游戏付费金额 —— 基于DC游戏数据（Brutal Age）

背景

“《野蛮时代》（Brutal Age）是一款风靡全球的SLG类型手机游戏。根据App Annie统计，《野蛮时代》在12个国家取得游戏畅销榜第1，在82个国家取得游戏畅销榜前10。准确了解每个玩家的价值，对游戏的广告投放策略和高效的运营活动（如精准的促销活动和礼包推荐）具有重要意义，有助于给玩家带来更个性化的体验。因此，我们希望能在玩家进入游戏的前期就对于他们的价值进行准确的估算。在这个竞赛里，想请各位选手利用玩家在游戏内前7日的行为数据，预测他们每个人在45日内的付费总金额”。

下面就针对这个游戏数据集进行分析和建模，因为比赛已经结束了，后面的分析只针对训练集样本。

数据一览

训练集样本总共2288007条数据，109个变量，主要涉及用户在注册7天内的游戏表现和付费信息。

import warnings
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.preprocessing import LabelEncoder, scale
from sklearn.metrics import mean_squared_error
from sklearn.decomposition import PCA
from sklearn.ensemble import GradientBoostingRegressor
from sklearn.model_selection import KFold

warnings.filterwarnings('ignore')
pd.set_option('display.max_columns', 150)
pd.set_option('display.max_rows', 150)
plt.style.use('ggplot')
%matplotlib inline

train = pd.read_csv('tap_fun_train.csv')
float_feat = train.select_dtypes(include='float64').columns.values
int_feat = train.select_dtypes(include='int64').columns.values
train[float_feat] = train[float_feat].astype(np.float32)
train[int_feat] = train[int_feat].astype(np.int32)
train.info()

RangeIndex: 2288007 entries, 0 to 2288006
Columns: 109 entries, user_id to prediction_pay_price
dtypes: float32(13), int32(95), object(1)
memory usage: 960.1+ MB

train.head()

	user_id	register_time	wood_add_value	wood_reduce_value	stone_add_value	stone_reduce_value	ivory_add_value	ivory_reduce_value	meat_add_value	meat_reduce_value	magic_add_value	magic_reduce_value	infantry_add_value	infantry_reduce_value	cavalry_add_value	cavalry_reduce_value	shaman_add_value	shaman_reduce_value	wound_infantry_add_value	wound_infantry_reduce_value	wound_cavalry_add_value	wound_cavalry_reduce_value	wound_shaman_add_value	wound_shaman_reduce_value	general_acceleration_add_value	general_acceleration_reduce_value	building_acceleration_add_value	building_acceleration_reduce_value	reaserch_acceleration_add_value	reaserch_acceleration_reduce_value	training_acceleration_add_value	training_acceleration_reduce_value	treatment_acceleraion_add_value	treatment_acceleration_reduce_value	bd_training_hut_level	bd_healing_lodge_level	bd_stronghold_level	bd_outpost_portal_level	bd_barrack_level	bd_healing_spring_level	bd_dolmen_level	bd_guest_cavern_level	bd_warehouse_level	bd_watchtower_level	bd_magic_coin_tree_level	bd_hall_of_war_level	bd_market_level	bd_hero_gacha_level	bd_hero_strengthen_level	bd_hero_pve_level	sr_scout_level	sr_training_speed_level	sr_infantry_tier_2_level	sr_cavalry_tier_2_level	sr_shaman_tier_2_level	sr_infantry_atk_level	sr_cavalry_atk_level	sr_shaman_atk_level	sr_infantry_tier_3_level	sr_cavalry_tier_3_level	sr_shaman_tier_3_level	sr_troop_defense_level	sr_infantry_def_level	sr_cavalry_def_level	sr_shaman_def_level	sr_infantry_hp_level	sr_cavalry_hp_level	sr_shaman_hp_level	sr_infantry_tier_4_level	sr_cavalry_tier_4_level	sr_shaman_tier_4_level	sr_troop_attack_level	sr_construction_speed_level	sr_hide_storage_level	sr_troop_consumption_level	sr_rss_a_prod_levell	sr_rss_b_prod_level	sr_rss_c_prod_level	sr_rss_d_prod_level	sr_rss_a_gather_level	sr_rss_b_gather_level	sr_rss_c_gather_level	sr_rss_d_gather_level	sr_troop_load_level	sr_rss_e_gather_level	sr_rss_e_prod_level	sr_outpost_durability_level	sr_outpost_tier_2_level	sr_healing_space_level	sr_gathering_hunter_buff_level	sr_healing_speed_level	sr_outpost_tier_3_level	sr_alliance_march_speed_level	sr_pvp_march_speed_level	sr_gathering_march_speed_level	sr_outpost_tier_4_level	sr_guest_troop_capacity_level	sr_march_size_level	sr_rss_help_bonus_level	pvp_battle_count	pvp_lanch_count	pvp_win_count	pve_battle_count	pve_lanch_count	pve_win_count	avg_online_minutes	pay_price	pay_count	prediction_pay_price
0	1	2018-02-02 19:47:15	20125.0	3700.0	0.0	0.0	0.0	0.0	16375.0	2000.0	0.0	0.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	50	0	50	0	0	0	0	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.333333	0.0	0	0.0
1	1593	2018-01-26 00:01:05	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.333333	0.0	0	0.0
2	1594	2018-01-26 00:01:58	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1.166667	0.0	0	0.0
3	1595	2018-01-26 00:02:13	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	3.166667	0.0	0	0.0
4	1596	2018-01-26 00:02:46	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2.333333	0.0	0	0.0

