Number Frequency Analysis

# Create a function to calculate frequencies
calculate_frequencies <- function(data, number_type, max_number) {
    # Reshape data to long format
    if (number_type == "main") {
        long_data <- data %>%
            select(year, main_1, main_2, main_3, main_4, main_5) %>%
            pivot_longer(
                cols = starts_with("main_"),
                names_to = "position",
                values_to = "number"
            )
    } else {
        long_data <- data %>%
            select(year, euro_1, euro_2) %>%
            pivot_longer(
                cols = starts_with("euro_"),
                names_to = "position",
                values_to = "number"
            )
    }

    # Calculate frequencies by year and number
    freq_data <- long_data %>%
        group_by(year, number) %>%
        summarise(frequency = n(), .groups = "drop") %>%
        # Add missing numbers with zero frequency
        complete(year, number = 1:max_number, fill = list(frequency = 0))

    return(freq_data)
}

# Calculate frequencies
main_freq <- calculate_frequencies(results, "main", 50)
euro_freq <- calculate_frequencies(results, "euro", 12)

# Add outlier detection based on uniform distribution
# For main numbers (1-50)
main_outlier_analysis <- main_freq %>%
    group_by(year) %>%
    mutate(
        # Expected frequency under uniform distribution
        expected = sum(frequency) / 50,
        # Calculate deviation from expected
        deviation = frequency - expected,
        # Calculate z-score (standardized deviation)
        z_score = (frequency - expected) / sqrt(expected * (1 - 1 / 50)),
        # Flag significant outliers (|z| > 1.96 for 95% confidence)
        is_outlier = abs(z_score) > 1.96
    ) %>%
    ungroup()

# For euro numbers (1-12)
euro_outlier_analysis <- euro_freq %>%
    group_by(year) %>%
    mutate(
        # Expected frequency under uniform distribution
        expected = sum(frequency) / 12,
        # Calculate deviation from expected
        deviation = frequency - expected,
        # Calculate z-score (standardized deviation)
        z_score = (frequency - expected) / sqrt(expected * (1 - 1 / 12)),
        # Flag significant outliers (|z| > 1.96 for 95% confidence)
        is_outlier = abs(z_score) > 1.96
    ) %>%
    ungroup()

# Visualize outliers for main numbers
main_outlier_plot <- ggplot(
    main_outlier_analysis,
    aes(x = number, y = frequency, fill = is_outlier)
) +
    geom_bar(stat = "identity") +
    scale_fill_manual(values = c("FALSE" = "steelblue", "TRUE" = "red")) +
    facet_wrap(~year, ncol = 1) +
    scale_x_continuous(breaks = seq(1, 50, by = 5)) +
    geom_hline(aes(yintercept = expected), linetype = "dashed", color = "black") +
    labs(
        title = "Main Number Frequency with Outliers Highlighted",
        subtitle = "Red bars indicate statistically significant deviations from uniform distribution",
        x = "Main Number (1-50)",
        y = "Frequency"
    ) +
    theme_minimal()

# Visualize outliers for euro numbers
euro_outlier_plot <- ggplot(
    euro_outlier_analysis,
    aes(x = number, y = frequency, fill = is_outlier)
) +
    geom_bar(stat = "identity") +
    scale_fill_manual(values = c("FALSE" = "steelblue", "TRUE" = "red")) +
    facet_wrap(~year, ncol = 1) +
    scale_x_continuous(breaks = 1:12) +
    geom_hline(aes(yintercept = expected), linetype = "dashed", color = "black") +
    labs(
        title = "Euro Number Frequency with Outliers Highlighted",
        subtitle = "Red bars indicate statistically significant deviations from uniform distribution",
        x = "Euro Number (1-12)",
        y = "Frequency"
    ) +
    theme_minimal()

# Display outlier plots
main_outlier_plot

euro_outlier_plot

# Summarize outliers in a table
main_outliers_summary <- main_outlier_analysis %>%
    filter(is_outlier) %>%
    arrange(year, desc(abs(z_score))) %>%
    select(year, number, frequency, expected, deviation, z_score)

euro_outliers_summary <- euro_outlier_analysis %>%
    filter(is_outlier) %>%
    arrange(year, desc(abs(z_score))) %>%
    select(year, number, frequency, expected, deviation, z_score)

