机器学习|用机器学习预测谁将夺得世界杯冠军（附代码）

原文来自CSDN，公众号ID：CSDNnews，对其结构略作改动。

写在前面

2018 年 FIFA 世界杯即将拉开帷幕，全世界的球迷都热切地想要知道：谁将获得那梦寐以求的大力神杯？如果你不仅是个足球迷，而且也是高科技人员的话，我猜你肯定知道机器学习和人工智能也是目前的流行词。让我们结合两者来预测一下本届俄罗斯 FIFA 世界杯哪个国家将夺冠。

作者：Gerald Muriuki，经济、数据科学专家

译者：弯月，责编：郭芮

点击此处获取完整的代码：https://github.com/itsmuriuki/FIFA-2018-World-cup-predictions

译文

足球比赛涉及的因素非常繁多，我无法将所有因素都融入机器学习模型中。本文只是一个黑客想用数据尝试一些很酷的东西。本文的目标是：

用机器学习来预测谁将赢得2018 FIFA世界杯的冠军；
预测整个比赛的小组赛结果；
模拟四分之一决赛、半决赛以及决赛。

这些目标代表了独一无二的现实世界里机器学习的预测问题，并将解决机器学习中的各种任务：数据集成、特征建模和结果预测。

数据

我采用了两个来自 Kaggle 的数据集，我们将使用自 1930 年第一届世界杯以来所有参赛队的历史赛事结果。

FIFA 排名是于 90 年代创建的，因此这里缺失很大一部分数据，所以我们使用历史比赛记录。点击以下链接获取所有数据：

https://www.kaggle.com/martj42/international-football-results-from-1872-to-2017/data；

本文中主要使用的环境和工具有：jupyter notebook、numpy、pandas、seaborn、matplotlib 和 scikit-learn。

首先，我们要针对两个数据集做探索性分析，然后经过特征工程来选择与预测关联性最强的特征，还有数据处理，再选择一个机器学习模型，最后将模型配置到数据集上。

让我们开始动手吧

首先，导入所需的代码库，并将数据集加载到数据框中：

1 import pandas as pd
2 import numpy as np
3 import matplotlib.pyplot as plt
4 import seaborn as sns
5 import matplotlib.ticker as ticker
6 import matplotlib.ticker as plticker
7 from sklearn.model_selection import train_test_split
8 from sklearn.linear_model import LogisticRegression

导入数据集：

1 #load data 
2 world_cup = pd.read_csv('C:CodingFIFA2018-World-cupdatasetsWorld Cup 2018 Dataset.csv')
3 results = pd.read_csv('C:/Coding/FIFA2018-World-cup/datasets/results.csv')

下一步是加载数据集。通过调用 world_cup.head() 和 results.head() ，务必将两个数据集都加载到数据框中，如下所示：

探索性分析

在分析了两组数据集后，所得的数据集包含了以往赛事的数据——这个新的（所得的）数据集对于分析和预测将来的赛事非常有帮助。

探索性分析和特征工程：需要建立与机器学习模型相关的特征，在任何数据科学的项目中，这部分工作都是最耗时的。

现在我们把目标差异和结果列添加到结果数据集：

 1 #Adding goal difference and establishing who is the winner 
 2 winner = []
 3 for i in range (len(results['home_team'])):
 4     if results ['home_score'][i] > results['away_score'][i]:
 5         winner.append(results['home_team'][i])
 6     elif results['home_score'][i] < results ['away_score'][i]:
 7         winner.append(results['away_team'][i])
 8     else:
 9         winner.append('Draw')
10 results['winning_team'] = winner
11 
12 #adding goal difference column
13 results['goal_difference'] = np.absolute(results['home_score'] - results['away_score'])
14 
15 results.head()

检查一下新的结果数据框：

然后我们着手处理仅包含尼日利亚参加比赛的一组数据（这可以帮助我们集中找出哪些特征对一个国家有效，随后再扩展到参与世界杯的所有国家）：

1 #lets work with a subset of the data one that includes games played by Nigeria in a Nigeria dataframe
2 df = results[(results['home_team'] == 'Nigeria') | (results['away_team'] == 'Nigeria')]
3 nigeria = df.iloc[:]
4 nigeria.head()

