Beyond Linear: Navigating the Landscape of Multi-Touch Attribution

A Practical Guide to Understanding and Implementing Multi Touch Attribution

In today’s networked society, businesses engage their customer base across a vast array of marketing channels, from search engines and social media to messaging platforms and affiliate partnerships. With such a vast universe of channel at the disposal, it is highly critical to understand, interactions across which specific channel are the leading drivers for business conversions. Without this crucial insight, optimizing marketing spend and designing effective strategies becomes exceptionally difficult, often leading to inefficient resource allocation.

This challenge is particularly acute for organizations with diverse and complex marketing ecosystems, such as those engaged in heavy brand marketing, influencer collaborations, referral programs, and extensive CRM campaigns across numerous channels. For smaller organizations utilizing only one or two primary marketing channels, simpler attribution methods may suffice. However, for businesses where customer decision-making involves multiple interactions across various touchpoints, understanding channel efficacy is paramount. Attribution models address this challenge by identifying which customer touchpoints — be it a click, an impression, or an email — have an influence over driving conversions. It offers a structured way to trace the customer journey from first contact to purchase

For years, many teams and organizations have leaned on first-touch or last-touch models — simple frameworks that credit either the first or last customer interaction. These models are often favored due to their simplicity of calculation and ease of understanding, and they can still serve a basic purpose. However, a customer’s decision-making process typically involves multiple interactions across various channels. In such complex journeys, relying solely on single-touch attribution provides an inaccurate assessment of the customer experience, akin to cheering only at the start or finish line while ignoring everything in between. This simplification fails to reflect how customers truly engage, and how cross-channel interactions (like impressions or clicks) have influenced the customer to engage with the product/business. For advanced insights, such as calculating the impact on conversions if a specific channel were removed (removal effect) or deriving accurate Customer Acquisition Cost (CAC) versus the true value of each channel, more sophisticated approaches are required. This is precisely where multi-touch attribution models offer a marked advantage, providing a holistic view of channel collaboration essential for balanced strategic choices and optimized future marketing spend.

Multi Touch Attribution Framework

Multi-touch attribution recognizes that the customer journey is rarely linear. It is a rich tapestry woven from multiple interactions across diverse channels, spanned across different periods in time. Multi touch attribution models allocate credit across these different touchpoints, delivering a much more comprehensive and accurate interpretation of how marketing efforts collectively contribute to conversions.

The strength of multi-touch attribution is its flexibility. There isn’t a one-size-fits-all solution, as various models are designed to fit diverse business goals and the complexities of the customer journey. Consequently, there are multiple approaches through which multi-touch attribution is computed or derived, typically categorized as follows:

1. Linear Attribution: This framework assigns equal credit to every touchpoint in the customer journey and is ideal for acknowledging every marketing touchpoint equally and can serve as a baseline attribution framework.
2. Time Decay Attribution: Attributes more credit to touchpoints nearer the conversion event, with credit reducing for older touchpoints. This framework is best suited for businesses with shorter sales cycles or campaigns focused on immediate action.
3. Position-Based (U-Shaped) Attribution: Allocations robust credit to the earliest and latest touchpoints (typically 40% each), while the final 20% is divided between middle touches. It is ideal for highlighting both initial discovery and final conversion while still recognizing nurturing efforts of all touchpoints which occur in the middle of the journey.
4. W-Shaped Attribution: This framework gives substantial credit to the first touch, lead creation touch, and final conversion touch and is great for businesses with distinct lead generation stages within a longer sales funnel.
5. Markov Chain Attribution: This framework applies statistical modelling to calculate the probability of a conversion depending on the touchpoint sequence, the most effective routes and is ideal for intricate customer journeys, indicating which touchpoints are necessary for progressing users between stages.

Unpacking Markov Chain Attribution

While linear, time decay, and position-based models offer valuable insights, they often operate on predefined rules that may not be entirely able to encapsulate the complex, typically non-linear characteristics of actual customer journeys. This is where Markov Chain Attribution excels.

Instead of arbitrary rules, Markov Chain models leverage probability theory to understand how customers move between different marketing touchpoints (or “states”) on their way to a conversion. The core concept is the “memoryless property”: the probability of moving to the next state depends only on the current state, not on the entire history of how the customer arrived there. Think of it like a board game: your next move depends only on the square you’re currently on, not on all the squares you’ve landed on before.

Constructing the Markov Chain Model for Attribution

Implementing Markov Chain attribution involves several key steps:

1. Data Collection and Path Mapping: The first crucial step is to gather granular customer impressions data across all the channels. This involves recording every touchpoint (ad click, email open, website visit, social media interaction, etc.) for each individual customer, along with timestamps, from their first interaction until a conversion (or exit without conversion). These sequences of touchpoints are then mapped as “paths” or “chains.” You’ll also need to identify “Start” and “Conversion” (or “No Conversion/Exit”) states.
2. Calculating Transition Probabilities: For every possible pair of touchpoints (e.g., “Facebook Ad” to “Website Visit,” “Email” to “Conversion”), the model calculates the probability of a customer moving from the first to the second. the model estimates the chance of a customer transitioning from the first to the second. This is done by tallying up how many times each transition was made in all the customer journeys captured and dividing by how often the starting touchpoint was registered.
3. Constructing the Transition Matrix: These probabilities are subsequently arranged in a transition matrix, which is essentially a table displaying the likelihood of moving from any given state (marketing channel) to any other state, including the final “Conversion” or “Exit” states.
4. Constructing the Initial State Vector: This vector defines the initial probability distribution of customer journeys across the various marketing channels (transient states) at the beginning of their observed path. It represents the likelihood of a customer’s first interaction occurring within a specific channel.

• Uniform Distribution: Assigning an equal probability mass to each distinct marketing channel. This method is typically employed when historical data on initial touchpoints is unavailable or when a neutral starting assumption for customer entry is desired.
• Empirical Distribution: Deriving the initial state probabilities directly from the observed historical data. This involves calculating the actual frequency distribution of how customers began their journeys across different channels within the analyzed period.

5. Calculating Conversion Probabilities (Reaching Absorption State): Once the transition matrix is constructed, the Markov Chain model computes the probability of a customer ultimately reaching an absorbing state (e.g., “Conversion” or “Dropoff”) from any given marketing channel. This process involves mathematical operations on the transition matrix that effectively simulate the journey to its “steady state” or absorption, yielding the baseline total conversion probability.

FUNCTION markov_convergence(initial_vector, transition_matrix, convergence_tolerance, max_iterations):
    // This function calculates the steady-state probability distribution of a Markov chain.

    // 1. Initialize the current state vector
    current_vector = copy of initial_vector

    // 2. Iterate to find convergence (reaching a steady state)
    FOR each step from 1 to max_iterations:
        // a. Calculate the next state vector
        next_vector = dot_product(current_vector, transition_matrix)

        // b. Check for convergence: If the current and next vectors are very close
        IF next_vector is approximately equal to current_vector (within convergence_tolerance):
            // Stop iterating, as steady state has been reached
            BREAK loop

        // c. Update the current vector for the next iteration
        current_vector = next_vector

    // 3. Return the converged (steady-state) vector
    RETURN current_vector

END FUNCTION

6. The “Removal Effect”: The model calculates the “removal effect” for each channel. It mimics how the total conversion rate would change if a particular marketing channel is eliminated from every customer path. By comparing the total conversion probability with the channel to the total conversion probability without it, the model measures the distinct contribution of that channel. Channels with high removal effects are considered more essential to conversions. The removal effect for a channel X (REₓ) is calculated with the formula:

This formula quantifies the percentage decrease in the overall conversion probability when Channel X is removed.

FUNCTION removal_effect_with_convergence(channel_to_remove, original_transition_matrix, initial_probabilities_df, all_state_names):
    // This function calculates the steady-state probabilities after hypothetically removing a specific channel,
    // which is used to determine that channel's "removal effect."

    // 1. Identify states (channels) related to the channel_to_remove. These are typically states representing the channel itself, or transitions involving it.
    states_to_exclude = []
    FOR each state_name IN all_state_names:
        IF state_name CONTAINS channel_to_remove:
            ADD state_name TO states_to_exclude

    // 2. Create a new ordered list of states, excluding the removed ones
    new_ordered_states = []
    FOR each state_name IN all_state_names:
        IF state_name IS NOT IN states_to_exclude:
            ADD state_name TO new_ordered_states

    // 3. Adjust the initial probability vector for the removed channel
    //    Take the initial probabilities from the original dataframe, excluding columns that correspond to removed states.
    //    Then, reorder these probabilities according to 'new_ordered_states'.
    adjusted_initial_probabilities_series = initial_probabilities_df.DROP_COLUMNS(states_to_exclude).SELECT_COLUMNS(new_ordered_states).FIRST_ROW()
    initial_vector_for_removal = CONVERT adjusted_initial_probabilities_series TO FLOAT ARRAY

    // 4. Create a modified transition matrix (T_prime) by removing the specified channel
    //    a. Drop rows and columns corresponding to the removed states from the original transition matrix.
    modified_transition_matrix_df = original_transition_matrix.DROP_ROWS(states_to_exclude).DROP_COLUMNS(states_to_exclude)

    //    b. Re-normalize the rows of the modified matrix so probabilities still sum to 1.
    //       Fill any resulting NaN values with 0 (for states that might no longer have outgoing transitions).
    //    c. Reindex the matrix to match 'new_ordered_states' and convert to a numerical array.
    normalized_modified_matrix = modified_transition_matrix_df.DIVIDE_ROWS_BY_SUM().FILL_NA(0).REINDEX(rows=new_ordered_states, columns=new_ordered_states).TO_NUMPY_ARRAY()

    // 5. Calculate the steady-state vector for the modified Markov chain
    converged_vector_after_removal = markov_convergence(initial_vector_for_removal, normalized_modified_matrix)

    // 6. Identify the indices of the 'converted' state in the new ordered list
    indices_of_converted_state = []
    FOR each index, state_name IN ENUMERATE(new_ordered_states):
        IF state_name CONTAINS "converted":
            ADD index TO indices_of_converted_state

    // 7. Return the new converged vector and the indices of the 'converted' state
    RETURN converged_vector_after_removal, indices_of_converted_state

END FUNCTION

7. Attributing Credit: Lastly, the credit for conversions is allocated across the channels according to their calculated removal effects.

FUNCTION get_markov_importance(initial_vector, full_transition_matrix, all_state_names, pivoted_transition_matrix_for_removal, initial_probabilities_for_removal, list_of_channels):
    // This function calculates the overall conversion probability and the "removal effect" for each marketing channel.

    // 1. Calculate the baseline total conversion probability:
    //    a. Find the steady-state probabilities using the full transition matrix.
    baseline_steady_state_vector = markov_convergence(initial_vector, full_transition_matrix)

    //    b. Sum the probabilities corresponding to the 'converted' state(s) in the baseline vector.
    baseline_conversion_probability = SUM(probabilities in baseline_steady_state_vector where state name CONTAINS "converted")

    // 2. Calculate the removal effect for each individual channel:
    //    Initialize an empty dictionary to store removal effects.
    channel_removal_effects = {}

    //    FOR each channel IN list_of_channels:
    //        a. Simulate removing this channel from the customer journey:
    //           Call the 'removal_effect_with_convergence' function for the current channel.
    //           This returns a new steady-state vector (without the channel) and the new indices for 'converted' states.
    //        b. Sum the probabilities corresponding to the 'converted' state(s) in this new (removed-channel) vector.
    //        c. Calculate the removal effect percentage for this channel:
    //           ( (baseline_conversion_probability - conversion_probability_without_channel) / baseline_conversion_probability ) * 100
    //        d. Store this percentage in the 'channel_removal_effects' dictionary, using the channel name as the key.

    // 3. Return the baseline total conversion probability and the dictionary of channel removal effects.
    RETURN baseline_conversion_probability, channel_removal_effects

END FUNCTION

Insights Beyond the Surface

The output of a Markov Chain model provides a sophisticated attribution score for each marketing channel, often revealing a distribution of credit that differs significantly from simpler models. Some key observations made when comparing the result from Markov chain attribution models from other frameworks are as follows:

• Undervalued Channels: Channels usually appearing earlier in the funnel (such as brand awareness campaigns and organic search) tend to get more credit than in last click models since the Markov Chain appreciates their value in starting the journey.
• Overvalued Channels: On the other hand, channels that occur very last in a trip but may not be as important (e.g., direct traffic after a long nurturing process) could receive less credit than a last-click model would assign.
• Critical Path Identification: The model implicitly highlights the most common and effective sequences of touchpoints, facilitating to visualize and optimize these “golden paths” which have higher conversion rates.
• Bottleneck Identification: Upon analyzing transition probabilities, one can pinpoint where customers are most likely to drop off or get stuck, indicating areas for improvement in customer journey.

