BUG: Series.rank(pct=True, method='dense').max() != 1 for repeated values

[proinsias]

Code Sample, a copy-pastable example if possible

import pandas as pd

df = pd.DataFrame(data=[1,2,3,3,3,3,4,4,4,5,5,5], columns=['abc'], ).sort_values('abc')
df['Rank'] = df['abc'].rank(method='dense')
df['Rank_Pct']= df['abc'].rank(pct=True, method='dense', )
df['Rank_Pct_Manual']= df['Rank'] / df['Rank'].max()

df.head()

Output:

    abc  Rank  Rank_Pct  Rank_Pct_Manual
0     1   1.0  0.083333              0.2
1     2   2.0  0.166667              0.4
2     3   3.0  0.250000              0.6
3     3   3.0  0.250000              0.6
4     3   3.0  0.250000              0.6
5     3   3.0  0.250000              0.6
6     4   4.0  0.333333              0.8
7     4   4.0  0.333333              0.8
8     4   4.0  0.333333              0.8
9     5   5.0  0.416667              1.0
10    5   5.0  0.416667              1.0
11    5   5.0  0.416667              1.0

Problem description

If you chose both the pct=True and method='dense' options of Series.rank, you don't get the expected maximum percentile of 1 if there are repeated values in the Series. This is because the function (e.g., rank_1d_float64()) always divides by the total number of elements in the Series. But in the case of the dense method, we should divide by the maximum rank value.

I'm working on a PR now.

Expected Output

I would expect the values of Rank_Pct and Rank_Pct_Manual to be the same, and that the maximum of both should be 1.

    abc  Rank  Rank_Pct  Rank_Pct_Manual
0     1   1.0       0.2              0.2
1     2   2.0       0.4              0.4
2     3   3.0       0.6              0.6
3     3   3.0       0.6              0.6
4     3   3.0       0.6              0.6
5     3   3.0       0.6              0.6
6     4   4.0       0.8              0.8
7     4   4.0       0.8              0.8
8     4   4.0       0.8              0.8
9     5   5.0       1.0              1.0
10    5   5.0       1.0              1.0
11    5   5.0       1.0              1.0

Output of pd.show_versions()

commit: None
python: 3.6.3.final.0
python-bits: 64
OS: Darwin
OS-release: 16.7.0
machine: x86_64
processor: i386
byteorder: little
LC_ALL: None
LANG: en_US.UTF-8
LOCALE: en_US.UTF-8

pandas: 0.21.0
pytest: 3.2.3
pip: 9.0.1
setuptools: 36.3.0
Cython: None
numpy: 1.13.3
scipy: 0.19.1
pyarrow: 0.7.1
xarray: None
IPython: 6.2.1
sphinx: None
patsy: None
dateutil: 2.6.1
pytz: 2017.3
blosc: None
bottleneck: None
tables: None
numexpr: None
feather: None
matplotlib: 2.0.2
openpyxl: None
xlrd: None
xlwt: None
xlsxwriter: None
lxml: None
bs4: None
html5lib: 0.999999999
sqlalchemy: 1.1.15
pymysql: None
psycopg2: None
jinja2: 2.9.6
s3fs: None
fastparquet: None
pandas_gbq: None
pandas_datareader: None

[jreback]

duplicate of #15630.