第一届世界杯于 1930 年举行。我们为年份创建一列，并选择所有 1930 年之后举行的比赛：

1 #creating a column for year and the first world cup was held in 1930
2 year = []
3 for row in nigeria['date']:
4     year.append(int(row[:4]))
5 nigeria ['match_year']= year
6 nigeria_1930 = nigeria[nigeria.match_year >= 1930]
7 nigeria_1930.count()

现在我们可以用图形表示这些年来尼日利亚队最普遍的比赛结果：

#what is the common game outcome for nigeria visualisation
wins = []
for row in nigeria_1930['winning_team']:
    if row != 'Nigeria' and row != 'Draw':
        wins.append('Loss')
    else:
        wins.append(row)
winsdf= pd.DataFrame(wins, columns=[ 'Nigeria_Results'])

#plotting
fig, ax = plt.subplots(1)
fig.set_size_inches(10.7, 6.27)
sns.set(style='darkgrid')
sns.countplot(x='Nigeria_Results', data=winsdf)

每个参加世界杯的国家的胜率是非常有帮助性的指标，我们可以用它来预测此次比赛最可能的结果。

锁定参加世界杯的队伍

我们为2018世界杯所有参赛队伍创建一个数据框，然后从该数据框中进一步筛选出从 1930 年起参加世界杯的队伍，并去掉重复的队伍：

 1 #narrowing to team patcipating in the world cup
 2 worldcup_teams = ['Australia', ' Iran', 'Japan', 'Korea Republic', 
 3             'Saudi Arabia', 'Egypt', 'Morocco', 'Nigeria', 
 4             'Senegal', 'Tunisia', 'Costa Rica', 'Mexico', 
 5             'Panama', 'Argentina', 'Brazil', 'Colombia', 
 6             'Peru', 'Uruguay', 'Belgium', 'Croatia', 
 7             'Denmark', 'England', 'France', 'Germany', 
 8             'Iceland', 'Poland', 'Portugal', 'Russia', 
 9             'Serbia', 'Spain', 'Sweden', 'Switzerland']
10 df_teams_home = results[results['home_team'].isin(worldcup_teams)]
11 df_teams_away = results[results['away_team'].isin(worldcup_teams)]
12 df_teams = pd.concat((df_teams_home, df_teams_away))
13 df_teams.drop_duplicates()
14 df_teams.count()

为年份创建一列，去掉 1930 年之前的比赛，并去掉不会影响到比赛结果的数据列，比如 date（日期）、home_score（主场得分）、away_score（客场得分）、tournament（锦标赛）、city（城市）、country（国家）、goal_difference（目标差异）和 match_year（比赛年份）：

#create an year column to drop games before 1930
year = []
for row in df_teams['date']:
    year.append(int(row[:4]))
df_teams['match_year'] = year
df_teams_1930 = df_teams[df_teams.match_year >= 1930]
df_teams_1930.head()
#dropping columns that wll not affect matchoutcomes
df_teams_1930 = df_teams.drop(['date', 'home_score', 'away_score', 'tournament', 'city', 'country', 'goal_difference', 'match_year'], axis=1)
df_teams_1930.head()

为了简化模型的处理，我们修改一下预测标签。

如果主场队伍获胜，那么 winning_team（获胜队伍）一列显示“2”，如果平局则显示“1”，如果是客场队伍获胜则显示“0”：

1 #Building the model
2 #the prediction label: The winning_team column will show "2" if the home team has won, "1" if it was a tie, and "0" if the away team has won.
3 
4 df_teams_1930 = df_teams_1930.reset_index(drop=True)
5 df_teams_1930.loc[df_teams_1930.winning_team == df_teams_1930.home_team,'winning_team']=2
6 df_teams_1930.loc[df_teams_1930.winning_team == 'Draw', 'winning_team']=1
7 df_teams_1930.loc[df_teams_1930.winning_team == df_teams_1930.away_team, 'winning_team']=0
8 
9 df_teams_1930.head()

