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

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. 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. 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. 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. Visualizing the
relationship between
conversions and cost

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. Visualizing the
simulations in heatmaps
• To evaluate our distribution assumptions
and the simulation results

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. 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. 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. 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. Automating the procedure
in RShiny applications for
cross-agency use
Creating user friendly applications
in Shiny
• Allowing for analytical methods to be
standardized

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. Questions and discussion
Contact: simonl@ayima.com
Slides will be available on SlideShare
Email or www.ayima.com for access