# What operands are available for calculated metrics?

This document describes the operations used to build calculated metrics in Beckon.  The underlying logic is based on the premise of Reverse Polish Notation

Operation

Description

Use Case

Metric Sum

Beckon adds the data of two or more metric values.

ABC Company wants to know the total spend for Social and Online Display for week 1 and 2.

From Table 1, spend for Social and Online Display is \$29.9 for week 1 (\$27.6 + \$2.36) and \$282 for week 2 (\$28.5 + \$253).

Total Spend for Social and Online Display were added together by using the METRIC SUM operation.  Notice in this case, the sum values of the same metric but different dimensions were added together.  You may also use this to sum two or more unique metrics.

Metric Multiply

Beckon multiplies the value of two or more metrics

ABC Company wants to know the overall spend for their impressions for their recent Online Display campaign.

Total impressions for the recent campaign are 1,360 for week 1 and 1,940 for week 2.

Cost per impression is \$\$0.039 for week 1 and \$0.077 for week 2.

Total overall spend is \$53.04 for week 1 and \$150 for week 2.

Total Online Display impressions is MULTIPLIED by spend per impressions to determine overall spend for Online Display impressions for their recent campaign.

Metric Max

Beckon compares the value of two or more metric values and selects the highest value

ABC Company wants to know which channel had the highest spend.

Based on Table 1, Social had the highest maximum value of \$27.6 for week 1 and for week 2 Online Display had the highest maximum value of \$253.

The highest spend per week was determined applying the METRIC MAX operation to the Online Display Spend, the Email Spend and the Social Spend.  If data is missing for a metric, it is not considered when determining the maximum.  Notice in this case, the values of the same metric but different dimensions were considered.  You may also use this to find the maximum value between two or more unique metrics.

Metric Min

Beckon compares the value of two or more metric values and selects the lowest value

ABC Company wants to know which channel has the lowest spend.

Based on Table 1, Online Display had the lowest minimum value of \$2.36 for week 1 and for week 2 Email had the highest maximum value of \$6.09.

The lowest spend per week was determined applying the METRIC MIN operation to the Online Display Spend, the Email Spend and the Social Spend.  If data is missing for a metric, it is not considered when determining the minimum.  Notice in this case, the values of the same metric but different dimensions were considered.  You may also use this to find the minimum value between two or more unique metrics.

Metric Average

Beckon calculates the average for two or more metric values

ABC Company wants to know the average spend by week.

Based on Table 1, the average number of clicks for week 1 is \$12.3 (66.85+253+28.5)/3) and for week 2 it is  \$95.9 ((86.09+253+38.5)/3).

The average spend was determined by applying the METRIC AVERAGE operation to the Email Spend, Online Display Spend, and Social Spend.

Division

Beckon divides one metric value by another metric value

ABC Company wants to know how much they are spending per impression on a weekly basis.

Week 1: Spend = \$254     Impressions = 6,600

Week 2: Spend = \$500     Impressions = 6,470

The cost per impression for  week 1 is \$0.039 (\$254/6,600) and for week 2 it is \$0.077 (\$500/6,470).

The spend per impression is calculated by applying the operation, DIVISION:  taking the total spend by week as the numerator and dividing it by weekly impressions as the denominator.

Negation

Beckon multiplies any metric by -1

ABC Company wants to know for week 2, how many more Online Display impressions they had compared to Social impressions.

Based on Table 1, the difference in week 2 of Online Display impressions compared to Social impressions is 470 (1,940-1,470).

The difference was calculated by applying the NEGATION operation to Social impressions, which multiplies the impressions value by -1 making it a negative number. Online Display and Social impressions are then summed for week 2, which equates to a difference between the two impressions.  Essentially, by applying the NEGATION operation it enables you to subtract one metric value from another unique metric value.

Inversion

Beckon divides 1 by any single metric

ABC Company wants to know what is the spend per impression.

Based on Table 1, the inverse of total impressions for social is 1/2,890 or .035%  (1/(1,420 + 1,470)).

The inverse rate was calculated by applying the INVERSION operation to social impressions.

Based on Table 1, total spend for social is \$56.1 (\$27.6 + \$28.5).  Multiply \$56.1 with .035%, which is \$.019.

Spend per Impressions was calculated by applying the METRIC MULTIPLY, to multiply \$56.1 to the formula metric of .035%.

