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# Statistical modelling to optimise paid media campaigns

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Using regression Analysis, Monte Carlo simulations and more to optimise paid media budget allocations

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### Statistical modelling to optimise paid media campaigns

1. 1. Using regression analysis, Monte Carlo simulations and more to optimise paid media budget allocations Simon Löfwander – Data Analyst, Ayima 25/03/17 Contact: simonl@ayima.com
2. 2. Introduction and problem description • How do we find the optimal allocations to spend on our campaigns to maximise the total amount of conversions? • Inspiration from financial statistics and portfolio theory • We view each account as a portfolio. Each campaign in a portfolio is considered an asset
3. 3. Adjusting the method to fit our domain • Omitting risk Maximise conversions w.r.t. cost. Minimising volatility would favour stable campaigns. • Using a proxy for stock returns Interpretable and suitable in our domain • Weighting factor for campaigns If conversions from specific campaigns are more valuable • Adjusted model for e-commerce Maximise conversion value when plausible • Versatile Applicable for all paid media campaigns
4. 4. Calculating a proxy for stock returns • Square root rule Conversion as a function of the square root of spend • K = conversions per unit of square root of spend Our proxy. The higher K, the more conversions per money spent • Controlling spend The square root rule makes sure the model won’t recommend too high allocations Conversions = K√Spend
5. 5. Visualizing the relationship between conversions and cost
6. 6. Simulating possible outcomes • Robustness Leverage the distribution of data to simulate many possible scenarios • Monte Carlo simulations We obtain a distribution of outcomes – can conveniently pick the most likely • Technical details Inverse CDF to transform simulations to appropriate distributions • Conversions distribution Positive integer. Negative binomial distribution • Cost distribution Continuous variable ≥ 0. Truncated normal distribution
7. 7. Visualizing the simulations in heatmaps • To evaluate our distribution assumptions and the simulation results
8. 8. Solving for the optimal weights • The total amount of conversions is maximized • We obtain optimal weights for each campaign and each simulation run • For every campaign we get a distribution of optimal weights
9. 9. Campaign Recommended allocation % Current allocation % Difference % Campaign A 3.81 9.91 -6.1 Campaign B 14.64 2.91 11.73 Campaign C 5.87 6.05 -0.18 Campaign D 4.71 6.8 -2.1 Campaign E 6.89 18.06 -11.16 Campaign F 8.37 7.12 1.25 Campaign G 4.93 4.06 0.87 Campaign H 11.32 5.34 5.98 Campaign I 10.27 19.68 -9.41 Campaign J 17.39 3.03 14.36 Campaign K 11.8 17.04 -5.24 Interpreting and using the results • Model outputs are recommended spend allocations
10. 10. Visualizing the expected uplifts in conversions Explaining the plot • Expected conversions with current and recommended allocations • By setting a target CPA, we obtain a suggested max budget to not exceed to stay within target
11. 11. How do we Know this works? We can’t do A/B testing if we reallocate budgets throughout an entire account. Need to make sure of causality Causal Impact • Predicts what should have happened and compares to what happened • Confidence intervals with predictions • Great R-coverage and library developed by Google. “CausalImpact” is available on CRAN
12. 12. Automating the procedure in RShiny applications for cross-agency use Creating user friendly applications in Shiny • Allowing for analytical methods to be standardized
13. 13. 1 Reasonable amount of conversions and spend for each campaign The simulations will work best for data rich campaigns 2 Maxed out campaigns will be favoured if they have good performance Hence, campaigns in e.g. an AdWords context that has Search Impression share ~100% should be omitted 3 For seasonal data, we need overlapping time periods The same time period for all campaigns should be used Limitations
14. 14. Questions and discussion Contact: simonl@ayima.com Slides will be available on SlideShare Email or www.ayima.com for access