Control Your Future
with Precision Analytics

Quantify the impact of your advertising spend, brand, and the economy on your business performance.

Welcome to the future of marketing analytics.

Our cutting-edge solutions empower enterprise brands to quantify and optimize media performance, measure the true impact of brand and customer experience on revenue, and forecast business outcomes by analyzing leading macroeconomic indicators. Through advanced modeling, our intuitive online dashboard and planning tool delivers actionable insights, enabling you to drive growth and maximize ROI across industries.

The Box-Jenkins Transfer Function Model

Polaris Research develops custom statistical models (transfer function models, pooled time series models, etc.) to link your complete marketing mix to your desired outcomes. This process links fluctuations in media and tactics to sales, revenue, etc., while controlling for issues such as seasonality, competition, pricing, etc., and results in media and tactic-specific elasticities (i.e., sales / revenue impacts) and quantifies cross-media synergies (e.g., lift generated by Radio / TV / Display / Social running simultaneously).

>> Quantify media elasticity / impact.

>> Decompose sales by medium / tactic.

>> Calculate ROI & CPS.

>> Optimize your marketing mix.

>> Forecast sales, revenue, etc.

The Box-Jenkins Transfer Function Model

Though the equation appears complex, it distills into a few straightforward yet crucial components:

  • Y represents a company’s weekly Traffic / Sales.

  • Xs represent a company’s marketing and advertising inputs (TV, Radio, Print, Search, Display, etc.) as well as other critical inputs such as Consumer Confidence, Weekly Wages, Inflation, and other factors.

  • βo represents non-media stimulated sales commonly referred to as BAU (Business-As-Usual).

  • Φ (Phi) represents multiple seasonal or non-seasonal trends in sales, such as trends generated by the economy or competition.

  • Θ (Theta) represents regular seasonal or non-seasonal, positive or negative shocks to sales which might be caused by competitive media blitzes / promotions, product introductions, economic fluctuations, etc.

  • βk represents the elasticity for each of media and tactics. These media-specific elasticities attribute Traffic / Sales volumes to the specific media, such as TV, Radio, Print, Search, Display, etc., and are used to quantify the medium / tactic ROI and CPS.

This parameter drives everything in the Omnichannel solution:

  • Marketing effectiveness / media Impact

  • Media synergy & buildup

  • Traffic / sales decomposition

  • Media ROI & CPS calculation

  • Determination of Economic Optimum by medium (i.e., point of diminishing returns)

  • Optimization of the company’s marketing mix

  • Forecasting sales / revenue based on a media calendar / outlook

Diagram of the Box-Jenkins model with variables such as outcome, input-specific elasticity, error term, marketing and environmental inputs, moving average term, constant, potential past values, and how they interconnect for forecasting and analysis.

We simplify the interpretation of these parameters through the calculation of the Marketing Effectiveness Statistic® (MES®) for each medium / tactic. The economic optimum (i.e., Point of Diminishing Returns) is 100%. The Critical Mass Threshold is 10%, and the Effects Ceiling is 300%. Examples of media specific MES® are reflected below.

Marketing Effectiveness Statistic® (MES®)

Based on multiple inputs including the elasticity (b) and spending by medium & tactic, Polaris Research has developed the Marketing Effectiveness Statistic - MES® which quantifies the effectiveness of a medium or tactic. A MES® of 100% equals the Economic Optimum on the s-shaped curve. The Economic Optimum is the most advantageous point on the curve. Beyond the Economic Optimum, marginal returns decrease at an increasing rate. Funding for all media should exceed the Critical Mass Threshold (10%) at all times. Given equivalent funding increases / decreases, different media and tactics move up and down the curve at different rates depending on the magnitude of the elasticity. The MES® is a standardized measure and is comparable across models, products, and industries making it ideal for benchmarking and heuristic learning and planning.

A line graph illustrating the relationship between advertising spend and sales, with key points labeled: 'Critical Mass Threshold,' 'Min. CPS / Max. ROI,' 'Economic Optimum 100%,' and 'Effects Ceiling 300%.'

