In [38]:

obs = pd.read_csv("obs_matrix_newer_dataset.csv")
obs = obs.drop(['map_Cursed Hollow', 'allied_char_Gall', 'opposing_char_Gall', 'opposing_char_Zeratul', 'allied_char_Zeratul'], axis=1)

In [39]:

obs.head()

Out[39]:

	allied_avg_hero_level	allied_avg_mrr	allied_char_Artanis	allied_char_Auriel	...	opposing_char_Valla	opposing_char_Varian	outcome
0	13.0	1726.2	0.0	0.0	...	1.0	0.0	0
1	14.6	1616.8	0.0	0.0	...	0.0	0.0	1
2	14.4	2317.2	1.0	0.0	...	0.0	1.0	0
3	16.6	2068.8	0.0	0.0	...	0.0	0.0	1
4	13.4	2303.4	0.0	1.0	...	0.0	0.0	0

5 rows × 165 columns

In [40]:

obs.shape

Out[40]:

(238194, 165)

In [41]:

from statsmodels.discrete.discrete_model import Logit
from statsmodels.tools import add_constant

In [ ]:

In [43]:

def demean(s):
    return s - s.mean()


obs['allied_avg_mrr']        = demean(obs['allied_avg_mrr'])
obs['allied_avg_hero_level'] = demean(obs['allied_avg_hero_level'])
obs['opp_avg_hero_level']    = demean(obs['opp_avg_hero_level'])
obs['opp_avg_mrr']           = demean(obs['opp_avg_mrr'])


obs['allied_avg_mrr**2']          = obs['allied_avg_mrr']**2
obs['allied_avg_hero_level**2']   = obs['allied_avg_hero_level']**2
obs['opp_avg_hero_level**2']      = obs['opp_avg_hero_level']**2
obs['opp_avg_mrr**2']             = obs['opp_avg_mrr']**2
      

lg = Logit(obs['outcome'], add_constant(obs.drop('outcome', axis=1)))

In [44]:

results = lg.fit()

Optimization terminated successfully.
         Current function value: 0.668012
         Iterations 4

In [ ]:

In [45]:

results.summary()

Out[45]:

Logit Regression Results
Dep. Variable:	outcome	No. Observations:	238194
Model:	Logit	Df Residuals:	238025
Method:	MLE	Df Model:	168
Date:	Tue, 11 Sep 2018	Pseudo R-squ.:	0.03626
Time:	16:56:05	Log-Likelihood:	-1.5912e+05
converged:	True	LL-Null:	-1.6510e+05
		LLR p-value:	0.000