(Note: A simpler way to calculate spend per impression is by using the DIVISION operation dividing \$56.1/2,890.)

Beckon adds a constant number to any single metric

ABC Company wants to know the total weekly spend with the additional fixed cost of \$10

Based on Table 1, total weekly spend with the fixed cost of \$100 for each channel for week 1 is:

Email = \$6.95

Online Display = \$2.46

Social =  \$27.7

The weekly total spend  for each channel was increased by \$100 fixed cost by applying the SCALAR ADDITION operation to Total Spend.  The constant can also be a negative number where it is subtracted from a metric value.

Scalar Max

Beckon compares the value of a single metric to a selected constant number and determines the higher value

ABC Company wants to know if there are any engagement rates that are greater than 50%.

Based on Table 1, for week 1 the Email engagement rate of 128% and for week 2, the Email engagement rate of 125% are greater than the scalar max of 50%.

The engagement rates that are greater than 50% were determined based on applying the SCALAR MAX operation and defining the constant value as 50%.

Scalar Min

Beckon compares the value of a single metric to a selected constant number and determines the lower value.

ABC Company wants to know if there are any engagement rates that are less than 20%.

Based on Table 1, for week 1 the Online Display engagement rate of.27% and for week 2, the Social engagement rate of 19% are less than the scalar min of 20%.

The engagement rates that are less than 20% were determined based on applying the SCALAR MIN operation and defining the constant value as 20%.

Scalar Multiply

Beckon multiplies the value of a single metric by a selected constant number

ABC Company wants to know the CPM (cost per thousand impressions) for Email.

Based on Table 1, the CPM for Email is 0.0136 ((\$6.85+\$6.09) / (926+24.5))

The CPM for Email is calculated by applying the SCALAR MULTIPLY operation with a constant number of .001 to a cost-per-impression metric (formula).

Filter

The filter sifts a single metric by a dimension(s).

ABC Company wants to know what percentage of total spend was attributed to the Social for week 1.

Based on Table 1, the percentage of social spend to total spend for week 1 is 10% (\$27.6/\$254).

Percentage of social spend was calculated by selecting Percentage as the Format Type, and applying the FILTER operation.  Caveat in chart builder is if you selected the formula above (Percentage of Social Spend) as the metric and selected a dimension of Online Display, chart builder will display Social Spend + Online Display Spend/ Online Display Spend.

Dimension Product

Beckon calculates all the vectors for any user-selected dimension(s) and disregards any dimension that is not a number, then multiplies the values for all the valid vectors.

ABC Company wants to know what the percentage penetration growth of each country to global growth of 1,000 HH.

Country

2014 Total Growth

Penetration %

USA

100

10%

20

2%

Mexico

50

5%

Total

150

15%

In the example above, DIMENSON PRODUCT by “Country” is applied to multiply growth by 1/1000 (another formula metric).

Dimension Sum

Beckon calculates all the vectors for a single metric by a selected dimension(s).  All dimension+metric combinations that do not produce a number are not considered and  only sums the available values.

ABC Company wants to know what the total impressions are per DMA.

DMAs

Week 1: Impressions

Week 2: Impressions

Total by DMA

Western Region

1,000

2,000

3,000

Eastern Region

3,000

4,000

7,000

Southern Region

500

400

900

Northern Region

2,100

70

2,170

Total

6,600

6,470

13,070

Using the DIMENSION SUM operation, total impressions by DMA are displayed in the Total by DMA column.

Dimension Count

Beckon counts the number of vectors for a single metric for a selected dimension(s).  All dimension+metric  combinations that do not produce a number are not considered and  only counts available values.

ABC Company wants to know how many countries have activity for social clicks for week 1 and 2.

Countries

Week 1: Clicks

Week 2: Clicks

USA

15,200

16,000

Mexico

823

865

0

0

England

0

0

Total

16,023

16,865

By applying the DIMENSION COUNT,  week 1 and 2 both have 2 countries that had click activity.  Total dimension count by country for social clicks is 2 for both week 1 and 2.   Since Canada and England had 0 clicks, they are not considered in the dimension count formula.

Dimension Average

Beckon takes the Dimension Sum divided by Dimension Count. Beckon averages all the vectors for a single metric for a selected dimension(s).  All dimension+metric  combinations that do not produce a number are not considered and  only takes the average of available values.

