Multiple aggregated Counting in Pandas

This is also, a graph problem and you can use Networkx:

import networkx as nx
import pandas as pd
data = [["John","144","Smith","200"], ["Mia","220","John","144"],["Caleb","155","Smith","200"],["Smith","200","Jason","500"]]
data_frame = pd.DataFrame(data,columns = ["Name","ID","Manager_name","Manager_ID"])

#create a directed graph object using nx.DiGraph
G = nx.from_pandas_edgelist(data_frame, 
                            source='Name', 
                            target='Manager_name', 
                            create_using=nx.DiGraph())

#use nx.ancestors to get set of "ancenstor" nodes for each node in the directed graph
pd.DataFrame.from_dict({i:len(nx.ancestors(G,i)) for i in G.nodes()}, 
                       orient='index', 
                       columns=['Num of People reporting'])

Output:

       Num of People reporting
John                         1
Smith                        3
Mia                          0
Caleb                        0
Jason                        4

Draw newtorkx:

Scott Boston's Networkx solution is the preferred solution...

There are two solutions to this problem. The first one is a vectorized pandas type solution and should be fast over larger datasets, the second is pythonic and does not work well on the size of dataset the OP was looking for, the original df size is (223635,4).

1. PANDAS SOLUTION

This problem seeks to find out how many people each person in an organization manages, including subordinate's subordinates. This solution will create a dataframe by adding successive columns that are the managers of the previous columns, and then counting the occurance of each employee in that dataframe to determine the total number under them.

First we set up the input.

import pandas as pd
import numpy as np

data = [
    ["John", "144", "Smith", "200"],
    ["Mia", "220", "John", "144"],
    ["Caleb", "155", "Smith", "200"],
    ["Smith", "200", "Jason", "500"],
]
df = pd.DataFrame(data, columns=["Name", "SID", "Manager_name", "Manager_SID"])

df = df[["SID", "Manager_SID"]]

# shortening the columns for convenience
df.columns = ["1", "2"]

print(df)

     1    2
0  144  200
1  220  144
2  155  200
3  200  500

First the employees without subordinates must be counted and put into a seperate dictionary.

df_not_mngr = df.loc[~df['1'].isin(df['2']), '1']
non_mngr_dict = {str(key):0 for key in df_not_mngr.values}
non_mngr_dict

{'220': 0, '155': 0}

Next we will modify the dataframe by adding columns of managers of the previous column. The loop is stopped when there are no employees in the right most column

for i in range(2, 10):
    df = df.merge(
        df[["1", "2"]], how="left", left_on=str(i), right_on="1", suffixes=("_l", "_r")
    ).drop("1_r", axis=1)
    df.columns = [str(x) for x in range(1, i + 2)]
    if df.iloc[:, -1].isnull().all():
        break
    else:
        continue
print(df)

    1    2    3    4    5
0  144  200  500  NaN  NaN
1  220  144  200  500  NaN
2  155  200  500  NaN  NaN
3  200  500  NaN  NaN  NaN

All columns except the first columns are collapsed and each employee counted and added to a dictionary.

from collections import Counter

result = dict(Counter(df.iloc[:, 1:].values.flatten()))

The non manager dictionary is added to the result.

result.update(non_mngr_dict)
result

{'200': 3, '500': 4, nan: 8, '144': 1, '220': 0, '155': 0}

2. RECURSIVE PYTHONIC SOLUTION

I think this is probably way more pythonic than you were looking for. First I created a list 'all_sids' to make sure we capture all employees as not all are in each list.

import pandas as pd
import numpy as np

data = [
    ["John", "144", "Smith", "200"],
    ["Mia", "220", "John", "144"],
    ["Caleb", "155", "Smith", "200"],
    ["Smith", "200", "Jason", "500"],
]
df = pd.DataFrame(data, columns=["Name", "SID", "Manager_name", "Manager_SID"])

all_sids = pd.unique(df[['SID', 'Manager_SID']].values.ravel('K'))

Then create a pivot table.

dfp = df.pivot_table(values='Name', index='SID', columns='Manager_SID', aggfunc='count')

dfp

Manager_SID  144  200  500
SID                       
144          NaN  1.0  NaN
155          NaN  1.0  NaN
200          NaN  NaN  1.0
220          1.0  NaN  NaN

Then a function that will go through the pivot table to total up all the reports.

def count_mngrs(SID, count=0):
    if str(SID) not in dfp.columns:
        return count
    else:
        count += dfp[str(SID)].sum()
        sid_list = dfp[dfp[str(SID)].notnull()].index
        for sid in sid_list:
            count = count_mngrs(sid, count)
        return count

Call the function for each employee and print the results.

print('SID', '     Number of People Reporting')
for sid in all_sids: 
    print(sid, "     " , int(count_mngrs(sid)))

Results are below, sorry I was a bit lazy in putting the names with the sids.

SID      Number of People Reporting
144       1
220       0
155       0
200       3
500       4

Look forward to seeing a more pandas type solution!