Day | WinningTeamID | LosingTeamID | WinningPoints | LosingPoints | WinningFouls | ... |
1          13             1              45                5               3
1          12             4              21                12              4

Day | Points | Fouls | ... |
1       21       4     ...
2       32       6     ...

df[df[WinningTeamID == 12] | [LosingTeamID == 12]]

| Day | Outcome | TeamID | Points | Fouls |
|   1 | Winning |     13 |     45 |     3 |
|   1 | Losing  |      1 |      5 |   NaN |
|   1 | Winning |     12 |     21 |     4 |
|   1 | Losing  |      4 |     12 |   NaN |

import numpy as np
import pandas as pd

df = pd.DataFrame({'Day': [1, 1], 'LosingPoints': [5, 12], 'LosingTeamID': [1, 4], 'WinningFouls': [3, 4], 'WinningPoints': [45, 21], 'WinningTeamID': [13, 12]})
df = df.set_index(['Day'])
columns = df.columns.to_series().str.extract(r'^(Losing|Winning)?(.*)', expand=True)
columns = pd.MultiIndex.from_arrays([columns[col] for col in columns],
                                    names=['Outcome', None])
df.columns = columns
df = df.stack(level='Outcome').reset_index()
print(df)

Day  Outcome  Fouls  Points  TeamID
0    1   Losing    NaN       5       1
1    1  Winning    3.0      45      13
2    1   Losing    NaN      12       4
3    1  Winning    4.0      21      12

print(df.loc[df['TeamID']==12])
#    Day  Outcome  Fouls  Points  TeamID
# 3    1  Winning    4.0      21      12

In [26]: df.stack(level='Outcome')
Out[26]:
             Fouls  Points  TeamID
Day Outcome
1   Losing     NaN       5       1
    Winning    3.0      45      13
    Losing     NaN      12       4
    Winning    4.0      21      12

In [29]: df.stack(level='Outcome')
Out[29]:
           Day  Fouls  Points  TeamID
  Outcome
0 NaN      1.0    3.0      45      13
  Losing   NaN    NaN       5       1
  Winning  1.0    3.0      45      13
1 NaN      1.0    4.0      21      12
  Losing   NaN    NaN      12       4
  Winning  1.0    4.0      21      12

columns = df.columns.to_series().str.extract(r'^(Losing|Winning)?(.*)', expand=True)
columns = pd.MultiIndex.from_arrays([columns[col] for col in columns],
                                    names=['Outcome', None])

In [47]: df
Out[47]:
Outcome Losing        Winning
        Points TeamID   Fouls Points TeamID
Day
1            5      1       3     45     13
1           12      4       4     21     12

In [48]: df.stack(level="Outcome")
Out[48]:
             Fouls  Points  TeamID
Day Outcome
1   Losing     NaN       5       1
    Winning    3.0      45      13
    Losing     NaN      12       4
    Winning    4.0      21      12

df.query['WinningTeamID == 12 | LosingTeamID == 12']

df.query('columnX == 15 | columnY == 25')