Overview

Charizard Garchomp Blissey Aggron Tyranitar Metagross Lucario Scizor

A comprehensive dual-rating system for competitive Pokémon battling. Each Pokémon receives separate Offensive and Defensive ratings (100-point scale), enabling strategic team building and role identification.

100

Offensive Rating Scale

100

Defensive Rating Scale

Tier Levels (SS to F)

Battle Roles

Rating System Components

Offensive Rating (100 Points)

BST Score (40 points)

S-curve (logistic function) mapping for smooth strength scaling: - Inflection point: BST = 450 - Maximum: 40 points - Penalizes both very weak and recognizes elite stats

Offensive Stats Distribution (60 points)

Effective Attack Power (50%): Recognizes mixed vs specialized attackers
- Mixed attackers (ratio ≥ 0.9): weighted average of Attack and Sp. Attack
- Specialized attackers: use higher of Attack or Sp. Attack
Effective Speed Score (40%): Dual tactical value
- Fast sweepers (high speed) AND
- Trick Room users (very low speed) both valued
Durability Buffer (10%): Minimum survivability requirement

Defensive Rating (100 Points)

BST Score (40 points)

Same S-curve mapping as offensive rating (shared component)

Defensive Stats Distribution (30 points)

Durability Expectation (80%): HP × √(Def × SpDef)
- Uses geometric mean to penalize unbalanced defenses
- Rewards balanced defensive investment
Counter-Attack Ability (20%): Minimum offensive threat
- Ensures defensive Pokémon aren’t complete walls

Type Advantage (30 points)

Defensive type matchup score based on: - Resistances (×0.5, ×0.25) - Immunities (×0) - Weaknesses (×2, ×4) - Type combination synergy

Rating Formulas

# BST Score Calculator (40 points max)
calc_bst_score <- function(total, atk, spatk, eff_atk) {
  L <- 40      # Maximum score
  k <- 0.015   # Steepness
  x0 <- 450    # Inflection point
  bst <- total - atk - spatk + eff_atk
  score <- L / (1 + exp(-k * (bst - x0)))
  return(score)
}

# Effective Attack Power
calc_eff_atk <- function(atk, spatk){
  ratio <- pmin(atk, spatk) / pmax(atk, spatk)
  ifelse(ratio < 0.9, pmax(atk, spatk), 0.6*(atk + spatk))
}

# Durability Expectation
calc_eff_def <- function(hp, def, spdef){
  hp * sqrt(def * spdef)
}

# Effective Speed Score
calc_eff_spd <- function(spd, vmin, vmax, v0 = 80){
  B <- (spd - vmin) / (vmax - vmin)
  D <- (abs(spd - v0)) / max(v0 - vmin, vmax - v0)
  B + 0.5 * D
}

# Offensive Stat Distribution Score (60 points)
calc_atk_score <- function(eff_atk_s, eff_def_s, eff_spd_s){
  (0.5*eff_atk_s + 0.1*eff_def_s + 0.4*eff_spd_s) * 60
}

# Defensive Stat Distribution Score (60 points total)
calc_def_score <- function(eff_atk_s, eff_def_s, defensive_score){
  (0.8*eff_def_s + 0.2*eff_atk_s) * 30 + 30 * defensive_score/100
}

Visualization of Scoring Functions

library(patchwork)

# BST Score curve
bst_range <- seq(200, 800, by = 5)
bst_viz <- tibble(
  BST = bst_range,
  Score = sapply(bst_range, function(x) calc_bst_score(x, 100, 100, 100))
)

p1 <- ggplot(bst_viz, aes(x = BST, y = Score)) +
  geom_line(color = "#667eea", size = 1.5) +
  geom_vline(xintercept = 450, linetype = "dashed", color = "red", alpha = 0.5) +
  annotate("text", x = 450, y = 35, label = "Inflection\n(450)", color = "red", size = 3) +
  labs(title = "BST Score: S-Curve Mapping",
       x = "Base Stat Total", y = "Score (max 40)") +
  theme_minimal()

# Effective Attack heatmap
atk_pairs <- expand.grid(atk = seq(50, 200, 10), spatk = seq(50, 200, 10))
eff_atk_viz <- atk_pairs %>%
  mutate(eff_atk = calc_eff_atk(atk, spatk))

p2 <- ggplot(eff_atk_viz, aes(x = atk, y = spatk, fill = eff_atk)) +
  geom_tile() +
  geom_abline(slope = 1, linetype = "dashed", color = "white") +
  scale_fill_viridis_c(option = "plasma") +
  labs(title = "Effective Attack Power",
       x = "Attack", y = "Special Attack", fill = "Eff. Atk") +
  theme_minimal()

