A race is five seconds repeated thousands of times

The engine did not come from a feature list but from seven pillars, set down before the code and checked by tests. Each has a precise technical consequence, which is why the rest of this post reads as their implementation.

The engine advances in steps of 5 simulated seconds (TICK_S). Inertia is neglected at that granularity: the model is quasi-static, and a group’s speed is computed from each rider’s power, with no acceleration integrated.

The mechanical engine simply applies paces. What chooses them, the AI and the radio, sits behind an interface (PacingDecisions). With no policy, everyone rides at a default “tempo” pace, which lets the mechanics be tested without the decisions.

Two details matter more than they seem. First, every team’s decisions are read from the state at the start of the tick: nobody reacts to what another team has just decided in the same step, so the order in which teams are processed does not matter. Second, the finish is interpolated inside the tick: the crossing instant is not rounded to the 5-second step, which lets a sprint be decided by fractions of a second.

For a rider pushing a given power, speed is where the power delivered equals the forces opposing it: gravity, rolling resistance and air.

The engine has to find v given P: the speedForPower function inverts the relation by bisection, every tick and for every rider. That is why the sine and cosine of the slope angle never go through trigonometry: for a grade g/100, sin(atan g) = g/√(1 + g²) and cos(atan g) = 1/√(1 + g²), mathematically identical and much faster.

The surface enters through the rolling coefficient: 0.004 on asphalt, 0.0075 to 0.0315 on cobbles depending on the sector’s stars and the rider’s cobbles attribute. On descents, speed is capped by the technicality of the road and the rider’s descending skill. As for the draft, it is the factor from which almost all peloton tactics flow: 1 when alone, less than 1 inside a group (section 04).

Each rider carries fifteen integer attributes, from flat to composure. Converting them into physical parameters is the engine’s job, not the content’s: the content describes a rider, and the mechanics derive what he can sustain. The terrain attribute sets his critical power (CP); his reserves drain and refill tick after tick.

Day form is discreet but indispensable: without it, results followed the hierarchy of attributes almost exactly, and there was no point in racing. Its 3.5 % standard deviation is slightly above the measured day-to-day variability: it also absorbs what the model does not represent (positioning, motivation, small troubles).

A peloton is not a list of riders, it is a physical object. Two consecutive riders 20 m apart or less form a group; the peloton is the largest of them all. Gaps are not set by hand: the time gap between two groups is the distance separating them divided by the speed of the rear group. They emerge from the physics.

The draft multiplies drag: at 1 you take all the air, at 0.5 you take only half. It depends on your place in the group.

Then the rules chain together. Designated pullers aim for an intensity, a fraction of their effective CP, which is a power averaged over the rotation: a group that cooperates therefore goes faster than a lone rider at the same intensity. Each member computes the power he needs to hold that speed with his draft; as long as it is within his means he follows and dips into W′ above CP. When W′ is empty he gets dropped, rides at his CP and the gap opens by itself. To avoid yo-yoing, a dropped rider cannot push above CP to come back until W′ has recovered to 25 %.

A group where nobody wants to pull does not enjoy a rotation nobody decided on: its speed is the average of those each member would hold alone on the front at 60 % of his effective CP, which gives a peloton at 36 or 38 km/h on the flat. An attack is a move planned apart from the rest of the group: attackers aim for their intensity, capped by the power available over the tick, and the rest of the group is recomputed without them. A sprint, finally, is an all-out effort that fades once W′ is empty.

That rule is why a climb is not handled like the flat: from 2 % grade, a group’s pace slides from the average of its pullers toward the highest of their speeds, which it reaches at 5 %. There, the draft is worth almost nothing and the strongest rider sets the rhythm.

There is no intelligence for the opponents and another for you. There is decideTeam: one function that receives the team’s view, the public knowledge, its plan and its memory, and returns each rider’s decisions. The player’s team goes through it, with the plan the player wrote. The opposing teams do too, with the plan their staff derived from the public reputation of their riders.