通过设置哑变量（dummy variables），我们将 home_team（主场队伍）和away _team（客场队伍）从分类变量转换成连续的输入。

这时可以使用 pandas 的 get_dummies() 函数，它会将分类列替换成一位有效值（one-hot，由数字‘1’和‘0’组成），以便将它们加载到 Scikit-learn 模型中。

接下来，我们将数据按照 70% 的训练数据集和 30% 的测试数据集分成 X 集和 Y 集：

 1 #convert home team and away team from categorical variables to continous inputs 
 2 # Get dummy variables
 3 final = pd.get_dummies(df_teams_1930, prefix=['home_team', 'away_team'], columns=['home_team', 'away_team'])
 4 
 5 # Separate X and y sets
 6 X = final.drop(['winning_team'], axis=1)
 7 y = final["winning_team"]
 8 y = y.astype('int')
 9 
10 # Separate train and test sets
11 X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.30, random_state=42)

这里我们将使用分类算法：逻辑回归。这个算法的工作原理是什么？该算法利用逻辑函数来预测概率，从而可以测量出分类因变量与一个或多个自变量之间的关系。具体来说就是累积的逻辑分布。

换句话说，逻辑回归可以针对一组可以影响到结果的既定数据集（统计值）尝试预测结果（赢或输）。

在实践中这种方法的工作原理是：使用上述的两套“数据集”和比赛的实际结果，一次输入一场比赛到算法中。然后模型就会学习输入的每条数据对比赛结果产生了积极的效果还是消极的效果，以及影响的程度。

经过充分的（好）数据的训练后，就可以得到能够预测未来结果的模型，而模型的好坏程度取决于输入的数据。

之后我们将这些数据传递到算法中：

logreg = LogisticRegression()
logreg.fit(X_train, y_train)
score = logreg.score(X_train, y_train)
score2 = logreg.score(X_test, y_test)

print("Training set accuracy: ", '%.3f'%(score))
print("Test set accuracy: ", '%.3f'%(score2))

Training set accuracy:  0.573
Test set accuracy:  0.551

我们的模型子训练数据集的正确率为 57%，在测试数据集上的正确率为 55%。虽然结果不是很好，但是我们先继续下一步。

接下来我们建立需要配置到模型的数据框。

首先我们加载 2018 年 4 月 FIFA 排名数据和小组赛分组状况的数据集。由于世界杯比赛中没有“主场”和“客场”，所以我们把 FIFA 排名靠前的队伍作为“喜爱”的比赛队伍，将他们放到“home_teams”（主场队伍）一列。然后我们根据每个队伍的排名将他们加入到新的预测数据集中。下一步是创建默认变量，并部署机器学习模型。

2018 年 4 月 FIFA 排名数据：https://us.soccerway.com/teams/rankings/fifa/?ICID=TN_03_05_01

小组赛分组状况的数据集：https://fixturedownload.com/results/fifa-world-cup-2018

#adding Fifa rankings
#the team which is positioned higher on the FIFA Ranking will be considered "favourite" for the match
#and therefore, will be positioned under the "home_teams" column
#since there are no "home" or "away" teams in World Cup games. 

# Loading new datasets
ranking = pd.read_csv('C:/Coding/FIFA2018-World-cup/datasets/fifa_rankings.csv') 
fixtures = pd.read_csv('C:/Coding/FIFA2018-World-cup/datasets/fixtures.csv')

# List for storing the group stage games
pred_set = []


# Create new columns with ranking position of each team
fixtures.insert(1, 'first_position', fixtures['Home Team'].map(ranking.set_index('Team')['Position']))
fixtures.insert(2, 'second_position', fixtures['Away Team'].map(ranking.set_index('Team')['Position']))

