Ski Jumping Weekly Predictions Model Documentation

Overview

This document explains how the ski jumping weekly predictions model works, based on the weekly-picks2.R script. The model predicts position probabilities (win, podium, top 5, top 10, top 30) for individual athletes and teams across multiple race types.

Competition Types

Individual Competitions

  • Men’s Individual: Individual male athletes competing
  • Ladies’ Individual: Individual female athletes competing

Team Competitions

  • Men’s Team: Teams of male athletes (nation-based)
  • Ladies’ Team: Teams of female athletes (nation-based)
  • Mixed Team: Teams with both male and female athletes (nation-based)

Data Sources

Individual Data

  • Men: men_chrono_elevation.csv - Historical individual men’s results with elevation data
  • Ladies: ladies_chrono_elevation.csv - Historical individual ladies’ results with elevation data
  • Startlists: startlist_weekend_men.csv, startlist_weekend_ladies.csv

Team Data

  • Men’s Teams: men_team_chrono.csv - Historical men’s team results
  • Ladies’ Teams: ladies_team_chrono.csv - Historical ladies’ team results
  • Mixed Teams: mixed_team_chrono.csv - Historical mixed team results
  • Team Startlists: startlist_team_weekend_men.csv, startlist_team_weekend_ladies.csv, startlist_mixed_team_weekend_teams.csv

Points System

All ski jumping events use the same points system:

  • Top 30 get points: 100, 80, 60, 50, 45, 40, 36, 32, 29, 26, 24, 22, 20, 18, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

ELO Features

Individual Athletes

Hill-specific ELO ratings based on different hill sizes:

  • Normal_Elo_Pct - Performance on normal hills (K90-K99)
  • Large_Elo_Pct - Performance on large hills (K120-K130)
  • Flying_Elo_Pct - Performance on flying hills (K185+)
  • Elo_Pct - Overall ELO rating
  • Prev_Points_Weighted - Weighted average of recent points (last 5 races)

Team Competitions

Average ELO ratings of team members:

  • Avg_Normal_Elo_Pct - Team average normal hill ELO
  • Avg_Large_Elo_Pct - Team average large hill ELO
  • Avg_Flying_Elo_Pct - Team average flying hill ELO
  • Avg_Elo_Pct - Team average overall ELO

Race Filtering

Weekend Race Selection

# Individual races
men_races <- next_weekend_races %>%
  filter(Sex == "M", !grepl("Team", RaceType, ignore.case = TRUE))

ladies_races <- next_weekend_races %>%
  filter(Sex == "L", !grepl("Team", RaceType, ignore.case = TRUE))

# Team races  
men_teams <- next_weekend_races %>%
  filter(grepl("Team", RaceType, ignore.case = TRUE) & Sex == "M")

ladies_teams <- next_weekend_races %>%
  filter(grepl("Team", RaceType, ignore.case = TRUE) & Sex == "L")

# Mixed team races
mixed_teams <- next_weekend_races %>%
  filter(Sex == "Mixed")

Race Participation Probability

Individual Athletes

Calculates probability based on historical participation in the specific race type over the last 5 years:

get_race_probability <- function(chronos, participant, racetype, is_team = FALSE) {
  # Use 5 years of history or participant's first race date, whichever is later
  five_years_ago <- Sys.Date() - (5 * 365)
  start_date <- max(five_years_ago, first_race_date)
  
  # Count total races vs participant's races for this race type
  total_races <- count_distinct_races(chronos, racetype, start_date)
  participant_races <- count_participant_races(chronos, participant, racetype, start_date)
  
  probability <- min(1, participant_races / total_races)
  return(probability)
}

Team Competitions

Teams typically have probability = 1.0 (assumed to participate if entered)

Prediction Models

Points Prediction Model

Uses Generalized Additive Models (GAM) with feature selection:

Individual Model

explanatory_vars <- c("Prev_Points_Weighted", "Normal_Elo_Pct", "Large_Elo_Pct", 
                      "Flying_Elo_Pct", "Elo_Pct")

# Feature selection using regsubsets with BIC criterion
exhaustive_selection <- regsubsets(Points ~ ., data = race_df_75, method = "exhaustive")
best_bic_vars <- names(coef(exhaustive_selection, which.min(summary$bic)))

# GAM model with smooth terms
gam_formula <- as.formula(paste("Points ~", paste("s(", best_bic_vars[-1], ")", collapse=" + ")))
model <- gam(gam_formula, data = race_df_75)

Team Model

explanatory_vars <- c("Avg_Normal_Elo_Pct", "Avg_Large_Elo_Pct", 
                      "Avg_Flying_Elo_Pct", "Avg_Elo_Pct")

Position Probability Models

Creates separate GAM models for each position threshold (1, 3, 5, 10, 30):

for(threshold in position_thresholds) {
  # Binary response: did athlete finish in top N?
  race_df$position_achieved <- as.numeric(race_df$Place <= threshold)
  