	coef	std err	z	P>\|z\|	[0.025	0.975]
const	-5.004e-13	0.169	-2.97e-12	1.000	-0.331	0.331
allied_avg_hero_level	0.0526	0.002	30.211	0.000	0.049	0.056
allied_avg_mrr	0.0013	2.77e-05	48.231	0.000	0.001	0.001
allied_char_Abathur	-0.1298	0.033	-3.958	0.000	-0.194	-0.066
allied_char_Alarak	-0.0221	0.029	-0.752	0.452	-0.080	0.036
allied_char_Alexstrasza	-0.0179	0.037	-0.477	0.633	-0.091	0.055
allied_char_Ana	0.1026	0.038	2.701	0.007	0.028	0.177
allied_char_Anubarak	0.0114	0.030	0.382	0.703	-0.047	0.070
allied_char_Artanis	0.0908	0.028	3.290	0.001	0.037	0.145
allied_char_Arthas	-0.0320	0.030	-1.076	0.282	-0.090	0.026
allied_char_Auriel	-0.0145	0.038	-0.379	0.705	-0.089	0.060
allied_char_Azmodan	-0.0072	0.027	-0.269	0.788	-0.059	0.045
allied_char_Blaze	-0.0923	0.030	-3.086	0.002	-0.151	-0.034
allied_char_Brightwing	0.0156	0.037	0.420	0.675	-0.057	0.089
allied_char_Cassia	0.2426	0.028	8.572	0.000	0.187	0.298
allied_char_Chen	-0.1356	0.048	-2.848	0.004	-0.229	-0.042
allied_char_Cho	0.2554	0.064	3.972	0.000	0.129	0.381
allied_char_Chromie	-0.1465	0.029	-4.997	0.000	-0.204	-0.089
allied_char_D.Va	-0.0254	0.037	-0.678	0.498	-0.099	0.048
allied_char_Deckard	0.0341	0.037	0.933	0.351	-0.038	0.106
allied_char_Dehaka	0.0745	0.028	2.690	0.007	0.020	0.129
allied_char_Diablo	-0.1135	0.027	-4.207	0.000	-0.166	-0.061
allied_char_E.T.C.	-0.0825	0.029	-2.856	0.004	-0.139	-0.026
allied_char_Falstad	-0.0256	0.028	-0.913	0.361	-0.081	0.029
allied_char_Fenix	0.2055	0.027	7.636	0.000	0.153	0.258
allied_char_Garrosh	-0.1943	0.029	-6.635	0.000	-0.252	-0.137
allied_char_Gazlowe	0.0634	0.037	1.709	0.087	-0.009	0.136
allied_char_Genji	-0.0493	0.027	-1.825	0.068	-0.102	0.004
allied_char_Greymane	-0.0589	0.029	-2.057	0.040	-0.115	-0.003
allied_char_Guldan	-0.0910	0.027	-3.363	0.001	-0.144	-0.038
allied_char_Hanzo	-0.3126	0.028	-10.985	0.000	-0.368	-0.257
allied_char_Illidan	-0.0249	0.035	-0.717	0.474	-0.093	0.043
allied_char_Jaina	0.0605	0.026	2.313	0.021	0.009	0.112
allied_char_Johanna	-0.0529	0.028	-1.917	0.055	-0.107	0.001
allied_char_Junkrat	-0.1786	0.031	-5.690	0.000	-0.240	-0.117
allied_char_Kaelthas	-0.1015	0.026	-3.832	0.000	-0.153	-0.050
allied_char_KelThuzad	0.0832	0.031	2.721	0.007	0.023	0.143
allied_char_Kerrigan	0.1571	0.034	4.593	0.000	0.090	0.224
allied_char_Kharazim	0.0454	0.038	1.202	0.230	-0.029	0.119
allied_char_Leoric	0.1254	0.030	4.128	0.000	0.066	0.185
allied_char_Li Li	0.0545	0.036	1.532	0.126	-0.015	0.124
allied_char_Li-Ming	-0.1840	0.026	-6.979	0.000	-0.236	-0.132
allied_char_Lt. Morales	-0.0605	0.039	-1.540	0.124	-0.138	0.016