数据分析

付费金额分布

绝大部分用户的付费金额为0，45天内的人均付费金额为1.79元，即使是付费用户的付费金额也是集中在低金额区间，付费率情况后面和细看；最高金额高达3万以上，分布非常不均衡。

#整体金额分布，付费用户的金额分布
train['prediction_pay_price'].describe()

count    2.288007e+06
mean     1.793456e+00
std      8.844339e+01
min      0.000000e+00
25%      0.000000e+00
50%      0.000000e+00
75%      0.000000e+00
max      3.297781e+04
Name: prediction_pay_price, dtype: float64

fig, ax = plt.subplots(1, 2, figsize=(14, 6))
train['prediction_pay_price'].plot.hist(ax=ax[0])
train.loc[train['prediction_pay_price'] > 0, 'prediction_pay_price'].plot.hist(ax=ax[1])

付费金额和人数

注册后，

• 7天内的付费玩家41439人、付费总金额122万元
• 45天内的付费玩家45988人、付费总金额410万元，人数增长11%，金额增长却超过235%
• 新增加的付费玩家（7天内未付费，45天内有付费）4549人，只贡献了增长总额的6.5%，也就是说93.5%的增长来源于7天内就付费的玩家

#付费金额和人数，新增加人数贡献的金额
first_7_num = len(train[train['pay_price'] > 0])
first_45_num = len(train[train['prediction_pay_price'] > 0])
first_7_amt = train.loc[train['pay_price'] > 0, 'pay_price'].sum()
first_45_amt = train.loc[train['prediction_pay_price'] > 0, 'prediction_pay_price'].sum()
fig, ax = plt.subplots(1, 2, figsize=(14,6))
ax[0].bar(['first_7_num', 'first_45_num'], [first_7_num, first_45_num], color='lightblue')
ax[0].set_xlabel('First_7 VS First_45')
ax[0].set_ylabel('Number of Player Who Paid')
for i, j in zip([0, 1], [first_7_num, first_45_num]):
    ax[0].text(i, j+500, j, ha='center', fontsize=12)
ax[1].bar(['first_7_amt', 'first_45_amt'], [first_7_amt, first_45_amt], color='pink')
ax[1].set_xlabel('First_7 VS First_45')
ax[1].set_ylabel('Paid Amount')
for i, j in zip([0, 1], [first_7_amt, first_45_amt]):
    ax[1].text(i, j+10000, j, ha='center', fontsize=12)

train.loc[(train['pay_price'] == 0) & (train['prediction_pay_price'] > 0), 'prediction_pay_price'].sum()/(first_45_amt-first_7_amt)

0.06452517

付费率

7天内的付费率1.81%，再次付费的比例57%，45天内付费率2.01%。

#付费率，二次付费率
pay_rate_7 = len(train[train['pay_price'] > 0])/len(train)
pay_rate_45 = len(train[train['prediction_pay_price'] > 0])/len(train)
fig, ax = plt.subplots(figsize=(8,6))
ax.bar(['pay_rate_7', 'pay_rate_45'], [pay_rate_7, pay_rate_45], color='gold')
ax.set_xlabel('First_7 VS First_45')
ax.set_ylabel('Pay Rate')
for i, j in zip([0, 1], [pay_rate_7, pay_rate_45]):
    ax.text(i, j+0.0002, str(round(j*100, 2))+'%', ha='center', fontsize=12)

len(train[train['pay_count'] > 1])/len(train[train['pay_count'] > 0])

0.5747484253963657

人均付费金额（ARPU）

付费玩家的人均付费金额89元，45天内达到这个水平，很厉害了。

train.loc[train['prediction_pay_price'] > 0, 'prediction_pay_price'].sum()/len(train[train['prediction_pay_price'] > 0])

