%%capture
%config InlineBackend.figure_format = 'svg'
%matplotlib inline
import scipy as sc, pandas as pd, seaborn as sns
import gpflow as gp
import numpy as np
import matplotlib.pyplot as plt

sns.set()

Results of the go rank survey¶

Following are some visualizations and tables based on the data gathered in the march survey here. The raw data can be accessed here in the form of a .csv file.

The plots were made by mapping kyu ranks to negative integers, so that 1d corresponds to 0 (i.e. 1k -> -1, 2d -> 1). The tables are based on OGS ranks. They range from 15k to 7d as that's where almost all the responses lie.

data = pd.read_csv('Go Rank Survey March 2018.csv')

data.head()

How many responses were given for each server.¶

data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 253 entries, 0 to 252
Data columns (total 14 columns):
Timestamp    253 non-null object
OGS          159 non-null object
KGS          170 non-null object
DGS          21 non-null object
IGS          73 non-null object
Foxwq        41 non-null object
Tygem        94 non-null object
WBaduk       33 non-null object
GoQuest      36 non-null float64
AGA          29 non-null object
EGF          92 non-null object
Korea        2 non-null object
China        8 non-null object
Japan        15 non-null object
dtypes: float64(1), object(13)
memory usage: 27.8+ KB

def mapping(x):
    try:
        t = x[-1]
    except:
        return x
    if t == 'k':
        n = -int(x[:-1])
    else:
        n = int(x[:-1])-1
    return n
X = data.iloc[:,1:].copy()
X = X.applymap(mapping)
X=X.iloc[:,((X.shape[0]-X.isna().sum())>5).values]
X.dropna().shape

(0, 12)

# outliers
X.drop([164,95,], inplace=True)

Pair-wise plotting of server ranks with linear regression¶

%%capture --no-display
sns.pairplot(X.iloc[:,((X.shape[0]-X.isna().sum())>5*3).values], diag_kind='kde', kind='reg');

<seaborn.axisgrid.PairGrid at 0x7ff0bcf85278>

def plot(m, X, Y, lo=-20, hi=10, xlabel='X', ylabel='Y', sigma=2):
    lo = X.min()-abs(X.min()*.5/2)
    hi = X.max()+abs(X.max()*.5)
    xx = np.linspace(lo, hi, 1000)[:,None]
    mean, var = m.predict_y(xx)
    p=plt.figure()#figsize=(12, 6))
    plt.plot(X, Y, 'kx', mew=2)
    plt.plot(xx, mean, 'b', lw=2)
    plt.fill_between(xx[:,0], mean[:,0] - sigma*np.sqrt(var[:,0]), mean[:,0] + sigma*np.sqrt(var[:,0]), color='blue', alpha=0.2)
    plt.xlim(lo, hi)
    plt.xlabel(xlabel)
    plt.ylabel(ylabel)
    return p
#plot(m, x.T[0], x.T[1])
#sns.regplot(x.T[0], x.T[1])

def get_ranks_on_server(rank_start=-15, rank_end=7, fro='OGS', to='Tygem', lo=-20, hi=10, k=gp.kernels.RBF, meanf=gp.mean_functions.Zero, prior=(10,1e9), sigma=2):
    x=X[[fro,to,]].dropna().values
    ranks = sc.arange(rank_start, rank_end)
    with gp.defer_build():
        m=gp.models.GPR(X=x.T[0].reshape(-1, 1), Y=x.T[1].reshape(-1, 1), kern=k(1), mean_function=meanf())
        m.kern.lengthscales.prior = gp.priors.Gaussian(*prior)
    m.compile()
    gp.train.ScipyOptimizer(tol=1e-7).minimize(m)
    print('\n'+to)
    print(m.kern.lengthscales)
    mean, var = m.predict_y(ranks[:,None])
    return mean,(mean[:,0] - sigma*np.sqrt(var[:,0]), mean[:,0] + sigma*np.sqrt(var[:,0])), plot(m, x.T[0], x.T[1], lo=lo, hi=hi, xlabel=fro, ylabel=to, sigma=sigma)

def fillna(a='OGS', b='KGS'):
    with gp.defer_build():
        m=gp.models.GPR(X=X[[a,b]].dropna()[a].values[:,None], Y=X[[a,b]].dropna()[b].values[:,None], kern=gp.kernels.RBF(1), mean_function=gp.mean_functions.Linear())
        #m.kern.lengthscales.prior = gp.priors.Gaussian(10,10)
    m.compile()
    gp.train.ScipyOptimizer().minimize(m)
    xx=X[X[a].notna()&X[b].isna()][a].values[:,None]
    yy=m.predict_y(xx)[0]
    print(yy.shape)
    X.loc[X[a].notna()&X[b].isna(), b] = yy.ravel()