allied_char_Lunara	0.0221	0.030	0.741	0.459	-0.036	0.081
allied_char_Lúcio	-0.0914	0.038	-2.426	0.015	-0.165	-0.018
allied_char_Maiev	-0.0208	0.036	-0.583	0.560	-0.091	0.049
allied_char_Malfurion	-0.0682	0.036	-1.900	0.057	-0.139	0.002
allied_char_Malthael	0.0655	0.033	2.015	0.044	0.002	0.129
allied_char_Medivh	-0.1845	0.039	-4.690	0.000	-0.262	-0.107
allied_char_Muradin	-0.0081	0.027	-0.302	0.763	-0.061	0.044
allied_char_Murky	0.1365	0.043	3.204	0.001	0.053	0.220
allied_char_Nazeebo	0.0181	0.027	0.678	0.498	-0.034	0.071
allied_char_Nova	-0.0953	0.037	-2.586	0.010	-0.167	-0.023
allied_char_Probius	0.1713	0.062	2.752	0.006	0.049	0.293
allied_char_Ragnaros	0.0026	0.032	0.082	0.935	-0.060	0.066
allied_char_Raynor	0.3884	0.026	14.951	0.000	0.337	0.439
allied_char_Rehgar	0.0866	0.036	2.389	0.017	0.016	0.158
allied_char_Rexxar	0.0933	0.044	2.134	0.033	0.008	0.179
allied_char_Samuro	0.1838	0.039	4.726	0.000	0.108	0.260
allied_char_Sgt. Hammer	0.1132	0.037	3.092	0.002	0.041	0.185
allied_char_Sonya	0.0615	0.027	2.267	0.023	0.008	0.115
allied_char_Stitches	-0.0741	0.028	-2.681	0.007	-0.128	-0.020
allied_char_Stukov	-0.0402	0.037	-1.101	0.271	-0.112	0.031
allied_char_Sylvanas	-0.0508	0.030	-1.667	0.096	-0.111	0.009
allied_char_Tassadar	-0.3643	0.045	-8.132	0.000	-0.452	-0.277
allied_char_The Butcher	0.0559	0.033	1.684	0.092	-0.009	0.121
allied_char_The Lost Vikings	0.0413	0.064	0.642	0.521	-0.085	0.167
allied_char_Thrall	0.0489	0.027	1.805	0.071	-0.004	0.102
allied_char_Tracer	-0.0342	0.031	-1.118	0.264	-0.094	0.026
allied_char_Tychus	-0.0568	0.030	-1.877	0.061	-0.116	0.003
allied_char_Tyrael	-0.0131	0.035	-0.369	0.712	-0.083	0.056
allied_char_Tyrande	-0.0780	0.035	-2.220	0.026	-0.147	-0.009
allied_char_Uther	-0.0353	0.038	-0.930	0.352	-0.110	0.039
allied_char_Valeera	-0.1088	0.039	-2.760	0.006	-0.186	-0.032
allied_char_Valla	-0.0462	0.028	-1.649	0.099	-0.101	0.009
allied_char_Varian	0.0215	0.026	0.821	0.412	-0.030	0.073
allied_char_Xul	0.0868	0.041	2.119	0.034	0.007	0.167
allied_char_Yrel	0.1498	0.028	5.360	0.000	0.095	0.205
allied_char_Zagara	0.1467	0.031	4.781	0.000	0.087	0.207
allied_char_Zarya	-0.0007	0.034	-0.020	0.984	-0.068	0.067
allied_char_Zuljin	0.0294	0.030	0.984	0.325	-0.029	0.088
map_Braxis Holdout	-9.53e-16	0.015	-6.53e-14	1.000	-0.029	0.029
map_Infernal Shrines	6.13e-16	0.014	4.39e-14	1.000	-0.027	0.027
map_Sky Temple	2.046e-15	0.013	1.52e-13	1.000	-0.026	0.026
map_Towers of Doom	1.782e-15	0.013	1.32e-13	1.000	-0.026	0.026
opp_avg_hero_level	-0.0526	0.002	-30.211	0.000	-0.056	-0.049