# Effective Speed curve
spd_range <- seq(5, 200, by = 5)
spd_viz <- tibble(
  Speed = spd_range,
  Score = calc_eff_spd(spd_range, min(spd_range), max(spd_range))
)

p3 <- ggplot(spd_viz, aes(x = Speed, y = Score)) +
  geom_line(color = "#4CAF50", size = 1.5) +
  geom_vline(xintercept = 80, linetype = "dashed", color = "red", alpha = 0.5) +
  annotate("text", x = 80, y = 1.3, label = "Baseline\n(80)", color = "red", size = 3) +
  labs(title = "Effective Speed Score",
       x = "Speed Stat", y = "Normalized Score") +
  theme_minimal()

p1 + p2 + p3

Type Effectiveness Analysis

Defensive Type Rankings

# Calculate defense effectiveness
defense_stats <- type_df %>%
  group_by(def_type) %>%
  summarise(
    weaknesses = sum(multiplier == 2),
    weaknesses_x4 = sum(multiplier == 4),
    strong_resistances = sum(multiplier == 0.25),
    resistances = sum(multiplier == 0.5),
    immunities = sum(multiplier == 0),
    neutral = sum(multiplier == 1),
    .groups = "drop"
  )

# Calculate defensive score
def_stats_scaled <- defense_stats %>%
  mutate(
    defensive_score = (
      strong_resistances*0.2/max(strong_resistances) +
      resistances*0.45/max(resistances) +
      neutral*0.2/max(neutral) -
      weaknesses_x4*0.1/max(weaknesses_x4) -
      weaknesses*0.05/max(weaknesses)
    )*100 + immunities*5
  ) %>%
  arrange(desc(defensive_score))

# Top 15 defensive types
def_stats_scaled %>%
  slice_head(n = 15) %>%
  mutate(def_type = factor(def_type, levels = def_type)) %>%
  pivot_longer(
    cols = c(weaknesses_x4, weaknesses, neutral, strong_resistances, resistances, immunities),
    names_to = "effectiveness",
    values_to = "count"
  ) %>%
  mutate(
    effectiveness = factor(
      effectiveness,
      levels = c("weaknesses_x4", "weaknesses", "neutral",
                "strong_resistances", "resistances", "immunities")
    )
  ) %>%
  ggplot(aes(x = def_type, y = count, fill = effectiveness)) +
  geom_col(position = "dodge") +
  scale_fill_manual(
    values = c(
      "weaknesses_x4" = "#B71C1C",
      "weaknesses" = "#F44336",
      "neutral" = "#9E9E9E",
      "strong_resistances" = "#2E7D32",
      "resistances" = "#4CAF50",
      "immunities" = "#2196F3"
    ),
    labels = c(
      "4× Weak", "2× Weak", "Neutral",
      "¼× Resist", "½× Resist", "Immune"
    )
  ) +
  labs(
    title = "Top 15 Defensive Type Combinations",
    subtitle = "Best defensive typings based on resistance profile",
    x = "Type Combination",
    y = "Count",
    fill = "Effectiveness"
  ) +
  theme_minimal(base_size = 12) +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

Calculate Pokémon Ratings

# Type order for defensive typing
TYPE_ORDER <- c(
  "Normal","Fire","Water","Electric","Grass","Ice",
  "Fighting","Poison","Ground","Flying","Psychic",
  "Bug","Rock","Ghost","Dragon","Dark","Steel","Fairy"
)

# Add defense type column
pokemon_df_typed <- pokemon_df %>%
  mutate(
    idx1 = match(type_1, TYPE_ORDER),
    idx2 = match(type_2, TYPE_ORDER),
    def_type = case_when(
      is.na(type_2) ~ type_1,
      TRUE ~ paste(
        TYPE_ORDER[pmin(idx1, idx2)],
        TYPE_ORDER[pmax(idx1, idx2)],
        sep = "/"
      )
    )
  ) %>%
  left_join(
    def_stats_scaled %>% select(def_type, defensive_score),
    by = "def_type"
  )