  # Feature selection for this threshold
  pos_selection <- regsubsets(position_achieved ~ ., data = race_df_75, 
                             family = binomial, method = "exhaustive")
  pos_best_vars <- names(coef(pos_selection, which.min(summary$bic)))
  
  # GAM model with binomial family
  pos_gam_formula <- as.formula(paste("position_achieved ~", 
                                     paste("s(", pos_best_vars[-1], ")", collapse=" + ")))
  position_model <- gam(pos_gam_formula, data = race_df_75, family = binomial)
  
  # Store model for prediction
  position_models[[paste0("threshold_", threshold)]] <- position_model
}

Data Preprocessing

ELO Percentage Calculation

Converts absolute ELO ratings to percentages by dividing by historical maximum:

# Individual athletes
for(col in c("Normal_Elo", "Large_Elo", "Flying_Elo", "Elo")) {
  max_val <- max(race_df[[col]], na.rm = TRUE)
  result_df[[paste0(col, "_Pct")]] <- result_df[[col]] / max_val
}

# Team averages  
for(col in c("Avg_Normal_Elo", "Avg_Large_Elo", "Avg_Flying_Elo", "Avg_Elo")) {
  max_val <- max(race_df[[col]], na.rm = TRUE)
  result_df[[paste0(col, "_Pct")]] <- result_df[[col]] / max_val
}

Missing Value Handling

# Replace NAs with first quartile values
result_df <- result_df %>%
  mutate(across(ends_with("_Pct"), ~replace_na_with_quartile(.x)),
         Prev_Points_Weighted = replace_na(Prev_Points_Weighted, 0))

Probability Normalization

Multi-Step Process

  1. Race Participation Adjustment: Multiply position probabilities by race participation probabilities
  2. Target Sum Normalization: Scale probabilities to target sums (100% for win, 300% for podium, etc.)
  3. Individual Capping: Cap individual probabilities at 100%
  4. Excess Redistribution: Redistribute excess probability proportionally to other athletes
normalize_position_probabilities <- function(predictions, race_prob_col, position_thresholds) {
  for(threshold in position_thresholds) {
    prob_col <- paste0("prob_top", threshold)
    
    # Step 1: Apply race participation probability
    normalized[[prob_col]] <- normalized[[prob_col]] * normalized[[race_prob_col]]
    
    # Step 2: Normalize to target sum
    current_sum <- sum(normalized[[prob_col]], na.rm = TRUE)
    target_sum <- 100 * threshold
    scaling_factor <- target_sum / current_sum
    normalized[[prob_col]] <- normalized[[prob_col]] * scaling_factor
    
    # Step 3: Cap at 100%
    over_hundred <- which(normalized[[prob_col]] > 100)
    if(length(over_hundred) > 0) {
      excess <- sum(normalized[[prob_col]][over_hundred] - 100)
      normalized[[prob_col]][over_hundred] <- 100
      
      # Step 4: Redistribute excess
      under_hundred <- which(normalized[[prob_col]] < 100)
      if(length(under_hundred) > 0 && excess > 0) {
        under_sum <- sum(normalized[[prob_col]][under_hundred])
        redistrib_factor <- (under_sum + excess) / under_sum
        normalized[[prob_col]][under_hundred] <- normalized[[prob_col]][under_hundred] * redistrib_factor
      }
    }
  }
}

Hill Size Classification

  • Normal Hills: K90-K99 (most common World Cup venues)
  • Large Hills: K120-K130 (major championships, Four Hills Tournament)
  • Flying Hills: K185+ (ski flying competitions)

Output Format

Individual Results

  • Participant: Skier name
  • ID: FIS athlete ID
  • Nation: Country code
  • Race: Race number within weekend
  • Participation: Probability of racing (0-1)
  • Win: Win probability percentage
  • Podium: Top 3 probability percentage
  • Top5: Top 5 probability percentage
  • Top10: Top 10 probability percentage
  • Top30: Top 30 probability percentage

Team Results

  • Nation: Country/team name
  • Race: Race number within weekend
  • Participation: Probability of racing (typically 1.0)
  • Win: Win probability percentage
  • Podium: Top 3 probability percentage
  • Top5: Top 5 probability percentage
  • Top10: Top 10 probability percentage
  • Top30: Top 30 probability percentage

Key Differences from Alpine Skiing

  1. Hill-specific ELO: Uses hill size categories (Normal/Large/Flying) instead of discipline-specific ELO
  2. Team competitions: Includes sophisticated team prediction models using averaged athlete ELO ratings
  3. Mixed competitions: Handles mixed-gender team events
  4. Unified points system: Same points system across all event types
  5. Race type filtering: Uses RaceType and HillSize instead of Distance for race categorization

Model Validation

  • Uses Brier score for model evaluation
  • Applies period adjustments for trend changes
  • Includes fallback models for insufficient data scenarios
  • Logs detailed probability sum checks to ensure mathematical consistency
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