The Math of Marketing by Anthony Tirelli

April 3, 2016

As marketers and marketers in training, it is not enough to know what methods work and how to use them. Sometimes, we need to analyze their effectiveness and determine how well they work in the real world. What can we use to measure their effectiveness? Thankfully, there are a few equations and tactics that can give us such insight.


An easy way to measure the effectiveness of an advertisement is by using a “mention this ad” campaign. The way this works is simple: publish a number of ads in different publications or platforms, and be sure to list a promotion (discount or special offer) that comes when the ad is mentioned.

After each mention, record a tally of how many people mentioned each ad. To be accurate, I would recommend using this campaign for a month or two, so the advertisement has time to circulate and make impressions. After this time has passed, look at the tallies and see which ads were mentioned the most and which were mentioned the least. The ones that were mentioned the most likely did so because of their placement.

As marketers and marketers in training, it is not enough to know what methods work and how to use them. Sometimes, we need to analyze their effectiveness and determine how well they work in the real world. What can we use to measure their effectiveness? Thankfully, there are a few equations and tactics that can give us such insight.


An easy way to measure the effectiveness of an advertisement is by using a “mention this ad” campaign. The way this works is simple: publish a number of ads in different publications or platforms, and be sure to list a promotion (discount or special offer) that comes when the ad is mentioned. After each mention, record a tally of how many people mentioned each ad. To be accurate, I would recommend using this campaign for a month or two, so the advertisement has time to circulate and make impressions. After this time has passed, look at the tallies and see which ads were mentioned the most and which were mentioned the least. The ones that were mentioned the most likely did so because of their placement.

However, the ones that had the smallest reception may have had a small impact for two reasons.


1: The medium it was published through is not one frequented by your consumer base.
2: The advertisement was designed poorly.


Based on how poorly it did, consider redesigning it or doing away with it altogether.

The problem with “mention this ad” is how expensive it can be. Handing out discounts may affect the bottom line, and may be abused by customers seeking to take advantage of discounts. To better analyze an ad’s performance, we need to use mathematical equations to determine if there is solid basis to continue with an ad. One equation most of us know is return on advertisement investment, or ROAI. ROAI is much like ROI with the exception that it takes advertisement expense into account. The equation itself is as follows:


              ROAI=[(Sales- Advertisement expense)/Advertisement expense]x100


Plugging everything in, we will get a percent increase or decrease of cash from advertisement related costs. The outcome of this will tell you if something is worth the cost, or if it’s a waste of money. If sales is greater than what the advertisement cost, then you will have made a profit on your investment. If sales are low, however, then you will have made a loss, and will have to question your initial investment.

ROAI is great, but one goal for marketers is to attract customers to the store. This is where the CAC, or customer acquisition cost equation comes into play. Here, we divide advertising expenses by the number of new customers into the store. It’s a simple equation, and works in an interesting manner. Spending very little on an advertisement won’t bring in many customers. Then, spending more on advertisements will bring in more customers. This has a magnified effect, where up to a certain point, the cost per customer will get lower and lower. However, there is a tipping point.

After you spend so much, too much revenue will be dedicated to attracting a certain number of customers. At this point, scaling back on spending may be the best thing to do.


Finally, we will plug CAC into a final equation, which is the lifetime value to CAC metric. What we have here is how much a customer will stay loyal to you over a life time. Going back to what I was saying before, one of the more important goals for any business is to attract new customers, who may become lifetime supporters.

ROAI is great, but one goal for marketers is to attract customers to the store. This is where the CAC, or customer acquisition cost equation comes into play. Here, we divide advertising expenses by the number of new customers into the store. It’s a simple equation, and works in an interesting manner. Spending very little on an advertisement won’t bring in many customers. Then, spending more on advertisements will bring in more customers. This has a magnified effect, where up to a certain point, the cost per customer will get lower and lower. However, there is a tipping point. After you spend so much, too much revenue will be dedicated to attracting a certain number of customers. At this point, scaling back on spending may be the best thing to do.


Finally, we will plug CAC into a final equation, which is the lifetime value to CAC metric. What we have here is how much a customer will stay loyal to you over a life time. Going back to what I was saying before, one of the more important goals for any business is to attract new customers, who may become lifetime supporters.

You would divide the amount that they have spent by the amount of money it cost to acquire them. If a customer comes to your store, you want to keep them there, and may do that through many means. Like CAC, LTV:CAC will tell you how much you spent on getting a customer to shop with you, but in addition, how much it cost to keep them as a repeat customer.


Hopefully you have learned a thing or two about how math may be used to measure marketing performance, and will be more inclined to use it to determine the effectiveness of your various campaigns.

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