Monday, April 27, 2015

Annual Video spend to Cost CPM calculator

Video CPM as a function of Demand

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 (Atul's presentation) we know that about 15% of all our impressions (50% of all avails) 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. 

How do I put in formulas? dailySpend = AnnualSpend/365

dailyCost = (1-margin)*dailySpend

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

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

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).