89.21306101591719

注册日期和人数

样本数据的时间从2018年1月26日到3月06日，在这段时间内每日的注册人数有隐隐的下降趋势；2月19日是一个峰值，注册人数达到117311。

train['register_time'] = pd.to_datetime(train['register_time'])
train['register_date'] = train['register_time'].dt.date

train.groupby('register_date')['prediction_pay_price'].count().plot(figsize=(12,6), color='grey')

在线时长

人均一周游戏时长为10分钟，最高时长超过2000分钟，分布集中在偏低区间；游戏时长和付费金额没有很明显的线性关系，也可能是离群点太多了。

train['avg_online_minutes'].describe()

count    2.288007e+06
mean     1.016729e+01
std      3.869698e+01
min      0.000000e+00
25%      5.000000e-01
50%      1.833333e+00
75%      4.833333e+00
max      2.049667e+03
Name: avg_online_minutes, dtype: float64

train['avg_online_minutes'].plot.hist()

特征工程

下面进行特征工程，会增加一些变量，也会删除部分变量，最后会对游戏数据进行标准化。

train['register_month'] = train['register_time'].dt.month
train['register_day'] = train['register_time'].dt.day
train['register_week'] = train['register_time'].dt.week
train['register_weekday'] = train['register_time'].dt.weekday

# 计算一下达到某种等级建筑的数量
def level_num(num):
    data = train.loc[:,'bd_training_hut_level':'bd_hero_pve_level'].applymap(lambda x: 1 if x > num else 0)
    result = data.apply(sum, axis=1)
    return result
train['over_0_level'] = level_num(0)
train['over_3_level'] = level_num(3)
train['over_5_level'] = level_num(5)
train['over_10_level'] = level_num(10) 

# 计算完成科研的数量
train['sr_done_num'] = train.loc[:,'sr_scout_level':'sr_rss_help_bonus_level'].apply(sum, axis=1)

train['pvp_lanch_rate'] = train['pvp_lanch_count']/train['pvp_battle_count']
train['pvp_win_rate'] = train['pvp_win_count']/train['pvp_battle_count']
train['pve_lanch_rate'] = train['pve_lanch_count']/train['pve_battle_count']
train['pve_win_rate'] = train['pve_win_count']/train['pve_battle_count']
train['pvp_pve'] = train['pvp_battle_count']+train['pve_battle_count']
train['pvp_pve_win_rate'] = (train['pvp_win_count']+train['pve_win_count'])/train['pvp_pve']
train.fillna(0, inplace=True)

# 找出方差为0或者非常小的变量，sklearn中有个类似的方法可以调用
def low_var(df):
    columns = df.columns.values
    col_list = []
    for column in columns:
        unique_num = df[column].nunique()
        if unique_num > 1:
            unique_rate = unique_num/len(df)
            first_two = list(df[column].value_counts())[0:2]
            first_two_rate = first_two[0]/first_two[1]
            if (unique_rate < 0.01) and (first_two_rate > 80):
                col_list.append(column)
        else:
            col_list.append(column)
    return col_list
feats = list(train.columns.values)
del feats[106:109]
low_var_feat = low_var(train[feats])

# 对游戏数据进行标准化，同时使用主成分分析
train.loc[:,'wood_add_value':'avg_online_minutes'] = train.loc[:,'wood_add_value':'avg_online_minutes'].apply(scale)
pca = PCA(n_components=20)
pca.fit(train.loc[:,'wood_add_value':'avg_online_minutes'])
plt.plot(range(0, 20), np.cumsum(pca.explained_variance_ratio_))
pca_df = pd.DataFrame(pca.transform(train.loc[:,'wood_add_value':'avg_online_minutes']), columns=['components_'+str(i) for i in range(20)])

train = pd.concat([train, pca_df], axis=1)
train.drop(low_var_feat, axis=1, inplace=True)
train.drop(['register_time', 'user_id'], axis=1, inplace=True)
train['register_date'] = LabelEncoder().fit_transform(train['register_date'])
train['pay_price'] = np.log(train['pay_price'] + 1)
train['prediction_pay_price'] = np.log(train['prediction_pay_price'] + 1)
float_feat = train.select_dtypes(include='float64').columns.values
int_feat = train.select_dtypes(include='int64').columns.values
train[float_feat] = train[float_feat].astype(np.float32)
train[int_feat] = train[int_feat].astype(np.int32)
del pca_df