opp_avg_mrr	-0.0013	2.77e-05	-48.231	0.000	-0.001	-0.001
opposing_char_Abathur	0.1298	0.033	3.958	0.000	0.066	0.194
opposing_char_Alarak	0.0221	0.029	0.752	0.452	-0.036	0.080
opposing_char_Alexstrasza	0.0179	0.037	0.477	0.633	-0.055	0.091
opposing_char_Ana	-0.1026	0.038	-2.701	0.007	-0.177	-0.028
opposing_char_Anubarak	-0.0114	0.030	-0.382	0.703	-0.070	0.047
opposing_char_Artanis	-0.0908	0.028	-3.290	0.001	-0.145	-0.037
opposing_char_Arthas	0.0320	0.030	1.076	0.282	-0.026	0.090
opposing_char_Auriel	0.0145	0.038	0.379	0.705	-0.060	0.089
opposing_char_Azmodan	0.0072	0.027	0.269	0.788	-0.045	0.059
opposing_char_Blaze	0.0923	0.030	3.086	0.002	0.034	0.151
opposing_char_Brightwing	-0.0156	0.037	-0.420	0.675	-0.089	0.057
opposing_char_Cassia	-0.2426	0.028	-8.572	0.000	-0.298	-0.187
opposing_char_Chen	0.1356	0.048	2.848	0.004	0.042	0.229
opposing_char_Cho	-0.2554	0.064	-3.972	0.000	-0.381	-0.129
opposing_char_Chromie	0.1465	0.029	4.997	0.000	0.089	0.204
opposing_char_D.Va	0.0254	0.037	0.678	0.498	-0.048	0.099
opposing_char_Deckard	-0.0341	0.037	-0.933	0.351	-0.106	0.038
opposing_char_Dehaka	-0.0745	0.028	-2.690	0.007	-0.129	-0.020
opposing_char_Diablo	0.1135	0.027	4.207	0.000	0.061	0.166
opposing_char_E.T.C.	0.0825	0.029	2.856	0.004	0.026	0.139
opposing_char_Falstad	0.0256	0.028	0.913	0.361	-0.029	0.081
opposing_char_Fenix	-0.2055	0.027	-7.636	0.000	-0.258	-0.153
opposing_char_Garrosh	0.1943	0.029	6.635	0.000	0.137	0.252
opposing_char_Gazlowe	-0.0634	0.037	-1.709	0.087	-0.136	0.009
opposing_char_Genji	0.0493	0.027	1.825	0.068	-0.004	0.102
opposing_char_Greymane	0.0589	0.029	2.057	0.040	0.003	0.115
opposing_char_Guldan	0.0910	0.027	3.363	0.001	0.038	0.144
opposing_char_Hanzo	0.3126	0.028	10.985	0.000	0.257	0.368
opposing_char_Illidan	0.0249	0.035	0.717	0.474	-0.043	0.093
opposing_char_Jaina	-0.0605	0.026	-2.313	0.021	-0.112	-0.009
opposing_char_Johanna	0.0529	0.028	1.917	0.055	-0.001	0.107
opposing_char_Junkrat	0.1786	0.031	5.690	0.000	0.117	0.240
opposing_char_Kaelthas	0.1015	0.026	3.832	0.000	0.050	0.153
opposing_char_KelThuzad	-0.0832	0.031	-2.721	0.007	-0.143	-0.023
opposing_char_Kerrigan	-0.1571	0.034	-4.593	0.000	-0.224	-0.090
opposing_char_Kharazim	-0.0454	0.038	-1.202	0.230	-0.119	0.029
opposing_char_Leoric	-0.1254	0.030	-4.128	0.000	-0.185	-0.066
opposing_char_Li Li	-0.0545	0.036	-1.532	0.126	-0.124	0.015
opposing_char_Li-Ming	0.1840	0.026	6.979	0.000	0.132	0.236
opposing_char_Lt. Morales	0.0605	0.039	1.540	0.124	-0.016	0.138
opposing_char_Lunara	-0.0221	0.030	-0.741	0.459	-0.081	0.036
