Product Sales Analysis:
Sales Potential vs. Sales Growth

Business Intelligence Solutions
January 2015


  • Better understand the relationship between Product Sales Unmet Potential and Product Sales Growth
  • Study correlation between Potential and Growth variables using non-parametric correlation analysis
  • Evaluate usefulness of new copula apparatus in sales dependence analysis

Product Sales Unmet Potential vs. Product Sales Growth
(360 observations data set)

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Relationship between Sales Growth and Sales Unmet Potential variables

  • Correlations between Product Sales Growth and Product Sales Unmet Potential variables are highly significant and negative
  • On average, the larger the growth of sales, the smaller sales unmet potential
  • The highest negative correlation (-0.35 ) is between Product Dollar Growth and Product Dollar Unmet Potential

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Product Unit Growth Distribution

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Empirical Copula for 2-dimensional Product Potential – Growth Unit data

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Empirical Copula for 2-dimensional Product Potential – Growth Unit data

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Bivariate Clayton copula (best fit): generated 1000 data points on percentile scales

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Bivariate Clayton Copula (best fit) vs. Empirical copula for Product Unit Potential and Growth Unit

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Copula and Feasibility Evaluation of Product Sales Growth Plan

  • X is customer level estimated product sales unmet potential in dollars
    • for selected list of customers total potential Potential = sum(X)
  • Y is customer level product sales growth in dollars
    • according to the plan, product sales growth Growth = sum(Y) should be greater or equal to g_plan for selected list of customers
  • Plan feasibility can be estimated by the following metrics:
    • Pr(Growth >= a, Potential>=b) as a function of two thresholds a and b
    • Pr(Growth >= g_plan, Potential>=b) as a function of the only threshold b
    • max Pr(Growth >= a, Potential>=b) for all a from (a1, a2) as a function of threshold b
  • These probabilities can be estimated by copula

Concept of Feasibility of Product Sales Growth Plan

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  • Product Sales Unmet Potential is not Product Sales. Product Sales Unmet Potential is an additional maximum value that can be generated by product sales during next year in principle if the promotion efforts and the mechanism of data generation will be the same
  • All three non-parametric measures of association (Spearman, Kendall, and Hoeffding) are indicative of existing strong correlation between Product  Unmet Potential and  Product Growth variables
  • Product Unit Unmet Potential is negatively correlated with Product Sales Growth:
    • - 0.35 for Unit Growth
    • - 0.14 for Dollars Growth
    with p-value < 0.001 (Spearman correlation)
  • Copula is useful approach to estimate dependence structure in multidimensional settings, especially tail dependence, and evaluate probability of any event, and in particular, feasibility of a planned product growth