# We only need the group stage games, so we have to slice the dataset
fixtures = fixtures.iloc[:48, :]


# Loop to add teams to new prediction dataset based on the ranking position of each team
for index, row in fixtures.iterrows():
    if row['first_position'] < row['second_position']:
        pred_set.append({'home_team': row['Home Team'], 'away_team': row['Away Team'], 'winning_team': None})
    else:
        pred_set.append({'home_team': row['Away Team'], 'away_team': row['Home Team'], 'winning_team': None})
        
pred_set = pd.DataFrame(pred_set)
backup_pred_set = pred_set


# Get dummy variables and drop winning_team column
pred_set = pd.get_dummies(pred_set, prefix=['home_team', 'away_team'], columns=['home_team', 'away_team'])

# Add missing columns compared to the model's training dataset
missing_cols = set(final.columns) - set(pred_set.columns)
for c in missing_cols:
    pred_set[c] = 0
pred_set = pred_set[final.columns]

# Remove winning team column
pred_set = pred_set.drop(['winning_team'], axis=1)

pred_set.head()

比赛结果预测

首先，我们将模型部署到小组赛中：

#group matches 
predictions = logreg.predict(pred_set)
for i in range(fixtures.shape[0]):
    print(backup_pred_set.iloc[i, 1] + " and " + backup_pred_set.iloc[i, 0])
    if predictions[i] == 2:
        print("Winner: " + backup_pred_set.iloc[i, 1])
    elif predictions[i] == 1:
        print("Draw")
    elif predictions[i] == 0:
        print("Winner: " + backup_pred_set.iloc[i, 0])
    print('Probability of ' + backup_pred_set.iloc[i, 1] + ' winning: ', '%.3f'%(logreg.predict_proba(pred_set)[i][2]))
    print('Probability of Draw: ', '%.3f'%(logreg.predict_proba(pred_set)[i][1]))
    print('Probability of ' + backup_pred_set.iloc[i, 0] + ' winning: ', '%.3f'%(logreg.predict_proba(pred_set)[i][0]))
    print("")

Russia and Saudi Arabia
Winner: Russia
Probability of Russia winning:  0.667
Probability of Draw:  0.223
Probability of Saudi Arabia winning:  0.111

Uruguay and Egypt
Winner: Uruguay
Probability of Uruguay winning:  0.583
Probability of Draw:  0.352
Probability of Egypt winning:  0.065

Iran and Morocco
Draw
Probability of Iran winning:  0.217
Probability of Draw:  0.407
Probability of Morocco winning:  0.376

Portugal and Spain
Winner: Spain
Probability of Portugal winning:  0.302
Probability of Draw:  0.344
Probability of Spain winning:  0.354

France and Australia
Winner: France
Probability of France winning:  0.628
Probability of Draw:  0.227
Probability of Australia winning:  0.145

Argentina and Iceland
Winner: Argentina
Probability of Argentina winning:  0.803
Probability of Draw:  0.161
Probability of Iceland winning:  0.036

Peru and Denmark
Winner: Peru
Probability of Peru winning:  0.439
Probability of Draw:  0.171
Probability of Denmark winning:  0.391

Croatia and Nigeria
Winner: Croatia
Probability of Croatia winning:  0.590
Probability of Draw:  0.258
Probability of Nigeria winning:  0.152

Costa Rica and Serbia
Winner: Serbia
Probability of Costa Rica winning:  0.315
Probability of Draw:  0.324
Probability of Serbia winning:  0.361

Germany and Mexico
Winner: Germany
Probability of Germany winning:  0.567
Probability of Draw:  0.282
Probability of Mexico winning:  0.150

Brazil and Switzerland
Winner: Brazil
Probability of Brazil winning:  0.775
Probability of Draw:  0.138
Probability of Switzerland winning:  0.087

Sweden and Korea Republic
Winner: Sweden
Probability of Sweden winning:  0.503
Probability of Draw:  0.329
Probability of Korea Republic winning:  0.168

Belgium and Panama
Winner: Belgium
Probability of Belgium winning:  0.765
Probability of Draw:  0.145
Probability of Panama winning:  0.090