%%capture
cols = sorted(X.columns, key=lambda x: X[x].count(), reverse=True)
for c in [x for x in sorted(X.columns, key=lambda x: X[x].count(), reverse=True) if x!='OGS']:
    #fillna('MIX',c)
    fillna(c,'OGS')

def n_to_rank(n):
    if n>500:
        return int(round(n))
    n=int(round(n))
    if n<0:
        return f'{abs(n)}k'
    else:
        return f'{abs(n+1)}d'

def n_to_rank_float(n):
    if n>500:
        return round(n,1)
    n=round(n,1)
    if n<0:
        return f'{abs(n)}k'
    else:
        return f'{abs(n+1)}d'

def get_rank_tables(against='KGS', lo=-15, hi=7, prior=(10,1e6)):
    meantable = pd.DataFrame()
    stdtable = pd.DataFrame()
    combinedtable = pd.DataFrame()
    for s in X.drop(columns=[against,]).columns:
        mean,ci,p = get_ranks_on_server(
            lo,
            hi,
            against,
            s,
            k=lambda x: gp.kernels.RBF(1),
            meanf=gp.mean_functions.Linear,
            prior=prior,
            sigma=1,
        )
        meantable.insert(loc=0, column=s, value=[f'{n_to_rank(mean[x][0])}' for x,_ in enumerate(mean)])
        stdtable.insert(loc=0, column=s, value=[f'{n_to_rank(ci[0][x])} - {n_to_rank(ci[1][x])}' for x,_ in enumerate(ci[0])])
        combinedtable.insert(loc=0, column=s, value=[f'{n_to_rank_float(mean[x][0])} ± {round(ci[1][x]-mean[x][0],1)}' for x,_ in enumerate(mean)])
    meantable.insert(loc=0, column=against, value=[f'{n_to_rank(x)}' for x in sc.arange(lo,hi)])
    stdtable.insert(loc=0, column=against, value=[f'{n_to_rank(x)}' for x in sc.arange(lo,hi)])
    combinedtable.insert(loc=0, column=against, value=[f'{n_to_rank(x)}' for x in sc.arange(lo,hi)])
    return meantable, stdtable, combinedtable

GP regressions used for the following rank tables¶

The following plots are mainly for visually demonstrating the imprecision of the following estimates.

%%capture --no-display
a='OGS'
mt1,st1,ct1=get_rank_tables(against=a, prior=(10,10-2))

cols = ['KGS','OGS','IGS','DGS','Tygem','Foxwq','WBaduk','GoQuest','EGF','AGA','Japan','China',]

A table of rounded mean ranks¶

mt1[cols].set_index(a)

A table of rounded +/- 1 standard deviation of ranks¶

st1[cols].set_index(a)

A combined table of mean and standard deviation of ranks¶

ct1[cols].set_index(a)

	Timestamp	OGS	KGS	DGS	IGS	Foxwq	Tygem	WBaduk	GoQuest	AGA	EGF	Korea	China	Japan
0	2018/03/25 10:04:02 AM GMT+3	1k	1k	NaN	1k	NaN	2d	NaN	NaN	NaN	NaN	NaN	NaN	NaN
1	2018/03/25 10:15:30 AM GMT+3	5k	4k	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2	2018/03/25 10:18:14 AM GMT+3	4k	3k	NaN	3k	NaN	1d	NaN	NaN	NaN	NaN	NaN	NaN	NaN
3	2018/03/25 10:18:50 AM GMT+3	14k	14k	NaN	14k	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
4	2018/03/25 10:31:37 AM GMT+3	NaN	5k	NaN	6k	3k	4k	NaN	NaN	NaN	NaN	NaN	NaN	NaN

