crosstab(): Frequency Tables

"After winning the toss, how often does each captain choose to bat or field?" "Do teams that field first win more?" Both are about two categorical columns and how often each combination happens. A table of those counts is called a cross-tabulation (or contingency table), and pandas builds it with pd.crosstab().

m = pd.DataFrame({
    "toss_winner":   ["MI", "CSK", "MI", "RCB", "CSK", "MI", "RCB", "CSK", "MI", "RCB"],
    "toss_decision": ["field", "bat", "field", "field", "field", "bat", "bat", "field", "field", "field"],
    "result":        ["won", "won", "lost", "won", "won", "lost", "lost", "won", "won", "lost"],
    "margin":        [6, 32, 4, 18, 7, 15, 9, 5, 8, 21],
})

Definition

pd.crosstab() computes a frequency table of two (or more) categorical variables: the unique values of one become the rows, the unique values of the other become the columns, and each cell holds how many rows have that combination (or, optionally, an aggregate of a third column).

• Frequency — a count of occurrences. By default every cell is a count.
• Contingency table — the statistics name for this table; it shows how one category's distribution depends on another.
• Specialised pivot table — crosstab is a pivot table whose default aggregation is counting, and it takes arrays/Series rather than column names.

Syntax

pd.crosstab(index, columns, values=None, aggfunc=None, margins=False,
            margins_name="All", normalize=False, rownames=None, colnames=None, dropna=True)

Example — toss winner vs decision

print(pd.crosstab(m["toss_winner"], m["toss_decision"], margins=True))

toss_decision  bat  field  All
toss_winner
CSK              1      2    3
MI               1      3    4
RCB              1      2    3
All              3      7   10

How it works: pandas counts every (toss_winner, toss_decision) pair: MI won the toss 4 times and fielded 3 of them. margins=True adds totals: 7 of 10 captains chose to field.

Example — normalize: shares instead of counts

print(pd.crosstab(m["toss_decision"], m["result"], normalize="index").round(2))

result         lost   won
toss_decision
bat            0.67  0.33
field          0.29  0.71

How it works: normalize="index" divides each cell by its row total, so each row sums to 1. Read it as: "Of the teams that chose to field, 71% won." Compare the options:

print(pd.crosstab(m["toss_decision"], m["result"], normalize="columns").round(2))
print(pd.crosstab(m["toss_decision"], m["result"], normalize="all"))

result         lost   won
toss_decision
bat             0.5  0.17
field           0.5  0.83
result         lost  won
toss_decision
bat             0.2  0.1
field           0.2  0.5

Example — aggregate a value instead of counting

print(pd.crosstab(m["toss_winner"], m["result"], values=m["margin"], aggfunc="mean"))

result       lost        won
toss_winner
CSK           NaN  14.666667
MI            9.5   7.000000
RCB          15.0  18.000000

With values + aggfunc, each cell is the average winning/losing margin. CSK never lost, so that cell is NaN.

Example — more than two variables, custom labels

print(pd.crosstab(m["toss_winner"], [m["toss_decision"], m["result"]]))
print(pd.crosstab(m["toss_winner"], m["result"], rownames=["Team"], colnames=["Outcome"],
                  margins=True, margins_name="Total"))

toss_decision  bat     field
result        lost won  lost won
toss_winner
CSK              0   1     0   2
MI               1   0     1   2
RCB              1   0     1   1
Outcome  lost  won  Total
Team
CSK         0    3      3
MI          2    2      4
RCB         2    1      3
Total       4    6     10

A list of Series gives MultiIndex columns. Note that crosstab fills impossible combinations with 0 counts (not NaN) when counting.

crosstab vs pivot_table vs groupby

All three can build the same count table:

pd.crosstab(m["toss_winner"], m["toss_decision"])
m.pivot_table(index="toss_winner", columns="toss_decision", aggfunc="size", fill_value=0)
m.groupby(["toss_winner", "toss_decision"]).size().unstack(fill_value=0)

toss_decision  bat  field
toss_winner
CSK              1      2
MI               1      3
RCB              1      2

Common mistakes

• ❌ pd.crosstab("toss_winner", "result") with column names. ✅ Pass Series: pd.crosstab(m["toss_winner"], m["result"]).
• ❌ Passing values without aggfunc (or vice versa) → ValueError. ✅ Always use them together.
• ❌ Using normalize=True when you wanted per-row percentages. ✅ normalize="index" for rows, "columns" for columns.
• ❌ Reading normalized numbers as percentages. ✅ They are fractions — multiply by 100.

Interview tip

Q: How would you check whether choosing to field after the toss leads to more wins? A: pd.crosstab(df["toss_decision"], df["result"], normalize="index") — each row then shows the win/loss share for that decision, so the two rows can be compared directly.