# Display outlier summaries

if (nrow(main_outliers_summary) > 0) {
    knitr::kable(main_outliers_summary, digits = 2)
} else {
    cat("No statistically significant outliers found in main numbers.\n")
}
year number frequency expected deviation z_score
2013 9 10 5.2 4.8 2.13
2016 10 11 5.3 5.7 2.50
2017 37 0 5.2 -5.2 -2.30
2017 40 10 5.2 4.8 2.13
2017 44 10 5.2 4.8 2.13
2017 46 10 5.2 4.8 2.13
2018 24 10 5.2 4.8 2.13
2018 33 10 5.2 4.8 2.13
2018 46 10 5.2 4.8 2.13
2019 21 10 5.2 4.8 2.13
2019 24 10 5.2 4.8 2.13
2019 35 10 5.2 4.8 2.13
2019 45 10 5.2 4.8 2.13
2020 49 10 5.2 4.8 2.13
2021 43 10 5.3 4.7 2.06
2023 16 20 10.4 9.6 3.01
2023 25 3 10.4 -7.4 -2.32
2023 31 17 10.4 6.6 2.07
2024 30 20 10.5 9.5 2.96
2024 45 19 10.5 8.5 2.65
2024 5 4 10.5 -6.5 -2.03 
if (nrow(euro_outliers_summary) > 0) {
    knitr::kable(euro_outliers_summary, digits = 2)
} else {
    cat("No statistically significant outliers found in euro numbers.\n")
}
year number frequency expected deviation z_score
2012 5 16 6.83 9.17 3.66
2012 9 0 6.83 -6.83 -2.73
2012 10 0 6.83 -6.83 -2.73
2012 11 0 6.83 -6.83 -2.73
2012 12 0 6.83 -6.83 -2.73
2012 3 12 6.83 5.17 2.06
2012 8 12 6.83 5.17 2.06
2013 7 18 8.67 9.33 3.31
2013 9 0 8.67 -8.67 -3.07
2013 10 0 8.67 -8.67 -3.07
2013 11 0 8.67 -8.67 -3.07
2013 12 0 8.67 -8.67 -3.07
2013 8 16 8.67 7.33 2.60
2013 2 15 8.67 6.33 2.25
2013 5 15 8.67 6.33 2.25
2014 4 22 8.67 13.33 4.73
2014 10 0 8.67 -8.67 -3.07
2014 11 0 8.67 -8.67 -3.07
2014 12 0 8.67 -8.67 -3.07
2014 6 16 8.67 7.33 2.60
2014 8 16 8.67 7.33 2.60
2015 3 20 8.67 11.33 4.02
2015 11 0 8.67 -8.67 -3.07
2015 12 0 8.67 -8.67 -3.07
2016 11 0 8.83 -8.83 -3.10
2016 12 0 8.83 -8.83 -3.10
2017 11 0 8.67 -8.67 -3.07
2017 12 0 8.67 -8.67 -3.07
2017 1 16 8.67 7.33 2.60
2017 10 2 8.67 -6.67 -2.37
2018 11 0 8.67 -8.67 -3.07
2018 12 0 8.67 -8.67 -3.07
2018 10 17 8.67 8.33 2.96
2018 1 2 8.67 -6.67 -2.37
2019 11 0 8.67 -8.67 -3.07
2019 12 0 8.67 -8.67 -3.07
2019 9 16 8.67 7.33 2.60
2020 11 0 8.67 -8.67 -3.07
2020 12 0 8.67 -8.67 -3.07
2021 11 0 8.83 -8.83 -3.10
2021 12 0 8.83 -8.83 -3.10
2021 8 17 8.83 8.17 2.87
2023 3 26 17.33 8.67 2.17
2024 1 27 17.50 9.50 2.37
2024 10 27 17.50 9.50 2.37

Most and Least Frequent Numbers

# Analyze the most and least frequently drawn numbers

# Function to create frequency analysis
analyze_number_frequency <- function(data, number_type, max_number) {
    # Create long format data
    if (number_type == "main") {
        long_data <- data %>%
            select(main_1, main_2, main_3, main_4, main_5) %>%
            pivot_longer(
                cols = everything(),
                names_to = "position",
                values_to = "number"
            )
    } else {
        long_data <- data %>%
            select(euro_1, euro_2) %>%
            pivot_longer(
                cols = everything(),
                names_to = "position",
                values_to = "number"
            )
    }