Media Synergy

The total market contribution of each medium is impacted by a medium’s individual effects AND the synergy it generates with other media. Synergy exists when spending on one medium increases the elasticity of another medium. This happens through a conditioning, synergistic multimedia effect. The strength of a medium’s elasticity and the synergistic relationship that the medium shares with other media in the mix also reduces the time it takes for a medium to build up to full effects in market (referred to as a medium’s lag structure). This synergistic buildup is an important factor in measuring performance and is built into all of our reporting and optimization routines. 

Omnichannel Optimization

By understanding media / tactic elasticities, budgets, and ROI, we can determine how to reallocate your ad budget to make every ad dollar work harder. This is how we maximize sales, market share, and ROI. Optimizing the marketing mix through reallocating budgets based on Omnichannel Optimization produces maximum lift at minimum costs and routinely generates 15%-30% increase in sales and 10-20% decrease in cost with the first to second quarter of optimized activity.

A line graph titled 'Before Optimization' showing the relationship between advertising spend and sales, with data points marked by circles in varying shades of blue and gray, and an upward trend indicating increased sales with increased advertising spend.
A graph titled 'After Optimization' shows the relationship between advertising spend and sales, with a curved line indicating increasing sales as advertising spend increases, and a star marker highlighting a point beyond which additional advertising yields diminishing returns.

Optimization Results

Bar chart comparing performance for four categories, with weekly spend decreasing by 3.2%, ROAS increasing by 14.5%, Sales increasing by 10.8%, and CPS decreasing by 12.7%.

Impact of Macroeconomic Leading Indicators

Your company operates within the landscape of the US and world economy. When the economy is expanding, it is like a lift that expands your market. When the economy is contracting, it is like a weight sitting on top of your footprint constricting your market. We maintain a library of 40+ US macroeconomic indicators that we test in all client models. This illustration is an example of factors that impact some retail businesses. 

Bar chart showing example of impact of leading macroeconomic indicators on the retail industry.

Media Flighting

Further, drawing upon the intelligence provided by the MES® and weekly media spending, the efficiency of media flights can be determined. In the illustration below, the GREEN line represents the Economic Optimum (MES = 100%) for TV.  The YELLOW line represents 50% on the MES curve (minimum Cost-Per-Sale). The BLUE line represents the medium’s average weekly spend. 

When the blue line is between the yellow line and the green line, the average weekly spending for the medium, Social in this case, is very efficient and operating week-to-week on the upper half of the MES curve (between 50% / minimum CPS and 100% / Economic Optimum). When the blue line is below the yellow line or above the green line, weekly spend levels should be closely evaluated.

Line graph weekly spend against the economic optimum at 100% (green line), the average weekly spending (blue line), and the median efficiency score (MES) at 50% (yellow line). The weekly spend shows fluctuations, peaking above and falling below these benchmarks, with a sharp rise towards the end.

Data Requirements

Portfolio (MACRO)

Media & Advertising

  • Historical weekly media spending / impressions / quantities for all media in the mix, for instance:

    • Paid Search, social, streaming video, terrestrial radio, OTT-CTV, magazines / print, direct mail, email, etc.

    • Minimum of 52 weeks required, 104 or more weeks preferred.  

  • Promotion calendar where applicable

  • Dates of any important occurrences identified by the client / industry (competitive initiatives, new product rollouts, etc.)

Customer Experience Data

  • Brand awareness (surveys, social mentions), sentiment (NPS, social media sentiment analysis), or engagement (website visits, social interactions).

  • Customer Experience Metrics: Customer satisfaction (CSAT), Net Promoter Score (NPS), customer retention rate, or average resolution time.

Econometric Data (provided by Polaris Research)

  • Inflation, CPI, CSI, unemployment, etc.

Campaign (MICRO)

  • Daily impressions for all media in the mix.

    • It is always best to include all media, but focus may be extended to digital media initially as data are readily available.

  • Daily sales or conversion rates.

    • A minimum of 365 days is best to incorporate at least one year of seasonality.

    • Again, the more data we have, the more we can do with it!