opposing_char_Lúcio	0.0914	0.038	2.426	0.015	0.018	0.165
opposing_char_Maiev	0.0208	0.036	0.583	0.560	-0.049	0.091
opposing_char_Malfurion	0.0682	0.036	1.900	0.057	-0.002	0.139
opposing_char_Malthael	-0.0655	0.033	-2.015	0.044	-0.129	-0.002
opposing_char_Medivh	0.1845	0.039	4.690	0.000	0.107	0.262
opposing_char_Muradin	0.0081	0.027	0.302	0.763	-0.044	0.061
opposing_char_Murky	-0.1365	0.043	-3.204	0.001	-0.220	-0.053
opposing_char_Nazeebo	-0.0181	0.027	-0.678	0.498	-0.071	0.034
opposing_char_Nova	0.0953	0.037	2.586	0.010	0.023	0.167
opposing_char_Probius	-0.1713	0.062	-2.752	0.006	-0.293	-0.049
opposing_char_Ragnaros	-0.0026	0.032	-0.082	0.935	-0.066	0.060
opposing_char_Raynor	-0.3884	0.026	-14.951	0.000	-0.439	-0.337
opposing_char_Rehgar	-0.0866	0.036	-2.389	0.017	-0.158	-0.016
opposing_char_Rexxar	-0.0933	0.044	-2.134	0.033	-0.179	-0.008
opposing_char_Samuro	-0.1838	0.039	-4.726	0.000	-0.260	-0.108
opposing_char_Sgt. Hammer	-0.1132	0.037	-3.092	0.002	-0.185	-0.041
opposing_char_Sonya	-0.0615	0.027	-2.267	0.023	-0.115	-0.008
opposing_char_Stitches	0.0741	0.028	2.681	0.007	0.020	0.128
opposing_char_Stukov	0.0402	0.037	1.101	0.271	-0.031	0.112
opposing_char_Sylvanas	0.0508	0.030	1.667	0.096	-0.009	0.111
opposing_char_Tassadar	0.3643	0.045	8.132	0.000	0.277	0.452
opposing_char_The Butcher	-0.0559	0.033	-1.684	0.092	-0.121	0.009
opposing_char_The Lost Vikings	-0.0413	0.064	-0.642	0.521	-0.167	0.085
opposing_char_Thrall	-0.0489	0.027	-1.805	0.071	-0.102	0.004
opposing_char_Tracer	0.0342	0.031	1.118	0.264	-0.026	0.094
opposing_char_Tychus	0.0568	0.030	1.877	0.061	-0.003	0.116
opposing_char_Tyrael	0.0131	0.035	0.369	0.712	-0.056	0.083
opposing_char_Tyrande	0.0780	0.035	2.220	0.026	0.009	0.147
opposing_char_Uther	0.0353	0.038	0.930	0.352	-0.039	0.110
opposing_char_Valeera	0.1088	0.039	2.760	0.006	0.032	0.186
opposing_char_Valla	0.0462	0.028	1.649	0.099	-0.009	0.101
opposing_char_Varian	-0.0215	0.026	-0.821	0.412	-0.073	0.030
opposing_char_Xul	-0.0868	0.041	-2.119	0.034	-0.167	-0.007
opposing_char_Yrel	-0.1498	0.028	-5.360	0.000	-0.205	-0.095
opposing_char_Zagara	-0.1467	0.031	-4.781	0.000	-0.207	-0.087
opposing_char_Zarya	0.0007	0.034	0.020	0.984	-0.067	0.068
opposing_char_Zuljin	-0.0294	0.030	-0.984	0.325	-0.088	0.029
allied_avg_mrr**2	3.066e-07	4.52e-08	6.784	0.000	2.18e-07	3.95e-07
allied_avg_hero_level**2	0.0002	0.000	0.468	0.640	-0.001	0.001
opp_avg_hero_level**2	-0.0002	0.000	-0.468	0.640	-0.001	0.001
opp_avg_mrr**2	-3.066e-07	4.52e-08	-6.784	0.000	-3.95e-07	-2.18e-07

