In an article I contributed to Team Bandit Gang’s website, data is shown about the number of games Pro Ranked players play at different ranks. Tough with the data that can be pulled from Gwent Masters assessing whether or not playing more will result in a higher ranking is difficult. So answering the question posed in the article, whether it is skill vs grinding games that will help you further, no definitive conclusions could be drawn.

The main issue with the data released at the end of the season is that there is no good way to judge a player’s actual skill. You could use the number of games played and peak MMR as a metric for efficiency, but that isn’t necessarily a good proxy for skill. Playing all six factions would affect that score negatively, as well as players that have a very good performance but decide to play more casually with fun, less optimal, decks after achieving an MMR score they are happy with. While this could be improved by scraping players’ profiles several times throughout the season, assumptions would still need to be made how to translate this into an approximation for skill.

While skill can’t be directly measured, we can model a population of players with different skill that all play a different number of games during a simulated season. In this post we’ll explore if an Agent Based Model (ABM), implemented using the Mesa library, can assess how much grinding can improve your ranking while playing Gwent or if pure skill prevails.

This post is about the technical details how to implement the model. If you want to jump directly into the results and conclusions about ranked ladder, skip right ahead to the next post where that will be covered.

Creating the GwentAgent Class

The full code for this project is available on GitHub, though some of the important part are highlighted here. When working with Mesa an Agent class needs to be defined. This class should contain all parameters an entity in the simulation would have and how that entity should behave. So here our agents will have two important traits :

• ELO level : This represents an entities proficiency at the game at the beginning of the season. Here an ELO level is selected at the beginning for each entity. This is a rating system used in Chess to rank players. (Note that the MMR system included in Gwent is essentially an ELO rating, where changes are calculated with a K-factor of 14.)
• Playrate : The chance a player will play at each step of the model, the higher this is, the more games that agent will play through a simulated season.

On top of that we’ll need to keep track of the number of games played, the number of games won, the current MMR and the peak MMR. So for all those properties fields are included in the GwentAgent class as well. With two functions decorated with @property to calculate the win rate and the ELO score with experience correction, which is the base ELO level + an experience score based on the number of games played.

from mesa import Agent, Model
from mesa.time import RandomActivation
from mesa.datacollection import DataCollector

import numpy as np
from numpy import random

max_playrate = 20
experience_factor = 20

def win_probability(elo_difference):
proba = 1 / (1 + 10 ** (-elo_difference / 400))
return proba

def elo_change(elo_difference, K=14):
return K * (1 - win_probability(elo_difference))

def pick_elo():
"""
Generate a random elo value from a distribution that mimicks the distribution
of chess elo scores on Lichess Blitz.
"""
return min(
1200 + (1500 / 14) * np.abs(51 - random.binomial(100, 0.5)), 2700
) - random.randint(100)

class GwentAgent(Agent):
def __init__(self, unique_id, model):
super().__init__(unique_id, model)
self.peak_mmr = 2400
self.current_mmr = 2400
self.games_played = 0
self.wins = 0

self.elo_level = pick_elo()
self.playrate = random.randint(1, max_playrate)

@property
def win_rate(self):
if self.games_played > 0:
return (self.wins * 100) / self.games_played
return None

@property
def elo_experience(self):
"""
Take the ELO increased with an experience score based on the number of
games played and the experience factor.
"""
return self.elo_level + np.sqrt(self.games_played) * experience_factor

def win(self, other_player):
mmr_change = elo_change(self.current_mmr - other_player.current_mmr)
self.current_mmr += mmr_change
self.peak_mmr = max(self.current_mmr, self.peak_mmr)
self.games_played += 1
self.wins += 1

def loss(self, other_player):
mmr_change = elo_change(other_player.current_mmr - self.current_mmr)
self.current_mmr -= mmr_change
self.games_played += 1

def find_opponent(self, min_number=20):
"""
Pick a random other agent to play against. This agent should have a
comparable current mmr. So we will grow the mmr range until there
are at least
"""
mmr_range = 10

while (
len(
[
a
for a in self.model.schedule.agents
if a.unique_id != self.unique_id
and abs(self.current_mmr - a.current_mmr) <= mmr_range
]
)
< min_number
):
mmr_range += 7

possible_opponents = [
a
for a in self.model.schedule.agents
if a.unique_id != self.unique_id
and abs(self.current_mmr - a.current_mmr) <= mmr_range
]

opponent = random.choice(
[a for a in possible_opponents],
1,
[a.playrate for a in possible_opponents],
)[0]

return opponent

def play_against(self, other_agent):
# Calculate win probability, check if player won, adjust scores accordingly
wp = win_probability(self.elo_experience - other_agent.elo_experience)
rp = random.random()
won = rp < wp

if won:
self.win(other_agent)
other_agent.loss(self)
else:
other_agent.win(self)
self.loss(other_agent)

def step(self):
# Check if this agent will play a round
rp = random.randint(max_playrate + 1)
if rp >= self.playrate:
return

# Find an opponent
other_agent = self.find_opponent()

# Play against opponent and adjust score
self.play_against(other_agent)


Furthermore, there are a few functions required, the win and loss functions to handle the MMR scores after an entity won or lost a game. find_opponent this is a function to mimic the queuing system in Gwent, where it will try to find an active player with a similar current MMR, if not enough players can be found in the current range it will increase the MMR range it is looking in and search again. play_against simulates a game played by two players, the outcome is calculated by their ELO score and experience. Based on that probability the victor is picked randomly and the players’ stats are updated accordingly. Finally, the required step function implements everything a player does at each step of the simulation. Here, based on the playrate, a player will play or sit this round out. If the player plays a game, another agent with a similar MMR will be found and they will face off in a game where the outcome is determined by their skill level and experience.