	KGS	IGS	DGS	Tygem	Foxwq	WBaduk	GoQuest	EGF	AGA	Japan	China
OGS
15k	13k	16k	11k	15k	11k	17k	1312	15k	14k	5k	4k
14k	12k	15k	11k	15k	10k	16k	1350	14k	13k	4k	4k
13k	11k	14k	10k	15k	10k	15k	1387	13k	12k	4k	3k
12k	10k	13k	9k	14k	9k	14k	1425	12k	11k	3k	3k
11k	9k	12k	8k	13k	8k	12k	1464	11k	10k	3k	2k
10k	8k	11k	7k	11k	7k	11k	1502	10k	9k	2k	2k
9k	7k	10k	7k	9k	6k	10k	1542	9k	8k	2k	2k
8k	6k	9k	6k	7k	5k	9k	1582	9k	8k	1k	1k
7k	5k	7k	5k	6k	4k	8k	1622	8k	7k	1k	1k
6k	4k	6k	4k	4k	3k	6k	1664	7k	6k	1d	1d
5k	4k	5k	3k	3k	2k	5k	1706	6k	5k	1d	1d
4k	3k	4k	3k	1k	2k	4k	1749	5k	4k	2d	1d
3k	2k	3k	2k	1d	1k	3k	1792	4k	3k	2d	2d
2k	2k	2k	1k	2d	1d	1k	1836	3k	2k	2d	2d
1k	1k	1k	1d	2d	2d	1d	1881	2k	1k	2d	3d
1d	1d	1d	1d	3d	3d	2d	1926	1k	1d	3d	3d
2d	2d	2d	2d	4d	4d	3d	1972	1d	2d	5d	4d
3d	2d	3d	3d	5d	5d	5d	2018	2d	3d	6d	4d
4d	3d	4d	4d	6d	6d	6d	2064	3d	4d	6d	4d
5d	4d	5d	5d	7d	7d	7d	2110	3d	5d	7d	5d
6d	5d	6d	5d	7d	8d	8d	2156	4d	6d	7d	5d
7d	6d	8d	6d	8d	8d	9d	2202	5d	7d	8d	6d

	KGS	IGS	DGS	Tygem	Foxwq	WBaduk	GoQuest	EGF	AGA	Japan	China
OGS
15k	14k - 11k	18k - 14k	13k - 10k	17k - 13k	13k - 10k	20k - 15k	1217 - 1408	17k - 13k	17k - 12k	6k - 4k	5k - 3k
14k	13k - 11k	17k - 13k	12k - 9k	16k - 13k	12k - 9k	19k - 14k	1255 - 1444	16k - 12k	16k - 11k	5k - 3k	5k - 2k
13k	12k - 10k	16k - 12k	11k - 8k	16k - 13k	11k - 8k	17k - 13k	1294 - 1481	15k - 11k	15k - 10k	5k - 3k	5k - 2k
12k	11k - 9k	15k - 11k	11k - 7k	16k - 12k	10k - 7k	16k - 11k	1332 - 1518	14k - 10k	14k - 9k	4k - 2k	4k - 2k
11k	10k - 8k	14k - 9k	10k - 7k	15k - 11k	9k - 6k	15k - 10k	1371 - 1556	13k - 9k	13k - 8k	4k - 2k	4k - 1k
10k	9k - 7k	13k - 8k	9k - 6k	13k - 10k	8k - 5k	14k - 9k	1411 - 1594	12k - 8k	12k - 7k	3k - 1k	3k - 1k
9k	8k - 6k	12k - 7k	8k - 5k	11k - 7k	8k - 4k	12k - 8k	1451 - 1633	11k - 8k	11k - 6k	3k - 1k	3k - 1d
8k	7k - 5k	11k - 6k	8k - 4k	9k - 5k	7k - 3k	11k - 6k	1491 - 1673	10k - 7k	10k - 5k	2k - 1d	3k - 1d
7k	7k - 4k	10k - 5k	7k - 3k	7k - 4k	6k - 3k	10k - 5k	1532 - 1713	10k - 6k	9k - 4k	2k - 1d	2k - 2d
6k	6k - 3k	9k - 4k	6k - 3k	6k - 3k	5k - 2k	9k - 4k	1573 - 1754	9k - 5k	8k - 3k	1k - 2d	2k - 2d
5k	5k - 2k	8k - 3k	5k - 2k	4k - 1k	4k - 1k	7k - 3k	1616 - 1796	8k - 4k	7k - 2k	1d - 2d	1k - 2d
4k	4k - 2k	6k - 2k	4k - 1k	3k - 1d	3k - 1d	6k - 1k	1659 - 1839	7k - 3k	6k - 1k	1d - 3d	1k - 3d
3k	4k - 1k	5k - 1k	4k - 1d	1k - 3d	2k - 2d	5k - 1d	1702 - 1882	6k - 2k	5k - 1d	2d - 3d	1d - 3d
2k	3k - 1d	4k - 1d	3k - 2d	1d - 4d	1k - 3d	4k - 2d	1746 - 1926	5k - 1k	4k - 2d	2d - 3d	1d - 4d
1k	2k - 1d	3k - 2d	2k - 2d	1d - 4d	1d - 4d	3k - 3d	1791 - 1971	4k - 1d	3k - 3d	2d - 3d	1d - 4d
1d	1k - 2d	2k - 3d	1k - 3d	1d - 4d	1d - 5d	1k - 4d	1836 - 2016	3k - 2d	2k - 4d	3d - 4d	2d - 4d
2d	1k - 3d	1k - 4d	1d - 4d	2d - 5d	2d - 6d	1d - 6d	1882 - 2062	2k - 3d	1k - 5d	4d - 6d	2d - 5d
3d	1d - 4d	1d - 6d	1d - 5d	3d - 6d	3d - 6d	2d - 7d	1927 - 2109	1k - 4d	1d - 6d	5d - 7d	3d - 5d
4d	2d - 4d	2d - 7d	2d - 6d	4d - 7d	4d - 7d	3d - 8d	1972 - 2156	1d - 4d	2d - 7d	6d - 7d	3d - 6d
5d	3d - 5d	3d - 8d	3d - 6d	5d - 8d	5d - 8d	5d - 9d	2017 - 2203	2d - 5d	3d - 8d	6d - 8d	4d - 6d
6d	4d - 6d	4d - 9d	4d - 7d	6d - 9d	6d - 9d	6d - 11d	2061 - 2251	2d - 6d	4d - 9d	6d - 8d	4d - 7d
7d	4d - 7d	5d - 10d	5d - 8d	6d - 10d	7d - 10d	7d - 12d	2105 - 2299	3d - 7d	5d - 10d	7d - 9d	4d - 7d