In [46]:

x = results.params.filter(like='allied_char')

In [57]:

y = pd.Series({c:obs.loc[obs[c].astype(bool)]['outcome'].mean() for c in x.index})
y_std = pd.Series({c:obs.loc[obs[c].astype(bool)]['outcome'].std()/np.sqrt(obs[c].astype(bool).sum()) for c in x.index})

In [58]:

y_std

Out[58]:

allied_char_Abathur             0.005426
allied_char_Alarak              0.004501
allied_char_Alexstrasza         0.003930
allied_char_Ana                 0.004317
allied_char_Anubarak            0.004249
allied_char_Artanis             0.003510
allied_char_Arthas              0.004095
allied_char_Auriel              0.004372
allied_char_Azmodan             0.003114
allied_char_Blaze               0.004390
allied_char_Brightwing          0.003926
allied_char_Cassia              0.003930
allied_char_Chen                0.010016
allied_char_Cho                 0.010510
allied_char_Chromie             0.004225
allied_char_D.Va                0.007085
allied_char_Deckard             0.003400
allied_char_Dehaka              0.003521
allied_char_Diablo              0.002510
allied_char_E.T.C.              0.003601
allied_char_Falstad             0.003780
allied_char_Fenix               0.003235
allied_char_Garrosh             0.003781
allied_char_Gazlowe             0.007034
allied_char_Genji               0.003467
allied_char_Greymane            0.004101
allied_char_Guldan              0.003194
allied_char_Hanzo               0.003822
allied_char_Illidan             0.006329
allied_char_Jaina               0.002703
allied_char_Johanna             0.002820
allied_char_Junkrat             0.005079
allied_char_Kaelthas            0.002880
allied_char_KelThuzad           0.004766
allied_char_Kerrigan            0.006168
allied_char_Kharazim            0.004638
allied_char_Leoric              0.004614
allied_char_Li Li               0.002817
allied_char_Li-Ming             0.002857
allied_char_Lt. Morales         0.004911
allied_char_Lunara              0.004558
allied_char_Lúcio               0.004135
allied_char_Maiev               0.006647
allied_char_Malfurion           0.002918
allied_char_Malthael            0.005585
allied_char_Medivh              0.007731
allied_char_Muradin             0.002341
allied_char_Murky               0.008671
allied_char_Nazeebo             0.003126
allied_char_Nova                0.006993
allied_char_Probius             0.014002
allied_char_Ragnaros            0.005342
allied_char_Raynor              0.002663
allied_char_Rehgar              0.003247
allied_char_Rexxar              0.008937
allied_char_Samuro              0.007627
allied_char_Sgt. Hammer         0.006855
allied_char_Sonya               0.003321
allied_char_Stitches            0.002956
allied_char_Stukov              0.003439
allied_char_Sylvanas            0.004782
allied_char_Tassadar            0.008974
allied_char_The Butcher         0.005780
allied_char_The Lost Vikings    0.014610
allied_char_Thrall              0.003471
allied_char_Tracer              0.004903
allied_char_Tychus              0.004678
allied_char_Tyrael              0.006352
allied_char_Tyrande             0.006253
allied_char_Uther               0.004385
allied_char_Valeera             0.007837
allied_char_Valla               0.003769
allied_char_Varian              0.002628
allied_char_Xul                 0.008215
allied_char_Yrel                0.003548
allied_char_Zagara              0.004847
allied_char_Zarya               0.006100
allied_char_Zuljin              0.004572
dtype: float64

In [48]:

%matplotlib inline
from matplotlib import pyplot as plt
from IPython.display import set_matplotlib_formats
set_matplotlib_formats('retina')
plt.style.use('bmh')

f, ax = plt.subplots(1,1,figsize=(12,12))
ax.scatter(x, y)

for i, txt in enumerate(x.index):
    txt = txt.lstrip("allied_char_")
    ax.annotate(txt, (x[i]+0.005, y[i]), fontsize=9)
    
#ax.set_ylabel("<--- lower naive winrate | higher naive winrate --->")

plt.hlines(0.5, -0.5, 0.5, lw=1, color='gray')
plt.vlines(0.0, 0.38, 0.6, lw=1, color='gray')

plt.xlim(-0.5, 0.5)
plt.ylim(0.38, 0.6)

ax.text(-0.025, 0.59, 'higher naive win rate -->', style='italic', rotation=90, fontsize=13)
ax.text(-0.025, 0.44, '<-- lower naive win rate', style='italic', rotation=90, fontsize=13)
ax.text(0.22, 0.503, 'higher causal win rate -->', style='italic', fontsize=13)
ax.text(-0.465, 0.503, '<-- lower causal win rate', style='italic', fontsize=13)


plt.ylabel("Naive win rate")
plt.xlabel("Causal win rate")

plt.savefig("causal_v_naive.png", bbox_inches='tight')

In [49]:

pd.DataFrame({'naive': y, 'causal': x}).to_csv("20180710_results.csv")

In [37]:

f, ax = plt.subplots(1,1,figsize=(15,12))

yerr = results.bse.filter(like='allied_char')

r = pd.DataFrame({'param': x, 'error': 1.96*yerr})
r.index = [_.lstrip('allied_char_') for _ in r.index]

r.sort_values('param').plot.barh(y='param', ax=ax, color='#348ABD', xerr='error', lw=0.1)
plt.savefig("coefs.png", bbox_inches='tight')

In [22]:

x.sort_values().index[int(len(x)/2)]

Out[22]:

'allied_char_Zeratul'

In [ ]: