Measures of Concentration in BigMart Sales

Up to this point in our exploratory data analysis, we have examined location, variability, shape, and heterogeneity across the primary features of the BigMart Sales dataset. We now address a dimension of fundamental importance in economic, commercial, and management analytics: concentration.

The core premise is straightforward: knowing average sales per product or store is insufficient; we must also understand how total revenue is distributed across categories, store types, or individual outlets. Two scenarios can share identical total sales and averages yet exhibit completely different internal structures: in one, sales may be evenly distributed across all units, whereas in the other, a tiny fraction of categories or branches generates the vast majority of revenue.

From an EDA perspective, concentration measures and visual diagnostics answer critical business questions:

• What percentage of overall revenue is driven by a handful of product categories?
• Do outlets contribute evenly to overall sales volume, or do a few dominant stores dominate revenue generation?
• Does the revenue distribution follow a Pareto-style structure, where a small minority of entities accounts for most of the volume?

In this chapter, we develop descriptive metrics and graphical representations to evaluate sales concentration in BigMart Sales, culminating in a concentration mini-dashboard.

Environment Setup

We will work with the following BigMart dataset. For this section, we will use Python alongside pandas, numpy, plotly, and matplotlib.

import numpy as np
import pandas as pd
import plotly.express as px
import plotly.graph_objects as go

DATA_PATH = "../../data/bigmart_sales.csv"  
df = pd.read_csv(DATA_PATH)

df.head()

	Item_Identifier	Item_Weight	Item_Fat_Content	Item_Visibility	Item_Type	Item_MRP	Outlet_Identifier	Outlet_Establishment_Year	Outlet_Size	Outlet_Location_Type	Outlet_Type	Item_Outlet_Sales
0	FDA15	9.30	Low Fat	0.016047	Dairy	249.8092	OUT049	1999	Medium	Tier 1	Supermarket Type1	3735.1380
1	DRC01	5.92	Regular	0.019278	Soft Drinks	48.2692	OUT018	2009	Medium	Tier 3	Supermarket Type2	443.4228
2	FDN15	17.50	Low Fat	0.016760	Meat	141.6180	OUT049	1999	Medium	Tier 1	Supermarket Type1	2097.2700
3	FDX07	19.20	Regular	0.000000	Fruits and Vegetables	182.0950	OUT010	1998	NaN	Tier 3	Grocery Store	732.3800
4	NCD19	8.93	Low Fat	0.000000	Household	53.8614	OUT013	1987	High	Tier 3	Supermarket Type1	994.7052

As in previous sections, we ensure relevant categorical fields are standardized before aggregation.

# Basic standardization of categorical values in BigMart
if "Item_Fat_Content" in df.columns:
    df["Item_Fat_Content"] = (
        df["Item_Fat_Content"]
        .replace({
            "LF": "Low Fat",
            "low fat": "Low Fat",
            "reg": "Regular"
        })
    )

candidate_cols = [
    "Item_Identifier",
    "Item_Type",
    "Outlet_Identifier",
    "Outlet_Type",
    "Outlet_Location_Type",
    "Outlet_Size",
    "Item_Outlet_Sales",
]

existing = [c for c in candidate_cols if c in df.columns]
df[existing].head()

	Item_Identifier	Item_Type	Outlet_Identifier	Outlet_Type	Outlet_Location_Type	Outlet_Size	Item_Outlet_Sales
0	FDA15	Dairy	OUT049	Supermarket Type1	Tier 1	Medium	3735.1380
1	DRC01	Soft Drinks	OUT018	Supermarket Type2	Tier 3	Medium	443.4228
2	FDN15	Meat	OUT049	Supermarket Type1	Tier 1	Medium	2097.2700
3	FDX07	Fruits and Vegetables	OUT010	Grocery Store	Tier 3	NaN	732.3800
4	NCD19	Household	OUT013	Supermarket Type1	Tier 3	High	994.7052

Conceptual Foundations

Relative Share

Let \(x_i\) be the total sales generated by category or unit \(i\). Its relative share relative to total sales is defined as:

\[ p_i = \frac{x_i}{\sum_{j=1}^{n} x_j}. \]

Expressed as a percentage:

\[ p_i^{(\%)} = 100 \cdot p_i. \]

Cumulative Share

Sorting units in descending order by contribution, the cumulative share up to position \(k\) is given by:

\[ P_k = \sum_{i=1}^{k} p_{(i)}, \]

where \(p_{(i)}\) represents the share of the \(i\)-th ranked unit.

