In ‘The Executive Decision Series,’ I’m exploring key decision science concepts that empower leaders to make smarter, data-driven choices. Today’s focus: understanding how saturation curves optimize marketing spend by balancing growth opportunities and avoiding waste.

What Are Saturation Curves?

Saturation curves represent how marketing inputs, such as advertising spend, lead to diminishing returns as the spend increases. Initially, a small investment in marketing may generate a substantial response, but as investment continues, the incremental returns tend to decrease. Saturation curves provide a solution by modelling diminishing returns and helping businesses identify the optimal spend level for each channel.

This concept is vital for decision-making in marketing because it helps businesses allocate budgets more effectively, ensuring that resources aren’t wasted on oversaturated channels. These curves are commonly used optimize spend in Marketing Mix Modelling (MMM).

Why Saturation Curves Matter: Overspending Without Results

Imagine investing more and more into a marketing channel, only to realize later that additional spending didn’t generate additional value. This is a common pitfall in budget allocation when businesses assume a linear relationship between spend and response. This misconception can lead to overspending on oversaturated channels while underfunding those with untapped potential.

Failing to use saturation curves can lead to:

1. Overspending: wasting resources on channels that have already reached their saturation point.
2. Underinvestment: missing opportunities in channels that could generate higher returns with additional spend.

Using saturation curves ensures you’re allocating your budget strategically, maximizing the impact of every dollar spent.

Saturation vs. Linear Curves

Below is a visualization of a saturation curve, showing the diminishing returns of marketing spend. The curve starts steep, representing high returns on initial spend, and flattens out as it approaches the saturation point. The dashed vertical line marks the inflection point where the growth rate begins to slow. 

We can perhaps best understand the purpose of a saturation curve by comparing it with a linear curve:

• The linear curve assumes constant returns per dollar spent, which can mislead decision-makers into overestimating the effectiveness of high marketing spend.
• The saturation curve shows diminishing returns, with a steep rise initially and a plateau as it approaches saturation.

The graph above demonstrates these differences:

• Lower Left Corner: the saturation curve rises slowly at first — called a “lagged effect” — reflecting the delayed response at lower levels of spend.
• Inflection Point: the steep middle portion, marked by a dashed vertical line, shows the most efficient spend range and highlights the transition between high efficiency and diminishing returns.
• Upper Section: the flat part illustrates saturation, where additional spend has no impact.

The lagged effect at lower levels of spend reflects real-world scenarios where minimal investment may not immediately generate a noticeable response. Certain marketing channels or campaigns require a minimum investment to activate effectively. For instance, launching a paid search campaign may require a baseline spend to generate any measurable impact.

Example Spend Analysis:

In practice, we model historical spend data against a desired success event, or conversion, and plot each channel on a saturation curve, like bellow:

This example analysis illustrates spending that is saturated versus spending that shows a growth opportunity:

• Growth Opportunity Point: represented at lower spend levels, where additional investment could yield significant returns.
• Saturation Zone Points: represented at higher spend levels, where the curve has begun to flatten, indicating diminishing returns.

How Do Data Scientists Fit Saturation Curves?

Fitting a saturation curve is an iterative process. Data scientists test different parameter combinations to find the one that minimizes error, ensuring the curve closely aligns with observed data. Below, we illustrate this progression.

Progression of the Line of Best Fit

The following plots demonstrate how the line of best fit improves over five attempts:

1. Initial Guesses: early attempts underestimate or overestimate the curve’s growth rate and saturation point.
2. Refinement: each successive attempt improves the alignment between the curve and observed data by reducing errors.
3. Optimal Fit: the final model achieves the smallest error, accurately reflecting the real-world relationship.

Below are the five fits with progressively better parameters. Errors are shown in each legend, illustrating how they decrease with each refinement

Iteration 1:

Iteration 2:

Iteration 3:

Iteration 4:

Iteration 5:

Reducing Error:

The goal of the process above is to minimize residuals, or errors (differences between observed data and the model), ensuring the curve accurately reflects reality.

Error Iteration #1 (Initial Guess = Large Residuals):

Error Iteration #5 (Optimal Fit – Small Residuals):

How Do Saturation Curves Help Decision-Making?

Saturation curves answer critical questions for budget optimization:

• Where to stop spending: identify when additional investment stops adding value.
• Where to invest more: spot high-potential channels with room for growth.
• How to allocate budgets: optimize spending to maximize ROI and avoid waste.

By aligning spend with real-world dynamics, saturation curves help executives make confident, data-driven decisions that balance efficiency and impact.

Executive Takeaways

1. Pinpoint Efficiency: use saturation curves to identify the spend levels that maximize returns while avoiding waste.
2. Avoid Overspending: by identifying when additional investment in a channel no longer delivers significant returns, saturation curves prevent wasteful spending on oversaturated channels.
3. Identify Growth Opportunities: they reveal underfunded channels with high potential, helping you reallocate budgets to maximize ROI.
4. Make Data-Driven Decisions: saturation curves transform complex spend data into actionable insights, empowering you to more confidently allocate spend across marketing channels.