That symmetry is tested. Identical squads under different team identifiers receive the same roles, and a team’s decisions do not change when an opponent’s reserves are altered.

The staff’s default plan is that of every opposing team and the draft offered to the player. It only reads public reputation and the reading of the course: offensive doctrine for a team that does not aim to win, otherwise sprint on a flat course and finale elsewhere; attack zones placed on the finale’s climbs, and on the hardest cobbled sectors of a classic.

That reading of the course is code too. The engine classifies a race as flat, hilly, mountain, cobbles or gravel; it spots the climbs, their difficulty and, recently, the walls (200 m at 6 % or more); and it determines the finale, which starts 30 km from the finish (earlier on cobbled classics and gravel), pulled forward to the foot of the climb or sector it overlaps.

Every tick, the AI evaluates for each team and each group who should pull and at what intensity. Five rules share the task: the breakaway and front groups, the controlled chase, defence in the finale, climbing tempo and the sprint lead-out. The most telling is the chase, where the team of a trapped leader aims for a target gap that shrinks as the finish approaches: G*(D) = min(240 s, max(0, (D − Dcatch) · 4 s/km)). The 4 seconds per kilometre is what an organised chase can really claw back with the drafts of section 04. The actual gap to that target then picks the effort level:

On top of those collective rules, each rider has his own list of priorities, evaluated in this order:

An attack is never triggered by a script: it is a rate per minute converted into a probability per tick, p = 1 − e^(−λ·Δt/60), drawn from the rider’s own random stream, and only when his conditions are met. A rider with aggression 0.8, as leader in an attack zone of his plan with enough W′ and a timing of 1, has a rate of 0.5 · (0.5 + 0.8) = 0.65 per minute, which is roughly a 5 % chance per tick of launching the attack. It will start at 130 % of his critical power, capped by what he can actually produce.

The engine knows everything. The teams do not. Between the exact state and the policy that decides, there is a perception layer, identical for all. Each team knows the race through two sources.

A group known only from the bulletin is therefore estimated: its position is projected forward with the elapsed time. A rider the bulletin placed in a group that is now in view, who is no longer there and is seen nowhere, has an unknown group until the next bulletin. Finishes and abandonments, for their part, are public.

And you, the director? You receive an even poorer projection: groups with their source and age, and for your riders, feelings in words reported every three minutes, staggered from one rider to the next. Never a reserve, a power or a speed, and a test checks that those fields do not exist in the projection.

Your only actions during a race are radio instructions. An instruction has recipients, an intent (help the chase, save energy, protect the leader, attack in a zone, mark an opponent, change leader or doctrine, resume the plan) and an end condition (until further notice, until a point, until a gap). Only structural errors refuse it: a questionable tactic is accepted, then possibly reported as impossible.

On reception, three things can happen. If a more recent instruction for the same slot has already arrived, this one is too late and is discarded. If it is a sacrifice (chase, protect, save energy) addressed to a leader, an alternate or a free rider, the rider can refuse it, depending on his character. Otherwise it replaces the previous one on the same slot only: marking an opponent while saving energy remains possible, because those are two distinct slots.

The probability of refusal is clamp((ambition − (loyalty + teamwork)/2) / 100, 0, 0.5). With an average personality (50, 50, 50) it is 0. For a rider with ambition 80, loyalty 30 and teamwork 40, the calculation gives (80 − 35) / 100 = 0.45. A domestique never refuses.

Finally, repeating an order gives no bonus. A recipient who already has the same instruction in transit or in force is removed from the send; if nobody is left, the instruction is refused as a duplicate. Repeating restarts no delay.

The day’s weather is a piece of race data, not an engine draw: wind (speed and direction), rain or not, constant throughout the race and public. The headwind enters the aerodynamic term of section 02. The crosswind does not change the physics: it makes echelons.

When the crosswind exceeds 3 m/s, an echelon forms. Its strength is s = clamp((crosswind − 3) / (7 − 3), 0, 1). In a group of more than 12 riders, that is the width of the road: the first 12 keep their draft, the rest ride “in the gutter”, almost fully exposed, spend more and end up dropping. The group splits. Order in the echelon goes first to the pullers, then to a score placement + team bonus + a little luck. The AI knows it: a contending team has two riders pull at 0.9 to slide its leader into the right echelon.

The results say something about the sport. In calm weather, incidents change neither speed nor hierarchy: a rider who stops mostly gets back behind the cars. Rain multiplies crashes and produces surprise winners. Crosswind breaks the peloton into echelons and favours rouleurs. And in strong wind, the best sprinters run short of glycogen and lose the sprint to fresher riders: twenty winners out of thirty outside the top 40 in a north wind, despite thirty bunch finishes.

Every tick, each rider who is riding makes a draw: he has an incident with probability 1 − exp(−λ · d), d being the distance covered in the previous tick in kilometres, and a second draw picks the nature. All these draws come from a separate random stream (engine.incidents).

The base engine grew in layers, and each added a rule without breaking another. This post does not detail them, but here is what they bring.

Determinism is the pillar that costs the most and pays back the most. Without it, you cannot reproduce a bug, compare two versions, save a race in progress or calibrate anything at all. It rests on four things.

That sentence is the reason for the third point. The test labs ran under Node, the application under Electron, and their maths functions did not return exactly the same bit. One ulp of difference on a form value, and the next season’s race changed. The fix is a port of fdlibm 5.3, checked on 30 million values identical bit for bit with the original C library, and a test that runs the same career under Node and under Electron then compares the fingerprint of the complete state.

The journal also protects pillar 6. The controller that plays the race takes its stop decisions tick by tick: slicing the playback differently changes neither the race, nor the feed, nor the stops, and a test checks it. Presentation therefore cannot alter the simulation. In return, a save carries the version of every model (physics, engine, AI, perception, radio, random draw): if any has changed, it is refused, with a message naming the model and both versions, rather than replayed wrongly.

A deterministic engine guarantees that a race can be replayed, not that it looks like cycling. For that there is directeur lab: it runs hundreds of races with no instructions, using the staff’s plans, in the real session (perception, radio, incidents, day form), and measures what comes out. It reads the engine’s exact state: it is a diagnostic tool, never something the player reads.

Seven targets say what a peloton should look like. A target is not judged below 20 races on the terrain, each measurement carries its 95 % confidence interval, and a gap is significant only if the whole interval lies outside the target. The 35 % ceiling for the most frequent winner was first set at 25 % without measurement, then revised along the way.

The targets drove ten adjustments in the first pass. Four tell the story well:

The bench also runs as a test suite: 100 seeds per course, drawn weather, failure on any significant gap, about 45 seconds on nine threads at the time of T10. And since it is deterministic, its results depend neither on the number of threads nor on the clock: a test checks that.

The engine’s sporting numbers are calibration hypotheses, not validated truths, and we would rather say so up front. Here is what we know we do not yet do well.

• Hilly courses were still too bunched at the T10 measurement. The peloton arrived almost whole at the foot of the final wall: 98 % of races ended with at least 20 riders within 5 s, and breakaways almost never won there (1 %). Calibration tickets have revisited the question since, but it is the kind of race where we stay vigilant.
• Strong wind on the flat needs watching. At 7 m/s or more (21 races out of 200 at the T10 measurement), 43 % of winners were favourites and 38 % came from outside the top 40: more surprises than on the rest of the flat. It is an open calibration point.
• The physics is quasi-static. Inertia is neglected at the 5-second scale, and air density is constant at 1.225 kg/m³ everywhere, altitude included. When altitude was added (T66), the drop in critical power was modelled but acclimatisation was not.
• Outside careers, knowledge of roles stays exact and shared. In free races and on the bench, every team reads the same exact aptitudes; only in a career does each team read its own riders in its own dossier and the others through public reputation.