Number Patterns Analysis

Consecutive Number Differences

# Calculate pairwise differences between consecutive numbers
# For main numbers
main_diffs <- results %>%
    mutate(
        diff_1_2 = main_2 - main_1,
        diff_2_3 = main_3 - main_2,
        diff_3_4 = main_4 - main_3,
        diff_4_5 = main_5 - main_4
    ) %>%
    select(draw_date, year, contains("diff_"))

# For euro numbers
euro_diffs <- results %>%
    mutate(
        diff_euro = euro_2 - euro_1
    ) %>%
    select(draw_date, year, diff_euro)

# Reshape data for visualization
main_diffs_long <- main_diffs %>%
    pivot_longer(
        cols = starts_with("diff_"),
        names_to = "pair",
        values_to = "difference"
    ) %>%
    mutate(pair = factor(pair,
        levels = c("diff_1_2", "diff_2_3", "diff_3_4", "diff_4_5"),
        labels = c("1→2", "2→3", "3→4", "4→5")
    ))

# Visualize distribution of differences
ggplot(main_diffs_long, aes(x = difference)) +
    geom_histogram(binwidth = 1, fill = "steelblue", color = "black", alpha = 0.7) +
    facet_wrap(~pair, ncol = 2) +
    labs(
        title = "Distribution of Differences Between Consecutive Main Numbers",
        subtitle = "How far apart are consecutive numbers in Eurojackpot draws?",
        x = "Difference Between Numbers",
        y = "Frequency"
    ) +
    theme_minimal() +
    facet_wrap(~year)

Euro Number Differences

# Visualize difference between euro numbers
ggplot(euro_diffs, aes(x = diff_euro)) +
    geom_histogram(binwidth = 1, fill = "orange", color = "black", alpha = 0.7) +
    labs(
        title = "Distribution of Differences Between Euro Numbers",
        subtitle = "How far apart are the two euro numbers in Eurojackpot draws?",
        x = "Difference Between Euro Numbers",
        y = "Frequency"
    ) +
    theme_minimal() +
    facet_wrap(~year)

Yearly Trends in Number Differences

# Calculate average differences by year
yearly_avg_diffs <- main_diffs_long %>%
    group_by(year, pair) %>%
    summarise(
        avg_diff = mean(difference, na.rm = TRUE),
        median_diff = median(difference, na.rm = TRUE),
        .groups = "drop"
    )

# Visualize yearly trends
ggplot(yearly_avg_diffs, aes(x = year, y = avg_diff, color = pair, group = pair)) +
    geom_line(size = 1) +
    geom_point(size = 3) +
    labs(
        title = "Average Difference Between Consecutive Main Numbers by Year",
        x = "Year",
        y = "Average Difference",
        color = "Number Pair"
    ) +
    theme_minimal() +
    scale_color_brewer(palette = "Set1")

Heatmap of Pairwise Differences

# Create a heatmap of pairwise differences
heatmap_data <- main_diffs_long %>%
    group_by(pair) %>%
    count(difference) %>%
    mutate(percentage = n / sum(n) * 100)

ggplot(heatmap_data, aes(x = pair, y = difference, fill = percentage)) +
    geom_tile() +
    scale_fill_viridis_c(name = "Percentage (%)") +
    labs(
        title = "Heatmap of Pairwise Differences Between Main Numbers",
        x = "Number Pair",
        y = "Difference Value"
    ) +
    theme_minimal() +
    theme(axis.text.x = element_text(angle = 0))

Heatmap of Pairwise Differences per year

# Create a heatmap of pairwise differences
heatmap_data <- main_diffs_long %>%
    group_by(pair, year) %>%
    count(difference) %>%
    mutate(percentage = n / sum(n) * 100)

ggplot(heatmap_data, aes(x = pair, y = difference, fill = percentage)) +
    geom_tile() +
    scale_fill_viridis_c(name = "Percentage (%)") +
    labs(
        title = "Heatmap of Pairwise Differences Between Main Numbers",
        x = "Number Pair",
        y = "Difference Value"
    ) +
    theme_minimal() +
    theme(axis.text.x = element_text(angle = 0)) +
    facet_wrap(~year)