Going to Higher-Order Markov Chains

While useful, this can be an oversimplification. A higher-order Markov Chain handles this by considering several preceding states to forecast the next.

For instance, a second-order Markov Chain would consider the previous two touchpoints (e.g., “Facebook Ad” -> “Email”) to project the probability of the next step. This enables the model to learn more subtle dependencies and patterns.

Advantages of Higher-Order Chains:

• Richer Context: They paint a more realistic picture of customer behavior, since whether a customer chooses to interact with “Email” may not solely be contingent on the “Facebook Ad” they recently viewed, but rather on the “Google Search” they conducted previously.
• Improved Accuracy: Through the addition of more past context, higher-order models have the potential to deliver more accurate attribution results, particularly for products with extended or more involved sales cycles.
• Understanding Sequences: They help uncover specific sequences of interactions that are particularly effective or problematic, allowing for highly targeted optimization.

However, higher-order chains require significantly more data to be statistically robust and can be more computationally intensive to build and interpret. In practice, Markov chains higher than third or fourth order are rarely used, as the marginal benefit often diminishes beyond that point.

Empirical Results of Markov Chain Application:

To analyze the importance of various marketing channels in driving conversions in a given month, Markov Chain attribution model was implemented. For the period spanning from February to April, impression data was collected for all users. Customers who purchased the product within a given month were categorized as ‘converted,’ while all others were marked as ‘drop-off. For each month, we considered the multiple channel impression from last 2 months before the customer reached the terminal state (converted/drop-off) within the given month.

Both first order and second order Markov chains were implemented. Please note that for data security and confidentiality, the names of the marketing channels have been masked. The results of this implementation are detailed below:

The graph above provides a keen insight into the channel importance as a result of different marketing strategies

1. Channel A’s importance exhibited a consistent upward trend, demonstrating increasing dominance across the observed months, a development notably supported by increased budget allocation to this channel during March and April.

2. Channel D also showed a progressive increase in its importance over the given period. As a free channel frequently serving as an initial customer touchpoint, its contribution was often underestimated in prior attribution models. However, strategically scaling this channel has demonstrably led to a reduction in Customer Acquisition Cost (CAC).

3. The contribution of Channels B and C appears to fluctuate, likely reflecting the impact of evolving marketing strategies implemented during these periods. Notably, efforts on Channel C were strategically reduced over these months due to its consistently higher Customer Acquisition Cost (CAC).

4. The remaining channels consistently demonstrate negligible or no discernible influence on driving customer conversions and can be run with minimal costs.

The Future of Attribution: Towards Higher Predictive Power

Marketing attribution, particularly with sophisticated models like Markov Chains, provides invaluable insights into current and past performance. However, the field is constantly evolving. As data volume and computational power continue to grow, the next frontier in attribution lies in moving beyond simply understanding what happened to predicting what will happen.

This is where deep learning models and other advanced machine learning techniques come into play. Models like Recurrent Neural Networks (RNNs) or Transformer networks, often used in natural language processing, are uniquely suited to analyze sequences of events. They can uncover highly complex, non-linear relationships and hidden patterns within customer journeys that traditional models might miss. By leveraging these models, marketers can potentially not only attribute credit but also forecast the impact of future marketing investments, identify at-risk customers, and even personalize journeys in real-time.

Stepping Forward with Data-Driven Decisions

Whether beginning with simpler multi-touch models or exploring the depths of Markov Chains and deep learning, the core principle remains the same: data-driven decision-making is paramount. In this fast-evolving digital era, adopting multi-touch attribution isn’t just beneficial; it’s the undisputed need of the hour. It is required to highlight the true impact of marketing efforts, strategically optimize spends across multiple channels, and meticulously craft customer journeys that profoundly resonate and consistently drive conversions. Understanding the customer’s journey isn’t just a cost; it’s the most strategic investment any organization can make as a first step towards securing a more successful marketing future.