methodology skiing weekly-recap

Weekly Recap Methodology

Overview

The weekly recap system provides three key analytical components for tracking World Cup season progress:

  1. Elo Change Tracking - Monitors week-over-week changes in athlete Elo ratings
  2. Season Simulation - Monte Carlo simulation of remaining season outcomes
  3. Magic Numbers - Mathematical elimination thresholds for the overall standings

This methodology applies to all winter sports covered: Alpine, Biathlon, Cross-Country, Nordic Combined, and Ski Jumping.

Elo Change Tracking

Purpose

Track the changes in Elo ratings for athletes who have competed in the last week.

Calculation

For each athlete who competed in the past week:

Elo_Change = Current_Elo - Previous_Week_Elo

Where:

  • Current_Elo is the athlete’s Elo rating after their most recent race
  • Previous_Week_Elo is the athlete’s Elo rating from 7+ days ago

Output

The weekly Elo change report includes:

  • Skier: Athlete name
  • Nation: Country code
  • Current Elo: Most recent overall Elo rating
  • Previous Elo: Elo rating from 7+ days ago
  • Change: Difference between current and previous Elo

Season Simulation

Purpose

Estimate the probability distribution of final season standings by simulating the remaining races thousands of times using Monte Carlo methods.

Methodology

Remaining Races Calculation

The system dynamically calculates remaining races from the official race calendar by:

  1. Reading the races CSV file containing the full season schedule
  2. Filtering for races with Date >= today (using UTC time)
  3. Excluding championship races (Championship != 1)
  4. Excluding team events (relays, team sprints)
  5. Categorizing races by type and point value

Cross-Country Point Values:

  • World Cup races: 100 points maximum
  • Stage races: 50 points maximum
  • Tour de Ski stages: 300 points maximum

Other Sports:

  • Alpine: 100 points maximum per race
  • Biathlon: 90 points maximum per race (60 base + 30 bonus)
  • Nordic Combined: 100 points maximum per race
  • Ski Jumping: 100 points maximum per race

Historical Performance Modeling

For each athlete, the simulation uses their 10 most recent races of each type to model expected performance. The system:

  • Retrieves the athlete’s points history for each race type (distance/sprint categories)
  • Uses exponentially weighted recent performances (more recent races weighted higher)
  • Falls back to overall race type history if discipline-specific data is insufficient

Single Race Simulation

Each race is simulated using:

Simulated_Points = Mean_Historical_Points + N(0, σ)

Where:

  • Mean_Historical_Points is the weighted average of recent performances
  • N(0, σ) is normally distributed noise with σ = max(5, Mean_Points × 0.15)
  • Results are bounded to [0, Max_Points] for the race type

The 15% coefficient of variation captures the inherent uncertainty in race outcomes while the minimum standard deviation of 5 points ensures variability even for low-scoring athletes.

Monte Carlo Simulation

The full simulation process:

  1. Initialize each athlete’s total with their current season points
  2. For each of n simulations (default: 100-500):
    • For each remaining race:
      • Determine if each athlete participates using their participation probability (based on exponentially-weighted historical participation in that race type)
      • For participating athletes, simulate points based on historical performance
      • Add simulated points to running totals
    • Record final standings
  3. Calculate win probability as (Simulations_Won / Total_Simulations)

The participation probability ensures that athletes who frequently skip certain race types (e.g., sprinters skipping distance races) are modeled realistically.

Output Metrics

The simulation produces:

  • Current Points: Actual points in current standings
  • Mean Final Points: Average total points across all simulations
  • Mean Points Gained: Expected points from remaining races
  • Win Probability: Percentage of simulations where athlete finishes first

Magic Numbers

Purpose

Calculate the “magic number” - the minimum points the current leader needs to mathematically clinch the overall title over each competitor.

Mathematical Definition

For each athlete still mathematically alive in the standings:

Magic_Number = max(0, Athlete_Points + Points_Remaining + 1 - Leader_Points)

Where:

  • Athlete_Points is the competitor’s current season points
  • Points_Remaining is the maximum points available in remaining races
  • Leader_Points is the current leader’s season points
  • The +1 ensures the leader must have strictly more points

Interpretation

The magic number answers: “If this athlete wins every remaining race, how many points does the leader need to clinch the title?”

Example:

  • Leader has 1,500 points
  • Athlete B has 1,200 points
  • 600 points remaining in season
  • Magic Number = 1,200 + 600 + 1 - 1,500 = 301

This means if the leader gains 301 more points than Athlete B in remaining races, Athlete B is mathematically eliminated.

Mathematical Elimination

An athlete is mathematically eliminated when:

Max_Possible_Points = Current_Points + Points_Remaining
Mathematical_Chance = (Max_Possible_Points > Leader_Points)

If Mathematical_Chance = FALSE, the athlete cannot win even by winning all remaining races.

Points Remaining Calculation

Cross-Country:

Total_Remaining = (WC_Races × 100) + (Stage_Races × 50) + (TdS_Stages × 300)

Alpine:

Total_Remaining = Total_Races × 100

Biathlon:

Total_Remaining = Total_Races × 90

Nordic Combined / Ski Jumping:

Total_Remaining = Total_Races × 100

Output

The magic numbers report includes only athletes with a mathematical chance, showing:

  • Skier: Athlete name
  • Rank: Current position in standings
  • Points: Current season points
  • Magic #: Points leader needs to clinch over this athlete
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