	KGS	IGS	DGS	Tygem	Foxwq	WBaduk	GoQuest	EGF	AGA	Japan	China
OGS
15k	12.8k ± 1.3	16.0k ± 2.3	11.4k ± 1.7	14.8k ± 1.9	11.3k ± 1.6	17.4k ± 2.4	1312.3 ± 95.3	15.0k ± 1.9	14.4k ± 2.2	5.1k ± 1.0	4.2k ± 1.3
14k	11.8k ± 1.3	15.0k ± 2.3	10.6k ± 1.7	14.6k ± 1.8	10.4k ± 1.6	16.2k ± 2.4	1349.6 ± 94.5	14.1k ± 1.9	13.4k ± 2.2	4.4k ± 1.0	3.7k ± 1.3
13k	10.8k ± 1.3	13.9k ± 2.3	9.8k ± 1.7	14.6k ± 1.7	9.5k ± 1.6	14.9k ± 2.4	1387.3 ± 93.7	13.2k ± 1.9	12.4k ± 2.2	3.8k ± 0.9	3.3k ± 1.3
12k	9.8k ± 1.3	12.8k ± 2.3	9.0k ± 1.7	14.2k ± 1.7	8.6k ± 1.6	13.7k ± 2.4	1425.2 ± 93.0	12.2k ± 1.9	11.5k ± 2.2	3.2k ± 0.8	2.9k ± 1.3
11k	8.9k ± 1.3	11.7k ± 2.3	8.2k ± 1.7	13.1k ± 1.7	7.7k ± 1.6	12.5k ± 2.4	1463.6 ± 92.3	11.3k ± 1.9	10.5k ± 2.2	2.7k ± 0.9	2.5k ± 1.3
10k	7.9k ± 1.3	10.7k ± 2.3	7.4k ± 1.7	11.3k ± 1.7	6.9k ± 1.6	11.2k ± 2.4	1502.4 ± 91.8	10.4k ± 1.9	9.5k ± 2.2	2.2k ± 1.0	2.1k ± 1.3
9k	7.0k ± 1.3	9.6k ± 2.3	6.6k ± 1.7	9.0k ± 1.7	6.0k ± 1.6	10.0k ± 2.4	1541.8 ± 91.3	9.5k ± 1.9	8.5k ± 2.2	1.8k ± 1.0	1.6k ± 1.3
8k	6.1k ± 1.3	8.5k ± 2.3	5.9k ± 1.7	7.0k ± 1.7	5.1k ± 1.6	8.8k ± 2.4	1581.8 ± 90.9	8.6k ± 1.9	7.5k ± 2.2	1.3k ± 1.0	1.2k ± 1.3
7k	5.2k ± 1.3	7.4k ± 2.3	5.1k ± 1.7	5.5k ± 1.6	4.2k ± 1.6	7.6k ± 2.4	1622.5 ± 90.6	7.7k ± 1.9	6.5k ± 2.2	0.8k ± 1.0	0.8k ± 1.3
6k	4.4k ± 1.3	6.4k ± 2.3	4.3k ± 1.7	4.2k ± 1.6	3.3k ± 1.6	6.3k ± 2.4	1663.8 ± 90.3	6.7k ± 1.9	5.5k ± 2.2	0.3k ± 0.9	0.4k ± 1.3
5k	3.7k ± 1.3	5.3k ± 2.3	3.5k ± 1.7	2.8k ± 1.6	2.4k ± 1.6	5.1k ± 2.4	1705.9 ± 90.1	5.8k ± 1.9	4.5k ± 2.2	1.5d ± 0.8	1.1d ± 1.3