England and Tunisia
Winner: England
Probability of England winning:  0.649
Probability of Draw:  0.292
Probability of Tunisia winning:  0.059

Colombia and Japan
Winner: Colombia
Probability of Colombia winning:  0.511
Probability of Draw:  0.210
Probability of Japan winning:  0.280

Poland and Senegal
Winner: Poland
Probability of Poland winning:  0.612
Probability of Draw:  0.223
Probability of Senegal winning:  0.165

Egypt and Russia
Winner: Russia
Probability of Egypt winning:  0.225
Probability of Draw:  0.297
Probability of Russia winning:  0.478

Portugal and Morocco
Winner: Portugal
Probability of Portugal winning:  0.486
Probability of Draw:  0.377
Probability of Morocco winning:  0.138

Uruguay and Saudi Arabia
Winner: Uruguay
Probability of Uruguay winning:  0.668
Probability of Draw:  0.259
Probability of Saudi Arabia winning:  0.073

Spain and Iran
Winner: Spain
Probability of Spain winning:  0.695
Probability of Draw:  0.247
Probability of Iran winning:  0.058

Denmark and Australia
Winner: Denmark
Probability of Denmark winning:  0.551
Probability of Draw:  0.241
Probability of Australia winning:  0.207

France and Peru
Winner: France
Probability of France winning:  0.635
Probability of Draw:  0.215
Probability of Peru winning:  0.150

Argentina and Croatia
Winner: Argentina
Probability of Argentina winning:  0.599
Probability of Draw:  0.255
Probability of Croatia winning:  0.146

Brazil and Costa Rica
Winner: Brazil
Probability of Brazil winning:  0.800
Probability of Draw:  0.147
Probability of Costa Rica winning:  0.053

Iceland and Nigeria
Winner: Nigeria
Probability of Iceland winning:  0.278
Probability of Draw:  0.248
Probability of Nigeria winning:  0.474

Switzerland and Serbia
Winner: Switzerland
Probability of Switzerland winning:  0.402
Probability of Draw:  0.228
Probability of Serbia winning:  0.370

Belgium and Tunisia
Winner: Belgium
Probability of Belgium winning:  0.619
Probability of Draw:  0.253
Probability of Tunisia winning:  0.128

Mexico and Korea Republic
Winner: Mexico
Probability of Mexico winning:  0.504
Probability of Draw:  0.327
Probability of Korea Republic winning:  0.169

Germany and Sweden
Winner: Germany
Probability of Germany winning:  0.571
Probability of Draw:  0.228
Probability of Sweden winning:  0.201

England and Panama
Winner: England
Probability of England winning:  0.781
Probability of Draw:  0.178
Probability of Panama winning:  0.041

Senegal and Japan
Winner: Senegal
Probability of Senegal winning:  0.397
Probability of Draw:  0.278
Probability of Japan winning:  0.325

Poland and Colombia
Draw
Probability of Poland winning:  0.379
Probability of Draw:  0.391
Probability of Colombia winning:  0.230

Uruguay and Russia
Winner: Uruguay
Probability of Uruguay winning:  0.403
Probability of Draw:  0.388
Probability of Russia winning:  0.209

Egypt and Saudi Arabia
Winner: Egypt
Probability of Egypt winning:  0.544
Probability of Draw:  0.216
Probability of Saudi Arabia winning:  0.240

Portugal and Iran
Winner: Portugal
Probability of Portugal winning:  0.548
Probability of Draw:  0.353
Probability of Iran winning:  0.099

Spain and Morocco
Winner: Spain
Probability of Spain winning:  0.650
Probability of Draw:  0.267
Probability of Morocco winning:  0.083

France and Denmark
Winner: France
Probability of France winning:  0.621
Probability of Draw:  0.159
Probability of Denmark winning:  0.220

Peru and Australia
Winner: Peru
Probability of Peru winning:  0.463
Probability of Draw:  0.250
Probability of Australia winning:  0.288