    # Count frequency of each number
    number_freq <- long_data %>%
        count(number) %>%
        rename(frequency = n)

    # Add any missing numbers with zero frequency
    all_numbers <- tibble(number = 1:max_number)
    number_freq <- all_numbers %>%
        left_join(number_freq, by = "number") %>%
        mutate(frequency = ifelse(is.na(frequency), 0, frequency))

    # Calculate statistics
    number_freq <- number_freq %>%
        mutate(
            percentage = frequency / sum(frequency) * 100,
            expected = sum(frequency) / max_number,
            deviation = frequency - expected,
            relative_deviation = deviation / expected * 100
        )

    return(number_freq)
}

# Analyze main numbers (1-50)
main_number_freq <- analyze_number_frequency(results %>% filter(year >= 2022), "main", 50)

# Analyze euro numbers (1-12)
euro_number_freq <- analyze_number_frequency(results %>% filter(year >= 2022), "euro", 12)

# Create plots for frequency analysis
main_freq_plot <- ggplot(main_number_freq, aes(x = number, y = frequency)) +
    geom_bar(stat = "identity", fill = "steelblue") +
    geom_hline(aes(yintercept = expected), linetype = "dashed", color = "red") +
    labs(
        title = "Main Number Frequency Distribution",
        subtitle = "Red dashed line indicates expected frequency under uniform distribution",
        x = "Main Number (1-50)",
        y = "Frequency"
    ) +
    theme_minimal()

euro_freq_plot <- ggplot(euro_number_freq, aes(x = number, y = frequency)) +
    geom_bar(stat = "identity", fill = "steelblue") +
    geom_hline(aes(yintercept = expected), linetype = "dashed", color = "red") +
    labs(
        title = "Euro Number Frequency Distribution",
        subtitle = "Red dashed line indicates expected frequency under uniform distribution",
        x = "Euro Number (1-12)",
        y = "Frequency"
    ) +
    theme_minimal() +
    scale_x_continuous(breaks = 1:12)

# Display the plots
main_freq_plot

euro_freq_plot

# Find top and bottom 5 numbers
top_main_numbers <- main_number_freq %>%
    arrange(desc(frequency)) %>%
    head(5)

bottom_main_numbers <- main_number_freq %>%
    arrange(frequency) %>%
    head(5)

top_euro_numbers <- euro_number_freq %>%
    arrange(desc(frequency)) %>%
    head(5)

bottom_euro_numbers <- euro_number_freq %>%
    arrange(frequency) %>%
    head(5)

# Display summary tables

knitr::kable(top_main_numbers, digits = 2)
number frequency percentage expected deviation relative_deviation
11 44 2.78 31.7 12.3 38.80
17 41 2.59 31.7 9.3 29.34
2 40 2.52 31.7 8.3 26.18
20 40 2.52 31.7 8.3 26.18
45 40 2.52 31.7 8.3 26.18 
knitr::kable(bottom_main_numbers, digits = 2)
number frequency percentage expected deviation relative_deviation
25 19 1.20 31.7 -12.7 -40.06
33 19 1.20 31.7 -12.7 -40.06
19 20 1.26 31.7 -11.7 -36.91
40 24 1.51 31.7 -7.7 -24.29
12 25 1.58 31.7 -6.7 -21.14 
knitr::kable(top_euro_numbers, digits = 2)
number frequency percentage expected deviation relative_deviation
3 67 10.57 52.83 14.17 26.81
5 60 9.46 52.83 7.17 13.56
10 60 9.46 52.83 7.17 13.56
9 54 8.52 52.83 1.17 2.21
12 53 8.36 52.83 0.17 0.32 
knitr::kable(bottom_euro_numbers, digits = 2)
number frequency percentage expected deviation relative_deviation
8 45 7.10 52.83 -7.83 -14.83
11 45 7.10 52.83 -7.83 -14.83
4 47 7.41 52.83 -5.83 -11.04
2 50 7.89 52.83 -2.83 -5.36
6 50 7.89 52.83 -2.83 -5.36

Previous: Data Overview Next: Time Series