建模

X = list(train.columns.values)
X.remove('prediction_pay_price')
y = 'prediction_pay_price'
gbm = GradientBoostingRegressor(verbose=1, random_state=123)
kfold = KFold(n_splits=4, shuffle=True, random_state=123)
rmse_list = []
feature_importance = pd.DataFrame()

for fold, (train_idx, test_idx) in enumerate(kfold.split(train)):
    print('='*50)
    print('fold {}'.format(fold))
    gbm.fit(train.iloc[train_idx][X], train.iloc[train_idx][y])
    pred = gbm.predict(train.iloc[test_idx][X])
#    rmse = np.sqrt(mean_squared_error(train.iloc[test_idx][y], pred))
    rmse = np.sqrt(mean_squared_error(np.exp(train.iloc[test_idx][y])-1, np.exp(pred)-1))
    rmse_list.append(rmse)
    print('rmse {}'.format(rmse))
    
    importance_df = pd.DataFrame()
    importance_df['feature'] = X
    importance_df['importance'] = gbm.feature_importances_
    importance_df['fold'] = fold + 1
    feature_importance = pd.concat([feature_importance, importance_df], axis=0)

==================================================
fold 0
      Iter       Train Loss   Remaining Time 
         1           0.1259           23.10m
         2           0.1065           22.28m
         3           0.0908           21.97m
         4           0.0779           21.70m
         5           0.0675           21.52m
         6           0.0591           21.26m
         7           0.0522           21.12m
         8           0.0466           20.85m
         9           0.0421           20.59m
        10           0.0383           20.32m
        20           0.0240           17.91m
        30           0.0219           15.75m
        40           0.0215           13.55m
        50           0.0213           11.28m
        60           0.0213            9.01m
        70           0.0212            6.75m
        80           0.0211            4.49m
        90           0.0211            2.24m
       100           0.0210            0.00s
rmse 76.81655221125601
==================================================
fold 1
      Iter       Train Loss   Remaining Time 
         1           0.1260           22.07m
         2           0.1066           21.79m
         3           0.0908           21.59m
         4           0.0780           21.68m
         5           0.0675           21.39m
         6           0.0591           21.11m
         7           0.0522           20.91m
         8           0.0466           20.71m
         9           0.0420           20.55m
        10           0.0383           20.36m
        20           0.0239           18.40m
        30           0.0218           16.33m
        40           0.0214           14.15m
        50           0.0213           11.87m
        60           0.0212            9.51m
        70           0.0211            7.14m
        80           0.0210            4.77m
        90           0.0210            2.39m
       100           0.0209            0.00s
rmse 80.4590172800173
==================================================
fold 2
      Iter       Train Loss   Remaining Time 
         1           0.1259           22.36m
         2           0.1065           22.10m
         3           0.0908           21.89m
         4           0.0780           21.69m
         5           0.0676           21.45m
         6           0.0591           21.29m
         7           0.0522           21.24m
         8           0.0466           21.17m
         9           0.0421           21.08m
        10           0.0384           20.96m
        20           0.0240           19.00m
        30           0.0219           16.78m
        40           0.0215           14.45m
        50           0.0213           12.06m
        60           0.0212            9.66m
        70           0.0212            7.26m
        80           0.0211            4.84m
        90           0.0210            2.42m
       100           0.0210            0.00s
rmse 53.03963382354496
==================================================
fold 3
      Iter       Train Loss   Remaining Time 
         1           0.1261           24.34m
         2           0.1067           24.01m
         3           0.0908           23.76m
         4           0.0780           23.52m
         5           0.0675           23.23m
         6           0.0590           22.94m
         7           0.0522           22.69m
         8           0.0465           22.43m
         9           0.0420           22.19m
        10           0.0382           21.93m
        20           0.0238           19.49m
        30           0.0217           17.07m
        40           0.0213           14.64m
        50           0.0211           12.19m
        60           0.0210            9.74m
        70           0.0210            7.24m
        80           0.0209            4.79m
        90           0.0209            2.37m
       100           0.0208            0.00s
rmse 49.03841446816272

print('通过交叉验证，训练集的均方根误差为{}'.format(np.mean(rmse_list)))

通过交叉验证，训练集的均方根误差为64.83840444574524

feature_importance.groupby('feature')['importance'].mean().sort_values(ascending=True).plot.barh(figsize=(8, 16))

结语

因为没有玩过这款游戏，对其中的游戏内容和指标还有理解不到位的地方，相信玩过游戏后应该会有新的理解，找到其它的重要特征。上文中的模型没有调参，模型优化后结果还能提升。同时，还可以根据游戏的参与度对用户进行不同类型的划分，观察高氪用户和普通用户在游戏属性上的差异等其它方面。