Argentina and Nigeria
Winner: Argentina
Probability of Argentina winning:  0.708
Probability of Draw:  0.222
Probability of Nigeria winning:  0.070

Croatia and Iceland
Winner: Croatia
Probability of Croatia winning:  0.734
Probability of Draw:  0.185
Probability of Iceland winning:  0.080

Mexico and Sweden
Winner: Mexico
Probability of Mexico winning:  0.465
Probability of Draw:  0.264
Probability of Sweden winning:  0.271

Germany and Korea Republic
Winner: Germany
Probability of Germany winning:  0.598
Probability of Draw:  0.282
Probability of Korea Republic winning:  0.120

Brazil and Serbia
Winner: Brazil
Probability of Brazil winning:  0.714
Probability of Draw:  0.165
Probability of Serbia winning:  0.120

Switzerland and Costa Rica
Winner: Switzerland
Probability of Switzerland winning:  0.587
Probability of Draw:  0.213
Probability of Costa Rica winning:  0.200

Poland and Japan
Winner: Poland
Probability of Poland winning:  0.551
Probability of Draw:  0.242
Probability of Japan winning:  0.206

Colombia and Senegal
Winner: Colombia
Probability of Colombia winning:  0.577
Probability of Draw:  0.194
Probability of Senegal winning:  0.229

Tunisia and Panama
Winner: Tunisia
Probability of Tunisia winning:  0.631
Probability of Draw:  0.257
Probability of Panama winning:  0.113

Belgium and England
Winner: England
Probability of Belgium winning:  0.273
Probability of Draw:  0.235
Probability of England winning:  0.492

之后进行16强的模拟：

# List of tuples before 
group_16 = [('Uruguay', 'Portugal'),
            ('France', 'Croatia'),
            ('Brazil', 'Mexico'),
            ('England', 'Colombia'),
            ('Spain', 'Russia'),
            ('Argentina', 'Peru'),
            ('Germany', 'Switzerland'),
            ('Poland', 'Belgium')]
def clean_and_predict(matches, ranking, final, logreg):

    # Initialization of auxiliary list for data cleaning
    positions = []

    # Loop to retrieve each team's position according to FIFA ranking
    for match in matches:
        positions.append(ranking.loc[ranking['Team'] == match[0],'Position'].iloc[0])
        positions.append(ranking.loc[ranking['Team'] == match[1],'Position'].iloc[0])
    
    # Creating the DataFrame for prediction
    pred_set = []

    # Initializing iterators for while loop
    i = 0
    j = 0

    # 'i' will be the iterator for the 'positions' list, and 'j' for the list of matches (list of tuples)
    while i < len(positions):
        dict1 = {}

        # If position of first team is better, he will be the 'home' team, and vice-versa
        if positions[i] < positions[i + 1]:
            dict1.update({'home_team': matches[j][0], 'away_team': matches[j][1]})
        else:
            dict1.update({'home_team': matches[j][1], 'away_team': matches[j][0]})

        # Append updated dictionary to the list, that will later be converted into a DataFrame
        pred_set.append(dict1)
        i += 2
        j += 1

    # Convert list into DataFrame
    pred_set = pd.DataFrame(pred_set)
    backup_pred_set = pred_set

    # Get dummy variables and drop winning_team column
    pred_set = pd.get_dummies(pred_set, prefix=['home_team', 'away_team'], columns=['home_team', 'away_team'])

    # Add missing columns compared to the model's training dataset
    missing_cols2 = set(final.columns) - set(pred_set.columns)
    for c in missing_cols2:
        pred_set[c] = 0
    pred_set = pred_set[final.columns]