ABC Company wants to know what the average is for the number of engagements for week 1 and 2.

 Countries Week 1: Engagements Week 2: Engagements USA 1,720 1,720 Spain 0 11,100 Mexico 217 165 Italy 1,910 146 Total 3,847 13,131 Dimension Average 961.75 3,282.75

By applying the DIMENSION AVERAGE, week 1 average is 961.75 and week 2 is 3,282.75.

Dimension Median

Beckon locates the midpoint of a vector for a single metric for a selected dimension(s).  All dimension+metric  combinations that do not produce a number are not considered.

ABC Company wants to know what the median value is of engagements by channel.

Channels

January 2015 - Engagements

Email

\$27.9

Mobile

\$63.8

Online Display

\$240

Online Video

\$577

Social

\$261

Dimension Median

\$240

By applying the DIMENSION MEDIAN by channel (dimension)  for engagements (metric), the median value is \$240.

Dimension Max

Beckon compares the value of two or more metric values for a selected dimension(s) and selects the highest value.

All dimension+metric  combinations that do not produce a number are not considered.

ABC Company wants to know which channel had the highest dollar value of engagements.

Based on Table A above, Online Video with an engagement value of \$577 is determined as the dimension max.

By applying the DIMENSION MAX, the highest value based on channel is Online Video with a January 2015 engagement of \$577.

Dimension Min

Beckon compares the value of two or more metric values for a selected dimension(s) and selects the lowest value.

All dimension+metric  combinations that do not produce a number are not considered.

ABC Company wants to know which channel had the lowest dollar value of engagements.

Based on Table A above, Email with an engagement value of \$27.9 is determined as the dimension min.

By applying the DIMENSION MIN, the lowest value based on channel is Email with a January 2015 engagement of \$27.9.

Moving Average

Beckon calculates the moving average for a metric based on the time frequency and an integer value indicating the number of data points to be used to calculate the average (denominator).

ABC Company wants to know what the 2 month moving average is for the total monthly sales data below;

Month

Sales (\$M)

January

10

February

7

March

6

April

3.5

May

5

June

8

The two month moving average is as follows:

 Month Sales (\$M) Moving Average January n/a February 8.5 ((10+7)/2) March 6.5 ((7+6)/2) April 4.75 ((6+3.5)/2) May 4.25 ((3.5+5)/2) June 6.5 ((5+8)/2)

The moving average was calculated by applying the MOVING AVERAGE operation to the sales metric and selecting a frequency of monthly and an integer of 2 indicating two months.

Dimension Coefficient

Beckon calculates the coefficient for each dimension(s) where the coefficient represents the contribution of the selected dimension towards the overall metric value.

ABC Company has several banner ads displayed on various search sites.  They want to know how much (or if) the ad-size and ad-content impacts the engagement rate. They are assuming that a bigger ad size and animated content will result in more clicks, thus increase in engagements.

To calculate the impact of ad-size and/or ad-content, multiple ads have to be run with varying ad-sizes and content and its results compared to the base or “control” ad.

Title

Description (Dimensions)

Engagement Rate

Impressions

DIMENSION COEFFICIENT

Conclusion

Content: written

15%

1000

N/A

N/A

Content: video

4%

2000

(.04 - .15)/2000 = (-.006%)

0 Impact

Content: animated

20%

900

(.20 - .15)/900 = .0056%

Impact of .0056%

TOTAL

3,900

The DIMENSION COEFFICIENT was applied to the engagement rate and impressions to calculate the impact of the impact or contribution of the selected dimension(s) to the engagement.  The larger the resulting number, the greater the contribution to the overall engagement metric.  Ad #2 resulted in a negative number which means that there is a 0 impact or it did not contribute any increases to engagement.  This formula can be used to uncover how effective a specific change is dimension values are to the engagement level.

(Note: To see actual use of this operation, go to Yahoo and view the formula,  “Media Incremental Conversions w/ Coefficient (primary 1 & 2)”.  Yahoo uses displays ads about ‘Fantasy Football’ to engage its users with football. The two dimensions associated with these ads are Ad-Size and Ad-Content, its expected that changing these dimensions will cause change is corresponding ad metrics: a bigger ad-size might cause more users to click on the ad and get engaged. )