The Experience Factor

It is reasonable to assume that as a player plays more games his/her familiarity with the deck and the current meta will increase. As they learn how to play their deck against different popular decks their ability to win should become higher. To include this in the model the experience is included which is the square root of the number of games played multiplied with the experience factor which is the same for all players. In the examples here the factor is set to 20 which means that someone that played 100 games has an sqrt(10) * 20 ELO bonus when playing. While this factor was set arbitrarily, a 200 ELO bonus is a significant improvement and likely higher than you would expect in reality.

Setting up the GwentModel

The Mesa model here is simple, we create a number of N agents, a scheduler that will activate all the agents each step in random order and a DataCollector that will store all desired properties, for all agents each step so the history of those properties during the simulation can be stored and analysed later on.

class GwentModel(Model):
def __init__(self, N):
self.num_agents = N
self.schedule = RandomActivation(self)

for i in range(self.num_agents):
a = GwentAgent(i, self)

self.datacollector = DataCollector(
agent_reporters={
"Peak MMR": "peak_mmr",
"Current MMR": "current_mmr",
"Win Rate": "win_rate",
"Games Played": "games_played",
"Games Won": "wins",
"elo": "elo_level",
"elo_xp": "elo_experience",
}
)

def step(self):
self.datacollector.collect(self)
self.schedule.step()


Running the Model

With a few lines of code we can create a model with 8000 agents that will play for 100 steps. Here the tqdm module is used to create a progress bar for our simulation and estimated time. On a single core (Ryzen 7 3700X) it takes 20-30 minutes to go through the entire simulation (finding opponents in the correct range being the slowest step). So if you start this, grab a coffee or a snack, it will take some time !

from tqdm import tqdm

model = GwentModel(8000)
for i in tqdm(range(100)):
model.step()


Getting Data from the GwentModel

After the simulation (and that coffee or snack) is finished, we can extract data from the model to work with. There are two ways to do this, one is to grab data from the DataCollector included in the model. Which contains the state of all agents at all steps.

time_df = model.datacollector.get_agent_vars_dataframe()
time_df.to_csv(f"./data/simulation_steps_experience_factor_{experience_factor}.csv")

Peak MMR Current MMR Win Rate Games Played Games Won elo elo_xp
Step AgentID
0 0 2400.0 2400.0 NaN 0 0 1341.285714 1341.285714
1 2400.0 2400.0 NaN 0 0 1656.714286 1656.714286
2 2400.0 2400.0 NaN 0 0 1625.571429 1625.571429
3 2400.0 2400.0 NaN 0 0 1329.285714 1329.285714
4 2400.0 2400.0 NaN 0 0 1718.714286 1718.714286

While this is great to replay the model, it is overkill when you just want to examine the final state (or didn’t include the DataCollector). The code below will loop over all agents, grab certain properties and put them in a pandas dataframe. It will also put players in different bins based on skill and the number of games played.

df = pd.DataFrame(
{
"player": [f"Player {agent.unique_id}" for agent in model.schedule.agents],
"elo": [agent.elo_level for agent in model.schedule.agents],
"playrate": [agent.playrate for agent in model.schedule.agents],
"games played": [agent.games_played for agent in model.schedule.agents],
"current MMR": [agent.current_mmr for agent in model.schedule.agents],
"peak MMR": [agent.peak_mmr for agent in model.schedule.agents],
"win rate": [agent.win_rate for agent in model.schedule.agents],
}
)
df["rank"] = df["peak MMR"].rank(ascending=False)
df["elo bin"] = pd.cut(df["elo"], list(range(1100, 2800, 200)))
df["games played percentile"] = df["games played"].rank(pct=True)
df["games played bin"] = pd.cut(df["games played percentile"], [0, 0.25, 0.50, 0.75, 1])
df.to_excel(f"./data/final_data_experience_factor_{experience_factor}.xlsx")
df

player elo playrate games played current MMR peak MMR win rate rank elo bin games played percentile games played bin
Player 1 1284.142857 4 65 2344.332458 2408.421244 43.076923 5784.0 (1100, 1300] 0.179063 (0.0, 0.25]
Player 2 1299.142857 7 71 2357.819543 2400.000000 45.070423 7552.0 (1100, 1300] 0.243312 (0.0, 0.25]
Player 40 1238.142857 5 69 2329.815980 2406.859099 42.028986 6435.5 (1100, 1300] 0.221438 (0.0, 0.25]
Player 49 1291.142857 4 60 2363.915782 2400.000000 45.000000 7552.0 (1100, 1300] 0.128125 (0.0, 0.25]
Player 102 1212.142857 2 48 2349.541087 2413.726378 41.666667 5478.0 (1100, 1300] 0.028250 (0.0, 0.25]
Player 6289 2667.000000 18 139 2585.247562 2623.316703 59.712230 16.0 (2500, 2700] 0.957438 (0.75, 1.0]
Player 7196 2547.857143 18 130 2571.713937 2578.698543 59.230769 81.0 (2500, 2700] 0.876062 (0.75, 1.0]
Player 7523 2555.857143 12 120 2573.058829 2573.058829 60.000000 100.0 (2500, 2700] 0.778188 (0.75, 1.0]
Player 7604 2649.000000 17 134 2626.069166 2640.740116 61.940299 8.0 (2500, 2700] 0.915875 (0.75, 1.0]
Player 7794 2605.000000 13 120 2585.842820 2599.283118 60.833333 44.0 (2500, 2700] 0.778188 (0.75, 1.0]

Results

So using an Agent Based Model a very clean dataset, where the actual skill of each player is known and their final place on ladder. The Mesa library made it surprisingly easy to set up this system. With all data now included in the familiar pandas dataframe the actual analysis can begin. This however is reserved for the next post!