    # Remove winning team column
    pred_set = pred_set.drop(['winning_team'], axis=1)

    # Predict!
    predictions = logreg.predict(pred_set)
    for i in range(len(pred_set)):
        print(backup_pred_set.iloc[i, 1] + " and " + backup_pred_set.iloc[i, 0])
        if predictions[i] == 2:
            print("Winner: " + backup_pred_set.iloc[i, 1])
        elif predictions[i] == 1:
            print("Draw")
        elif predictions[i] == 0:
            print("Winner: " + backup_pred_set.iloc[i, 0])
        print('Probability of ' + backup_pred_set.iloc[i, 1] + ' winning: ' , '%.3f'%(logreg.predict_proba(pred_set)[i][2]))
        print('Probability of Draw: ', '%.3f'%(logreg.predict_proba(pred_set)[i][1])) 
        print('Probability of ' + backup_pred_set.iloc[i, 0] + ' winning: ', '%.3f'%(logreg.predict_proba(pred_set)[i][0]))
        print("")

clean_and_predict(group_16, ranking, final, logreg)

Portugal and Uruguay
Winner: Portugal
Probability of Portugal winning:  0.428
Probability of Draw:  0.285
Probability of Uruguay winning:  0.287

France and Croatia
Winner: France
Probability of France winning:  0.481
Probability of Draw:  0.252
Probability of Croatia winning:  0.267

Brazil and Mexico
Winner: Brazil
Probability of Brazil winning:  0.695
Probability of Draw:  0.209
Probability of Mexico winning:  0.096

England and Colombia
Winner: England
Probability of England winning:  0.516
Probability of Draw:  0.368
Probability of Colombia winning:  0.116

Spain and Russia
Winner: Spain
Probability of Spain winning:  0.529
Probability of Draw:  0.280
Probability of Russia winning:  0.191

Argentina and Peru
Winner: Argentina
Probability of Argentina winning:  0.713
Probability of Draw:  0.212
Probability of Peru winning:  0.075

Germany and Switzerland
Winner: Germany
Probability of Germany winning:  0.672
Probability of Draw:  0.192
Probability of Switzerland winning:  0.137

Belgium and Poland
Winner: Belgium
Probability of Belgium winning:  0.513
Probability of Draw:  0.202
Probability of Poland winning:  0.285

之后依次进行四分之一、半决赛、决赛的模拟：

四分之一：

# List of matches
quarters = [('Portugal', 'France'),
            ('Spain', 'Argentina'),
            ('Brazil', 'England'),
            ('Germany', 'Belgium')]
clean_and_predict(quarters, ranking, final, logreg)

Portugal and France
Winner: Portugal
Probability of Portugal winning:  0.437
Probability of Draw:  0.256
Probability of France winning:  0.307

Argentina and Spain
Winner: Argentina
Probability of Argentina winning:  0.518
Probability of Draw:  0.262
Probability of Spain winning:  0.220

Brazil and England
Winner: Brazil
Probability of Brazil winning:  0.525
Probability of Draw:  0.216
Probability of England winning:  0.260

Germany and Belgium
Winner: Germany
Probability of Germany winning:  0.563
Probability of Draw:  0.269
Probability of Belgium winning:  0.167

半决赛：

# List of matches
semi = [('Portugal', 'Brazil'),
        ('Argentina', 'Germany')]
clean_and_predict(semi, ranking, final, logreg)

Brazil and Portugal
Winner: Brazil
Probability of Brazil winning:  0.705
Probability of Draw:  0.152
Probability of Portugal winning:  0.143

Germany and Argentina
Winner: Germany
Probability of Germany winning:  0.441
Probability of Draw:  0.264
Probability of Argentina winning:  0.295

决赛：

# Finals
finals = [('Brazil', 'Germany')]
clean_and_predict(finals, ranking, final, logreg)

Germany and Brazil
Winner: Brazil
Probability of Germany winning:  0.359
Probability of Draw:  0.220
Probability of Brazil winning:  0.421

写在最后

根据该模型，巴西将有可能获得本届世界杯的冠军。

进一步的研究和提高领域：

为提高数据集的质量，可以利用 FIFA 的比赛数据评估每个球员的水平；

混淆矩阵可以帮助我们分析模型预测的哪场有误；

我们可以尝试将多个模型组合在一起，提高预测准确度。