# Calculate ratings
pokemon_rated <- pokemon_df_typed %>%
  mutate(
    # Step 1: Calculate raw effective values
    eff_atk = calc_eff_atk(attack, sp_atk),
    eff_def = calc_eff_def(hp, defense, sp_def),
    eff_spd = calc_eff_spd(speed, min(speed), max(speed)),

    # Step 2: Normalize to [0,1] scale
    eff_atk_s = eff_atk / max(eff_atk),
    eff_def_s = eff_def / max(eff_def),
    eff_spd_s = eff_spd / max(eff_spd),

    # Step 3: Calculate BST score (shared)
    bst_score = calc_bst_score(total, attack, sp_atk, eff_atk),

    # Step 4: Calculate final ratings
    offensive_rating = bst_score + calc_atk_score(eff_atk_s, eff_def_s, eff_spd_s),
    defensive_rating = bst_score + calc_def_score(eff_atk_s, eff_def_s, defensive_score),

    # Tier assignment
    tier = case_when(
      offensive_rating >= 75 | defensive_rating >= 65 ~ "SS",
      offensive_rating >= 65 | defensive_rating >= 55 ~ "S",
      offensive_rating >= 55 | defensive_rating >= 45 ~ "A",
      offensive_rating >= 45 | defensive_rating >= 35 ~ "B",
      offensive_rating >= 35 | defensive_rating >= 25 ~ "C",
      TRUE ~ "F"
    ),

    # Role classification
    role = case_when(
      offensive_rating / defensive_rating >= 1.15 ~ "Offensive",
      offensive_rating / defensive_rating <= 0.85 ~ "Defensive",
      TRUE ~ "Balanced"
    )
  )

# Set factors
pokemon_rated$tier <- factor(pokemon_rated$tier, levels = c("SS", "S", "A", "B", "C", "F"))
pokemon_rated$role <- factor(pokemon_rated$role, levels = c("Offensive", "Balanced", "Defensive"))

Rating Distribution

Tier Distribution

tier_summary <- pokemon_rated %>%
  count(tier) %>%
  mutate(percentage = round(100 * n / sum(n), 1))

kable(tier_summary, caption = "Pokémon Distribution by Tier", align = "lcc")

Pokémon Distribution by Tier
tier	n	percentage
SS	14	1.9
S	66	8.9
A	147	19.8
B	238	32.1
C	227	30.6
F	50	6.7

ggplot(tier_summary, aes(x = tier, y = n, fill = tier)) +
  geom_col(show.legend = FALSE) +
  geom_text(aes(label = paste0(n, "\n(", percentage, "%)")),
            vjust = -0.5, size = 4) +
  scale_fill_manual(values = c("SS" = "#FF3CAC", "S" = "#FFD700",
                                "A" = "#9C27B0", "B" = "#2196F3",
                                "C" = "#4CAF50", "F" = "#9E9E9E")) +
  labs(title = "Tier Distribution",
       x = "Tier", y = "Count") +
  theme_minimal(base_size = 12)

Role Distribution

role_summary <- pokemon_rated %>%
  count(role) %>%
  mutate(percentage = round(100 * n / sum(n), 1))

kable(role_summary, caption = "Pokémon Distribution by Battle Role", align = "lcc")

Pokémon Distribution by Battle Role
role	n	percentage
Offensive	369	49.7
Balanced	367	49.5
Defensive	6	0.8

Offensive vs Defensive Ratings

ggplot(pokemon_rated, aes(x = offensive_rating, y = defensive_rating)) +
  geom_point(aes(color = tier, shape = role), alpha = 0.6, size = 3) +
  geom_abline(slope = 1, linetype = "dashed", color = "gray50", alpha = 0.5) +
  geom_smooth(method = "lm", se = FALSE, linetype = "dashed", color = "gray30") +
  scale_color_manual(values = c("SS" = "#FF3CAC", "S" = "#FFD700",
                                 "A" = "#9C27B0", "B" = "#2196F3",
                                 "C" = "#4CAF50", "F" = "#9E9E9E")) +
  labs(
    title = "Offensive vs Defensive Rating Distribution",
    subtitle = "Points above diagonal = defense-oriented, below = offense-oriented",
    x = "Offensive Rating", y = "Defensive Rating",
    color = "Tier", shape = "Role"
  ) +
  theme_minimal(base_size = 12)

Rating Result

“The Strongest Sword”

