Video CPM as a Function of Demand - Complete

Experiment description and Analysis

13 biggest client tactics representing about 9% of total video revenue were duplicated with all prior restrictions (geo, site, device etc.), additionally restricted to Tier I-III inventory and budget-density tested at 1X, 2X, 6X and 12X daily budget on 25, 12, 4 and 2 buckets respectively.

For each of these budget points we have the spend, cost and impressions in the TierI-III inventory.

From other sources (Roni's presentation) we know that about 15% of all our impressions (50% of all avails and 20% of cost) are in Tier I-III,

so for all the video tactics which weren't restricted to TierI-III as part of this test, we uniformly apportioned 20% of spend and cost (assuming margin was same) and 15% impressions in the tested user buckets to TierI-III inventory.

The above spend cost and impressions were added to those for the tested tactics, 

and CPM vs daily cost was plotted and fitted to a power law. 

Why a power law? Because cost (CPM) elasticity of demand (total cost) is the ratio of the logarithmic derivatives, which is just the exponent in a power law. 

dailySpend = AnnualSpend/365

Enter Annual Spend in all Video ($Million) =

Daily Spend in all Video ($1K) =

dailyCost = (1-margin)*dailySpend

Enter Margin (%) =

Daily Cost in all Video ($1K) =

actualDailyCost = (spendFraction + (1-spendFraction)*costFraction) * dailyCost

Enter Current Tier I-III Inventory Cost fraction (%) =
Enter Fraction of Video spend in Tier restricted campaigns (%) =

Actual Daily Cost in Tier I-III Video ($1K) =

Cost Based CPM from fit to elasticity curve evaluated at actualDailyCost
Revenue CPM = CostCPM/(1-margin)

Enter Cost based CPM at $10K Daily cost in TierI-III =
Enter Elasticity of CBCPM vs Cost, exponent in power law =

Cost Based CPM ($) =
Revenue CPM ($) =

Effect of Geo, Site, Device and DealID restrictions

DealID restrictions were in effect for all 13 line_items, so effect cannot be measured.

All restrictions data:

As one can see from the following plots, none of the other three restrictions which were variously present/absent in the tested line_items show any significant effect on either the coefficient (CPM at $10K, multiplicative effect) or the elasticity (exponent, additive effect).