4k	3.0k ± 1.3	4.2k ± 2.3	2.7k ± 1.7	1.2k ± 1.6	1.5k ± 1.6	3.9k ± 2.4	1748.7 ± 90.0	4.9k ± 1.9	3.6k ± 2.2	2.2d ± 0.7	1.5d ± 1.3
3k	2.2k ± 1.3	3.1k ± 2.3	1.9k ± 1.7	1.2d ± 1.6	0.6k ± 1.6	2.6k ± 2.4	1792.2 ± 89.9	4.0k ± 1.9	2.6k ± 2.2	2.4d ± 0.8	1.9d ± 1.3
2k	1.6k ± 1.3	2.0k ± 2.3	1.1k ± 1.7	2.1d ± 1.6	1.3d ± 1.6	1.4k ± 2.4	1836.3 ± 89.8	3.1k ± 1.9	1.6k ± 2.2	2.3d ± 0.8	2.3d ± 1.3
1k	0.9k ± 1.3	1.0k ± 2.3	0.3k ± 1.7	2.5d ± 1.6	2.2d ± 1.6	0.2k ± 2.4	1881.0 ± 89.8	2.2k ± 1.9	0.6k ± 2.2	2.5d ± 0.8	2.7d ± 1.3
1d	0.2k ± 1.3	1.1d ± 2.3	1.5d ± 1.7	2.8d ± 1.6	3.1d ± 1.6	2.0d ± 2.4	1926.2 ± 90.0	1.2k ± 1.9	1.4d ± 2.2	3.5d ± 0.8	3.2d ± 1.3
2d	1.6d ± 1.3	2.2d ± 2.3	2.3d ± 1.7	3.6d ± 1.6	3.9d ± 1.6	3.3d ± 2.4	1971.9 ± 90.3	0.3k ± 1.9	2.4d ± 2.2	4.8d ± 0.8	3.6d ± 1.3
3d	2.3d ± 1.3	3.3d ± 2.3	3.1d ± 1.7	4.6d ± 1.6	4.8d ± 1.6	4.5d ± 2.4	2017.8 ± 91.0	1.6d ± 1.9	3.4d ± 2.2	5.8d ± 0.8	4.0d ± 1.3
4d	3.1d ± 1.3	4.3d ± 2.3	3.9d ± 1.7	5.8d ± 1.6	5.7d ± 1.6	5.7d ± 2.4	2063.9 ± 91.9	2.5d ± 1.9	4.3d ± 2.2	6.4d ± 0.7	4.4d ± 1.3
5d	3.9d ± 1.3	5.4d ± 2.3	4.7d ± 1.7	6.6d ± 1.6	6.6d ± 1.6	7.0d ± 2.4	2110.1 ± 93.1	3.4d ± 1.9	5.3d ± 2.2	6.8d ± 0.8	4.9d ± 1.3
6d	4.8d ± 1.3	6.5d ± 2.3	5.5d ± 1.7	7.3d ± 1.7	7.5d ± 1.6	8.2d ± 2.4	2156.1 ± 94.8	4.3d ± 1.9	6.3d ± 2.2	7.2d ± 0.9	5.3d ± 1.3
7d	5.7d ± 1.3	7.6d ± 2.3	6.3d ± 1.7	7.8d ± 1.7	8.4d ± 1.6	9.4d ± 2.4	2202.0 ± 96.8	5.3d ± 1.9	7.3d ± 2.2	7.6d ± 1.0	5.7d ± 1.3