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by Alec Sharratt on 4th June 2012

Mathematics as defined by Wikipedia is “the study of quantity, structure, space, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof.”

Probably the single most important benefit of online marketing compared to off-line marketing is that it affords us the ability to track success or failure to a granular level. Thus it has become entirely possible to calculate the return on investment (ROI); and for most, this is the bottom line. But in order to understand your data and to understand your ROI, you must have a firm grasp on some basic maths.

I love mathematics; I think there is a certain amount of almost tangible and ineffable beauty in equations. As they are what best and most accurately describe the world around us; mathematics, for me, is just such a perfect way to describe the relationship between values and data. It is through doing so that we are enabled to identify patterns that can lead to great insight and understanding.

**Ratios and Keyword Research**

Understanding relationships in maths between data could not be simpler or more aptly explained than through ratios. A ratio directly reflects a numerical relationship between two values and this can be useful in a number of applications. To give you a real world example: when performing keyword research there are only really two numerical factors to consider; Competition and Search Volume.

The basic premise of this process is to find keywords with an achievable level of competitiveness and reasonable search volumes. So there is a clear relationship between the effort required to achieve results and the gains to be made from that effort.

Below is a table with some examples of keywords with search volumes and competing websites… The third column in the table shows what I have simply called the “Ratio”, these values are calculated by dividing the ‘Competition’ by ‘Local Monthly Searches (UK)’.

What this value is; is the amount of competing websites per 1 search… What this indicates is the ratio of effort to reward, so the higher the value the less reward there is for the effort. If the ratio were to be equal to 1, then the proportion of reward to effort would be roughly equal. If the ratio is less than 1, then there is a relatively high return or reward for a relatively small effort.

This does not mean that because the ratio is a low number that the keyword is by default good… But if you are scanning through a long list, it is easy to see potential gems to target. Because the ratio is a relative value it means that we can easily compare several values to find the best option. For example; of the four keywords below, the bottom two are similar and have similar associated search volumes, however the ratio is a quick an obvious differentiator.

**Percentages and Traffic**

Traffic data can be confusing, deliberately confusing or it can be simplified… I touched on this in another article about understanding your SEO data, but here I will expand upon this a little more.

Let’s assume the following data:

Now at a glance we can see that conversions went up in April by 5% compared to March. This can be calculated thus: (April Conversions / March Conversions) x100 = % increase in April from March. With numbers we can see that (105/100)x100 = 105 and this means that April’s conversions are 105% of March’s conversions (which means that April saw a +5% increase from March)

But why is this important? Let’s look at the increase in traffic between the same period using the same maths (5,500/5,000)x100 = 10, (so 10%)…

Here we can see that traffic increased by 10% but that conversions increased by only 5%. That means that for some reason, as of yet un-established, the conversion rate actually dropped. But by how much did it drop? For this calculate the % of conversions to traffic for the same month for both March and April:

(100/5,000)x100 = 2 (which means 2%)

(105/5,500)x100 = 1.9 (which means 1.9%)

Then do: 2 – 1.9 = 0.1 (this is the actual difference between the two conversion rates, but is not the % difference)

Then do (0.1/2)x100 = 5 (which means that the conversion rate in April was 5% lower than in March)

Now we have a much greater insight into what is happening with regards to increases and decreases in conversion rates relative to traffic for those months. Noting a drop in the conversion rate would probably lead to some investigation as to why it dropped, but knowing that it had dropped would be the first step on the path to finding out why.

**Predictive Power in Numbers**

Now we all know that making guarantees in SEO and PPC is impossible, but that does not mean we cannot provide ballpark figures.

For example understanding the relationships between PPC metrics such as CPC, Clicks and Cost means that we can construct simple spreadsheets to calculate cost, or projected ROI based on current data. By making CPC a variable in the following equation, we can enter new values to see what outcome this would have on everything else:

Clicks x CPC = Cost

Cost / Conversions = Cost Per Conversion

Value of Conversion – Cost Per Conversion = Profit Per Conversion

Let’s plug some values into this equation:

1,000 (clicks) x £1.00 (CPC) = £1000

£1000 (Cost) / 25 (Conversions) = £40 (Cost Per Conversion)

£35 (Value of Conversion) – £40 (Cost Per Conversion) = -£5 (Profit Per Conversion)

So in order to break even, we need to reduce the cost per conversion by £5, if we make the CPC on the first line a variable, we aim to reduce this, by how much do we need to reduce CPC in order to break even?

To figure this out we must balance the equation by working it reverse, thus:

We need the Cost Per Conversion to equal £35…

£35 = 25 / *Y *

So… £35 x 25 = *Y *(y= £875)

So the Cost now needs to equal £875…

£875 = 1,000 x *B *(*B *= CPC)

So… £875 / 1,000 = *B* (*B*=0.875 or rounding up (*B* = £0.88)

And now we can say that the CPC needs to drop to around £0.88 (given that conversion rate and clicks stay the same) in order to break even. Of course we could assume that the conversion rate might improve and so that could be a variable to. Either way you can set out first what you need to achieve to reach a goal and then decide whether that is achievable when forecasting with your data.

**Summary**

Mathematics provides a beautiful and robust system for analysing data that we use all the time in our lives, whether it is adding up the value of a shopping basket or calculating ROI. A little bit of maths can go a long way in helping to drill down into data, understand it and represent it properly.

**Image Source**

Business person standing against the blackboard via BigStock

## 1 Comment

sunil11th September 2012Great alec, definitely i can say that you have seen some beauty in the mathematics as you can finding the some meaning the data and data relationship.

I learn alot from you sharing experience.