This metric forms the basis of Pareto analysis, determining how many categories account for a targeted percentage of revenue.

Concentration Curve

A concentration curve compares observed cumulative revenue against an idealized uniform distribution. When a few units account for most sales, the cumulative curve rises steeply at first before flattening, departing significantly from the diagonal line of equal distribution.

This visual representation serves as a conceptual foundation for advanced metrics like Lorenz curves and Gini indices.

Sales Concentration by Product Category

We begin by aggregating total sales across product types.

sales_by_item_type = (
    df.groupby("Item_Type", dropna=False)["Item_Outlet_Sales"]
      .sum()
      .sort_values(ascending=False)
      .reset_index()
)

sales_by_item_type["share"] = (
    sales_by_item_type["Item_Outlet_Sales"] /
    sales_by_item_type["Item_Outlet_Sales"].sum()
)

sales_by_item_type["cum_share"] = sales_by_item_type["share"].cumsum()
sales_by_item_type["share_pct"] = 100 * sales_by_item_type["share"]
sales_by_item_type["cum_share_pct"] = 100 * sales_by_item_type["cum_share"]

sales_by_item_type.head(10)

	Item_Type	Item_Outlet_Sales	share	cum_share	share_pct	cum_share_pct
0	Fruits and Vegetables	2.820060e+06	0.151688	0.151688	15.168849	15.168849
1	Snack Foods	2.732786e+06	0.146994	0.298683	14.699412	29.868261
2	Household	2.055494e+06	0.110563	0.409246	11.056317	40.924578
3	Frozen Foods	1.825735e+06	0.098205	0.507450	9.820464	50.745042
4	Dairy	1.522594e+06	0.081899	0.589349	8.189897	58.934939
5	Canned	1.444151e+06	0.077680	0.667029	7.767962	66.702901
6	Baking Goods	1.265525e+06	0.068071	0.735100	6.807148	73.510048
7	Health and Hygiene	1.045200e+06	0.056220	0.791321	5.622038	79.132086
8	Meat	9.175656e+05	0.049355	0.840676	4.935503	84.067590
9	Soft Drinks	8.928977e+05	0.048028	0.888704	4.802817	88.870407

Contribution Ranking

Ranking categories by total sales highlights their relative weight in overall enterprise revenue.

fig = px.bar(
    sales_by_item_type,
    x="Item_Type",
    y="share_pct",
    title="Sales Percentage Share by Product Type",
    labels={"share_pct": "Share (%)", "Item_Type": "Product Type"}
)
fig.update_layout(xaxis_tickangle=-45)
fig.show()

This visualization clarifies which product lines anchor total revenue and which represent minor contributors.

Pareto Chart

A Pareto chart combines individual contribution bars with a cumulative percentage line.

pareto_df = sales_by_item_type.copy()

fig = go.Figure()
fig.add_bar(
    x=pareto_df["Item_Type"],
    y=pareto_df["share_pct"],
    name="Individual Share (%)"
)
fig.add_scatter(
    x=pareto_df["Item_Type"],
    y=pareto_df["cum_share_pct"],
    mode="lines+markers",
    name="Cumulative Share (%)",
    yaxis="y2"
)

fig.update_layout(
    title="Pareto Chart of Sales by Product Type",
    xaxis=dict(title="Product Type"),
    yaxis=dict(title="Individual Share (%)"),
    yaxis2=dict(
        title="Cumulative Share (%)",
        overlaying="y",
        side="right",
        range=[0, 105]
    ),
    legend=dict(orientation="h"),
)
fig.update_xaxes(tickangle=-45)
fig.show()

Interpretation

When the cumulative line climbs rapidly across the first few categories, high concentration is present.

We quantify concentration using three standard threshold questions:

• How many categories generate 50% of total sales?
• How many categories generate 80% of total sales?
• What proportion of sales is concentrated within the top three categories?

def categories_to_reach_threshold(table, threshold=0.8):
    idx = np.argmax(table["cum_share"].to_numpy() >= threshold)
    return idx + 1

n50 = categories_to_reach_threshold(sales_by_item_type, 0.50)
n80 = categories_to_reach_threshold(sales_by_item_type, 0.80)

top3_share = sales_by_item_type["share"].head(3).sum() * 100

summary_concentration_item = pd.DataFrame({
    "Indicator": [
        "Categories needed to reach 50% of sales",
        "Categories needed to reach 80% of sales",
        "Cumulative share of top 3 categories (%)"
    ],
    "Value": [n50, n80, round(top3_share, 2)]
})

summary_concentration_item

	Indicator	Value
0	Categories needed to reach 50% of sales	4.00
1	Categories needed to reach 80% of sales	9.00
2	Cumulative share of top 3 categories (%)	40.92

