed. Elevation comes from lidar survey data where it exists, down to 50 cm resolution, falling back to the Copernicus 30 m global model elsewhere, because barometric drift and GPS noise on a phone will otherwise invent hundreds of metres of climbing that never happened. Wind comes from historical weather data for the actual hour you were out, sampled along the route rather than taken as a single value for the whole ride.

What this can't tell you

Plenty, and it's worth being direct about it.

It can't tell you what any individual rider was producing on any given day, and it isn't built to try. The model runs forward from an assumed profile. It never looks at a real performance, so it can't be pointed at one.

It can't account for what a race actually is: the surges, the cat and mouse, the twenty minutes at the front that decide everything. It models a steady, well-paced solo effort, which is a clean baseline and not a race.

It can't tell you what you'd do with a decade of professional training, better equipment and a team car. It tells you where you are today, on a road you've ridden, against a level that's been measured.

That last one turns out to be enough. Most people have never had a straight answer to the question, and the answer is more interesting than the guess.