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

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

Adjusting the method to fit our domain

• Omitting riskMaximise conversions w.r.t. cost. Minimising volatility would favour stable campaigns.

• Using a proxy for stock returnsInterpretable and suitable in our domain

• Weighting factor for campaignsIf conversions from specific campaigns are more valuable

• Adjusted model for e-commerceMaximise conversion value when plausible

• VersatileApplicable for all paid media campaigns

Calculating a proxy for stock returns

• Square root ruleConversion as a function of the square root of spend

• K = conversions per unit of square root of spendOur proxy. The higher K, the more conversions per money spent

• Controlling spendThe square root rule makes sure the model won’t recommend too high allocations

Conversions = K√Spend

Visualizing the relationship between conversions and cost

Simulating possible outcomes

• RobustnessLeverage the distribution of data to simulate many possible scenarios

• Monte Carlo simulationsWe obtain a distribution of outcomes – can conveniently pick the most likely

• Technical detailsInverse CDF to transform simulations to appropriate distributions

• Conversions distributionPositive integer. Negative binomial distribution

• Cost distributionContinuous variable ≥ 0. Truncated normal distribution

Visualizing the simulations in heatmaps

• To evaluate our distribution assumptions and the simulation results

Solving for theoptimal 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

CampaignRecommended 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 andusing the results

• Model outputs are recommended spend allocations

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

How do weKnow 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

Automating the procedure in RShiny applications for cross-agency use

Creating user friendly applications in Shiny

• Allowing for analytical methods to be standardized

1 Reasonable amount of conversions and spend for each campaignThe simulations will work best for data rich campaigns

2 Maxed out campaigns will be favoured if they have good performanceHence, campaigns in e.g. an AdWords context that has Search Impression share~100% should be omitted

3 For seasonal data, we need overlapping time periodsThe same time period for all campaigns should be used

Limitations

Questions and discussion

Contact: simonl@ayima.com

Slides will be available on SlideShare Email or www.ayima.com for access