Sales Concentration by Outlet

Evaluating sales concentration across individual stores reveals whether revenue is broadly distributed or heavily reliant on a few dominant outlets.

sales_by_outlet = (
    df.groupby("Outlet_Identifier", dropna=False)["Item_Outlet_Sales"]
      .sum()
      .sort_values(ascending=False)
      .reset_index()
)

sales_by_outlet["share"] = (
    sales_by_outlet["Item_Outlet_Sales"] /
    sales_by_outlet["Item_Outlet_Sales"].sum()
)
sales_by_outlet["cum_share"] = sales_by_outlet["share"].cumsum()
sales_by_outlet["share_pct"] = 100 * sales_by_outlet["share"]
sales_by_outlet["cum_share_pct"] = 100 * sales_by_outlet["cum_share"]

sales_by_outlet

	Outlet_Identifier	Item_Outlet_Sales	share	cum_share	share_pct	cum_share_pct
0	OUT027	3.453926e+06	0.185784	0.185784	18.578359	18.578359
1	OUT035	2.268123e+06	0.122000	0.307784	12.200030	30.778389
2	OUT049	2.183970e+06	0.117474	0.425258	11.747378	42.525768
3	OUT017	2.167465e+06	0.116586	0.541844	11.658602	54.184370
4	OUT013	2.142664e+06	0.115252	0.657096	11.525196	65.709565
5	OUT046	2.118395e+06	0.113947	0.771042	11.394658	77.104223
6	OUT045	2.036725e+06	0.109554	0.880596	10.955364	88.059587
7	OUT018	1.851823e+06	0.099608	0.980204	9.960789	98.020377
8	OUT010	1.883402e+05	0.010131	0.990334	1.013065	99.033442
9	OUT019	1.796941e+05	0.009666	1.000000	0.966558	100.000000

fig = go.Figure()
fig.add_bar(
    x=sales_by_outlet["Outlet_Identifier"],
    y=sales_by_outlet["share_pct"],
    name="Individual Share (%)"
)
fig.add_scatter(
    x=sales_by_outlet["Outlet_Identifier"],
    y=sales_by_outlet["cum_share_pct"],
    mode="lines+markers",
    name="Cumulative Share (%)",
    yaxis="y2"
)
fig.update_layout(
    title="Sales Concentration by Outlet",
    xaxis=dict(title="Outlet"),
    yaxis=dict(title="Individual Share (%)"),
    yaxis2=dict(
        title="Cumulative Share (%)",
        overlaying="y",
        side="right",
        range=[0, 105]
    ),
    legend=dict(orientation="h")
)
fig.show()

Analytical Commentary

Unlike category-level analysis, store-level concentration involves fewer entities, highlighting operational dependencies when a minority of outlets generates a major share of total revenue.

Concentration by Outlet Type

Aggregating sales across commercial store formats (Outlet_Type) provides strategic insights into revenue concentration across store models.

sales_by_outlet_type = (
    df.groupby("Outlet_Type", dropna=False)["Item_Outlet_Sales"]
      .sum()
      .sort_values(ascending=False)
      .reset_index()
)

sales_by_outlet_type["share"] = (
    sales_by_outlet_type["Item_Outlet_Sales"] /
    sales_by_outlet_type["Item_Outlet_Sales"].sum()
)
sales_by_outlet_type["cum_share"] = sales_by_outlet_type["share"].cumsum()
sales_by_outlet_type["share_pct"] = 100 * sales_by_outlet_type["share"]
sales_by_outlet_type["cum_share_pct"] = 100 * sales_by_outlet_type["cum_share"]

sales_by_outlet_type

	Outlet_Type	Item_Outlet_Sales	share	cum_share	share_pct	cum_share_pct
0	Supermarket Type1	1.291734e+07	0.694812	0.694812	69.481228	69.481228
1	Supermarket Type3	3.453926e+06	0.185784	0.880596	18.578359	88.059587
2	Supermarket Type2	1.851823e+06	0.099608	0.980204	9.960789	98.020377
3	Grocery Store	3.680343e+05	0.019796	1.000000	1.979623	100.000000

fig = px.bar(
    sales_by_outlet_type,
    x="Outlet_Type",
    y="share_pct",
    title="Sales Share by Outlet Type",
    labels={"share_pct": "Share (%)", "Outlet_Type": "Outlet Type"}
)
fig.update_layout(xaxis_tickangle=-20)
fig.show()

