How the ratings work
What θ is
θ (theta) is a skier's sprint strength on a relative scale. Only gaps matter. A gap of 1 means the stronger skier finishes ahead about 73% of the time when both start in the same heat. A gap of 2 means about 88%.
Where it comes from
The model reads every men's World Cup sprint from 2012/13 to 2025/26: the qualification and every quarterfinal, semifinal and final. It is a truncated Plackett–Luce model. A result is read as a chain of choices: who is first among the skiers still left, then who is next. Only the places that decide something count: the top 15 of qualification, the top two of each quarterfinal and semifinal, and the podium of the final.
Strength changes over time
Each skier has one θ per season and technique, and it can drift from one season to the next. That lets the ranking follow a rise or a decline. The model is Bayesian, so every θ comes with a range of plausible values instead of a single number.
Head-to-head chance
The chance that A finishes ahead of B in the same heat is P = 1 / (1 + e^−(θA − θB)). It doesn't depend on who else is in the heat. Right now in Free: KLAEBO 7.07, CHANAVAT 5.13, so Δθ = 1.94 and P = 1 / (1 + e^−1.94) = 0.87.
Likely place
We draw the whole field 4,000 times from the strength estimates and rank it each time. Likely place is the range that holds 90% of those draws. A skier ranked 4th with a likely place of 3–10 could easily be 8th.
What the ratings don't say
- Classic and Free are separate scales. Klaebo's Classic θ being higher than his Free θ says nothing about which technique he is better at.
- Strength is relative to the field. If the whole World Cup gets faster, θ doesn't show it.
- This is form at the end of 2025/26. Form changes over the summer, so the first races of the new season carry extra uncertainty.
- For now the ranges treat skiers as independent, which makes them somewhat wider than the model's own. They err on the cautious side.
Checking the model
From the 2026/27 season, predictions will be published before each race with an independent timestamp. After the season, a calibration page will show how often events given, say, a 30% chance actually happened.