Mega Mewtwo Y

“The Strongest Shield”

Zygarde Complete Forme

“The strongest ordinary Pokémon”

Mega Alakazam

Top 20 Offensive Pokémon

top_offensive <- pokemon_rated %>%
  arrange(desc(offensive_rating)) %>%
  select(name, type_1, type_2, role, offensive_rating, defensive_rating, tier)

top_offensive |> 
  head(20) |> 
  kable(caption = "Top 20 Offensive Pokémon",
        digits = 1,
        align = "lllcccc")

Top 20 Offensive Pokémon
name	type_1	type_2	role	offensive_rating	defensive_rating	tier
Mega Mewtwo Y	Psychic	NA	Offensive	82.0	59.9	SS
Mega Rayquaza	Dragon	Flying	Offensive	81.8	63.5	SS
Ultra Necrozma	Psychic	Dragon	Offensive	80.8	61.5	SS
Mega Mewtwo X	Psychic	Fighting	Offensive	80.1	60.5	SS
Shadow Rider Calyrex	Psychic	Ghost	Offensive	77.7	57.0	SS
Zacian Crowned Sword	Fairy	Steel	Balanced	76.9	68.7	SS
Mega Alakazam	Psychic	NA	Offensive	74.7	49.2	S
Eternatus	Poison	Dragon	Balanced	73.6	65.3	SS
Mega Diancie	Rock	Fairy	Offensive	73.2	54.6	S
Arceus	Normal	NA	Offensive	73.1	63.5	S
Primal Kyogre	Water	NA	Balanced	72.9	64.0	S
Primal Groudon	Ground	Fire	Balanced	72.9	64.8	S
Mewtwo	Psychic	NA	Offensive	71.8	55.4	S
Koraidon	Fighting	Dragon	Offensive	71.2	59.5	S
Miraidon	Electric	Dragon	Offensive	71.2	60.3	S
Palkia Origin Forme	Water	Dragon	Offensive	70.5	57.6	S
Zamazenta Crowned Shield	Fighting	Steel	Balanced	70.4	67.4	SS
Regigigas	Normal	NA	Offensive	70.1	59.9	S
White Kyurem	Dragon	Ice	Offensive	70.1	58.8	S
Black Kyurem	Dragon	Ice	Offensive	70.1	58.8	S

Top 20 Defensive Pokémon

top_defensive <- pokemon_rated %>%
  arrange(desc(defensive_rating)) %>%
  select(name, type_1, type_2, role, defensive_rating, offensive_rating, tier)

top_defensive |> 
  head(20) |> 
  kable(caption = "Top 20 Defensive Pokémon",
        digits = 1,
        align = "lllcccc")

Top 20 Defensive Pokémon
name	type_1	type_2	role	defensive_rating	offensive_rating	tier
Zygarde Complete Forme	Dragon	Ground	Balanced	72.5	66.4	SS
Giratina Altered Forme	Ghost	Dragon	Balanced	70.1	65.2	SS
Zacian Crowned Sword	Fairy	Steel	Balanced	68.7	76.9	SS
Zamazenta Crowned Shield	Fighting	Steel	Balanced	67.4	70.4	SS
Dialga Origin Forme	Steel	Dragon	Balanced	66.9	66.6	SS
Giratina Origin Forme	Ghost	Dragon	Balanced	66.7	66.8	SS
Solgaleo	Psychic	Steel	Balanced	65.9	65.3	SS
Eternatus	Poison	Dragon	Balanced	65.3	73.6	SS
Terapagos Stellar Form	Normal	NA	Balanced	65.1	65.4	SS
Primal Groudon	Ground	Fire	Balanced	64.8	72.9	S
Mega Metagross	Steel	Psychic	Balanced	64.7	69.3	S
Dusk Mane Necrozma	Psychic	Steel	Balanced	64.4	65.0	S
Dialga	Steel	Dragon	Balanced	64.4	64.9	S
Primal Kyogre	Water	NA	Balanced	64.0	72.9	S
Mega Aggron	Steel	NA	Balanced	63.9	61.9	S
Mega Rayquaza	Dragon	Flying	Offensive	63.5	81.8	SS
Arceus	Normal	NA	Offensive	63.5	73.1	S
Mega Tyranitar	Rock	Dark	Balanced	63.2	68.7	S
Melmetal	Steel	NA	Balanced	62.9	58.3	S
Lugia	Psychic	Flying	Balanced	62.8	66.1	S