Simplified Concentration Curve

We construct a concentration curve by plotting cumulative population fraction against cumulative revenue fraction.

def concentration_curve(values):
    values = np.asarray(values, dtype=float)
    values = np.sort(values)
    cum_values = np.cumsum(values)
    cum_values = cum_values / cum_values[-1]
    cum_units = np.arange(1, len(values) + 1) / len(values)
    return cum_units, cum_values

x_units, y_conc = concentration_curve(sales_by_item_type["Item_Outlet_Sales"])

curve_df = pd.DataFrame({
    "Fraction_units": x_units,
    "Fraction_sales": y_conc
})

fig = go.Figure()
fig.add_scatter(
    x=curve_df["Fraction_units"],
    y=curve_df["Fraction_sales"],
    mode="lines",
    name="Concentration Curve"
)
fig.add_scatter(
    x=[0, 1],
    y=[0, 1],
    mode="lines",
    name="Uniform Distribution"
)
fig.update_layout(
    title="Sales Concentration Curve by Product Type",
    xaxis_title="Cumulative Fraction of Categories",
    yaxis_title="Cumulative Fraction of Sales"
)
fig.show()

Reading the Curve

Greater separation between the concentration curve and the 45-degree diagonal indicates higher concentration.

Concentration Summary Indicators

We consolidate key concentration findings across features into a single summary table.

top1_item = sales_by_item_type["share"].iloc[0] * 100
top5_item = sales_by_item_type["share"].head(5).sum() * 100

top1_outlet = sales_by_outlet["share"].iloc[0] * 100
top3_outlet = sales_by_outlet["share"].head(3).sum() * 100

concentration_summary = pd.DataFrame({
    "Domain": [
        "Products",
        "Products",
        "Products",
        "Outlets",
        "Outlets"
    ],
    "Indicator": [
        "Top category share (%)",
        "Top 5 cumulative share (%)",
        "Categories needed for 80% of sales",
        "Top outlet share (%)",
        "Top 3 outlets cumulative share (%)"
    ],
    "Value": [
        round(top1_item, 2),
        round(top5_item, 2),
        n80,
        round(top1_outlet, 2),
        round(top3_outlet, 2)
    ]
})

concentration_summary

	Domain	Indicator	Value
0	Products	Top category share (%)	15.17
1	Products	Top 5 cumulative share (%)	58.93
2	Products	Categories needed for 80% of sales	9.00
3	Outlets	Top outlet share (%)	18.58
4	Outlets	Top 3 outlets cumulative share (%)	42.53

Concentration Mini-Dashboard

We synthesize revenue concentration metrics into a high-level KPI dashboard.

Primary KPIs

total_sales = df["Item_Outlet_Sales"].sum()
n_item_types = df["Item_Type"].nunique() if "Item_Type" in df.columns else np.nan
n_outlets = df["Outlet_Identifier"].nunique() if "Outlet_Identifier" in df.columns else np.nan

dashboard_kpis = pd.DataFrame({
    "Metric": [
        "Total Sales",
        "Product Types",
        "Outlets",
        "Top 3 Categories Share (%)",
        "Top 3 Outlets Share (%)"
    ],
    "Value": [
        round(total_sales, 2),
        n_item_types,
        n_outlets,
        round(sales_by_item_type["share"].head(3).sum() * 100, 2),
        round(sales_by_outlet["share"].head(3).sum() * 100, 2)
    ]
})

dashboard_kpis

	Metric	Value
0	Total Sales	18591125.41
1	Product Types	16.00
2	Outlets	10.00
3	Top 3 Categories Share (%)	40.92
4	Top 3 Outlets Share (%)	42.53

Final Discussion

Concentration analysis complements location, dispersion, shape, and heterogeneity by revealing how aggregate totals divide among constituent units. In BigMart Sales, this dimension highlights operational reliance on top product categories and store formats.

Suggested Exercises

1. Build a Pareto chart for Outlet_Location_Type and compare its concentration against Outlet_Type.
2. Compute the sales percentage accumulated by the top 20% of product categories.
3. Repeat concentration calculations using item counts per category instead of total monetary sales, comparing both distributions.
4. Provide a business summary evaluating whether sales structure is diversified or concentrated.