Best Regular Pokémon (For Beginners)

top_regular <- pokemon_rated %>%
  filter(category == "Regular") %>%
  arrange(desc(pmax(defensive_rating+10, offensive_rating))) %>%
  select(name, type_1, type_2, role, offensive_rating, defensive_rating, tier)

top_regular |> 
  head(20) |> 
  kable(caption = "Top 20 Regular Pokémon (Accessible for Beginners)",
        digits = 1,
        align = "lllcccc")

Top 20 Regular Pokémon (Accessible for Beginners)
name	type_1	type_2	role	offensive_rating	defensive_rating	tier
Mega Alakazam	Psychic	NA	Offensive	74.7	49.2	S
Mega Metagross	Steel	Psychic	Balanced	69.3	64.7	S
Mega Aggron	Steel	NA	Balanced	61.9	63.9	S
Mega Tyranitar	Rock	Dark	Balanced	68.7	63.2	S
Mega Steelix	Steel	Ground	Balanced	58.8	62.4	S
Mega Gyarados	Water	Dark	Balanced	65.1	61.1	S
Mega Salamence	Dragon	Flying	Offensive	69.9	58.7	S
Mega Gengar	Ghost	Poison	Offensive	69.8	51.6	S
Ash-Greninja	Water	Dark	Offensive	69.7	50.6	S
Mega Garchomp	Dragon	Ground	Offensive	69.5	59.2	S
Mega Aerodactyl	Rock	Flying	Offensive	69.4	53.2	S
Slaking	Normal	NA	Offensive	69.2	58.9	S
Mega Dragonite	Dragon	Flying	Balanced	66.8	59.0	S
Mega Gallade	Psychic	Fighting	Offensive	68.3	51.8	S
Hisuian Goodra	Steel	Dragon	Balanced	55.0	58.1	S
Mega Scizor	Bug	Steel	Balanced	60.3	57.7	S
Mega Heracross	Bug	Fighting	Offensive	67.6	55.8	S
Mega Swampert	Water	Ground	Balanced	61.4	57.2	S
Mega Sceptile	Grass	Dragon	Offensive	67.0	44.8	S
Galarian Darmanitan Zen Mode	Ice	Fire	Offensive	66.5	45.7	S

# Export Offensive Pokemon Ranking list
write_csv(top_offensive, "data/top_offensive.csv")

# Export Defensive Pokemon Ranking list
write_csv(top_defensive, "data/top_defensive.csv")

# Export Regular Pokemon Ranking list
write_csv(top_regular, "data/top_regular.csv")

Summary

Pikachu Eevee Snorlax Arcanine Lapras Gyarados Umbreon Sylveon

Dual Rating System Benefits

Separate Offensive & Defensive Evaluation: No longer forced to choose between attacking power and tanking ability
Type Synergy Recognition: Defensive typing contributes 30% to defensive rating
Mixed Attacker Support: Algorithm recognizes both specialized and versatile attackers
Speed Flexibility: Values both fast sweepers and Trick Room users
Balanced Defense Rewards: Geometric mean prevents glass cannon defenses

Key Statistics

Average Offensive Rating: 45.1/100
Average Defensive Rating: 39.3/100
SS Tier Pokémon: 14 (1.9%)
Most Common Role: Offensive (49.7%)

Best Type Combinations

Offensive: Ground, Fighting, Fire (high super-effective coverage) Defensive: Steel/Fairy, Steel/Flying, Water/Ground (few weaknesses, many resistances)

Rating system designed for competitive singles format • Based on final evolution forms only

Pokémon Dual Rating System

Overview

Rating System Components

Offensive Rating (100 Points)

BST Score (40 points)

Offensive Stats Distribution (60 points)

Defensive Rating (100 Points)

BST Score (40 points)

Defensive Stats Distribution (30 points)

Type Advantage (30 points)

Rating Formulas

Visualization of Scoring Functions

Type Effectiveness Analysis

Defensive Type Rankings

Calculate Pokémon Ratings

Rating Distribution

Tier Distribution

Role Distribution

Offensive vs Defensive Ratings

Rating Result

Top 20 Offensive Pokémon

Top 20 Defensive Pokémon

Best Regular Pokémon (For Beginners)

Summary

Dual Rating System Benefits

Key Statistics

Best Type Combinations