Conversion is more important than promotion
Most website owners and developers pay insufficient attention to conversion. In this article, with the help of school mathematics, I will show that doubling the conversion will have a much better effect than if you reduce the cost of one transition to the site by half.
The more traffic we need, the more we need to pay an average per visitor.
For example, we have two possible methods of promotion thanks to each of them we can attract 100 visitors. A visitor from the first method costs 1 cent, from the second to 3. If we need 100 visitors, we will pay one cent, if 200, then (1 + 3) / 2 = 2.
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Another example is to increase market share from 10% to 20% much easier than from 80% to 90%. From 90% to 100% is practically impossible, and from 100% to 110% is no longer possible even in theory.
This happens because the market volume is not equal to infinity. Therefore, the cost of the infinite visitor must be equal to infinity. Since the cost of the first visitor is finite, there is such a point A, after which the cost of the visitor is constantly growing.
Denote by X the number of users. We denote the profit derived from one user as P (Profit Per Visitor) is the conversion multiplied by the average profit per user. R (X) - the average cost of the user. C is a fixed cost. Salary, office rental hosting and more.
As a result, the profit of our site will be equal to:
x%20-%20C)
Assume the cost of the visitor increases linearly. R (X) = K * X.
This is an equation from the school curriculum. To find its maximum you need to take the derivative and equate to zero.
=%20P%20\frac{P}{2K}%20-%20K(\frac{P}{2K})^{2}%20-C%20=\frac{P^2}{2K}-\frac{P^2}{4K}-C%20=\frac{P^2}{4K}-C)
As a result, we get that profit (now and beyond: by the word profit, we mean the maximum profit without fixed costs) depends on the square of profit per visitor, and on the rate of cost growth only linear. Why it happens? High conversion not only increases the profit per visitor, but also allows us to buy more visitors.
In other words, having doubled the conversion (or profit from one order), we will increase profits by 4 times, and if we reduce the cost of a visitor by an average of half, then we will increase profit only twice. This is true only with a linear increase in value. In the general case, it can be shown that increasing the conversion by half will more than double the profit.
It is strictly possible to prove mathematically that from conversion it is more important for any if R (X) it is any polynomial of not infinite degree. Therefore, this is true for analytic functions. However, the proof of this will be tedious and you need to explain what an analytic function is. Therefore, I will use the evidence on the fingers.
From the limitations of the market, it follows that the cost of the visitor has at least one gap of increase and it is at the end. Those. any non-increasing gap ends with an increasing gap.
The maximum of the objective function (profit) cannot be reached at the price descending point, since at the “next” point the price will be even lower and the profit will be even higher ... In the interval of the fixed price, the maximum cannot be reached either, since the increase in the number of visitors in this case will linearly increase the profit. In other words, the maximum is always in the segment of the increase in user value.
Increasing the conversion will linearly increase the profit and at the same time move this maximum point forward. Those. with increasing conversion, there is more than a linear increase in profit.
Although, strictly mathematically, it is possible to choose such a function of the cost of the visitor, at which the increase will be strictly linear, however, such a function will not be smooth and it is rather an exception to the rule.
Wholesale more expensive
The more traffic we need, the more we need to pay an average per visitor.
For example, we have two possible methods of promotion thanks to each of them we can attract 100 visitors. A visitor from the first method costs 1 cent, from the second to 3. If we need 100 visitors, we will pay one cent, if 200, then (1 + 3) / 2 = 2.
')
Another example is to increase market share from 10% to 20% much easier than from 80% to 90%. From 90% to 100% is practically impossible, and from 100% to 110% is no longer possible even in theory.
This happens because the market volume is not equal to infinity. Therefore, the cost of the infinite visitor must be equal to infinity. Since the cost of the first visitor is finite, there is such a point A, after which the cost of the visitor is constantly growing.
School math
Denote by X the number of users. We denote the profit derived from one user as P (Profit Per Visitor) is the conversion multiplied by the average profit per user. R (X) - the average cost of the user. C is a fixed cost. Salary, office rental hosting and more.
As a result, the profit of our site will be equal to:
Assume the cost of the visitor increases linearly. R (X) = K * X.
This is an equation from the school curriculum. To find its maximum you need to take the derivative and equate to zero.
As a result, we get that profit (now and beyond: by the word profit, we mean the maximum profit without fixed costs) depends on the square of profit per visitor, and on the rate of cost growth only linear. Why it happens? High conversion not only increases the profit per visitor, but also allows us to buy more visitors.
In other words, having doubled the conversion (or profit from one order), we will increase profits by 4 times, and if we reduce the cost of a visitor by an average of half, then we will increase profit only twice. This is true only with a linear increase in value. In the general case, it can be shown that increasing the conversion by half will more than double the profit.
It is strictly possible to prove mathematically that from conversion it is more important for any if R (X) it is any polynomial of not infinite degree. Therefore, this is true for analytic functions. However, the proof of this will be tedious and you need to explain what an analytic function is. Therefore, I will use the evidence on the fingers.
Proof on fingers
From the limitations of the market, it follows that the cost of the visitor has at least one gap of increase and it is at the end. Those. any non-increasing gap ends with an increasing gap.
The maximum of the objective function (profit) cannot be reached at the price descending point, since at the “next” point the price will be even lower and the profit will be even higher ... In the interval of the fixed price, the maximum cannot be reached either, since the increase in the number of visitors in this case will linearly increase the profit. In other words, the maximum is always in the segment of the increase in user value.
Increasing the conversion will linearly increase the profit and at the same time move this maximum point forward. Those. with increasing conversion, there is more than a linear increase in profit.
Although, strictly mathematically, it is possible to choose such a function of the cost of the visitor, at which the increase will be strictly linear, however, such a function will not be smooth and it is rather an exception to the rule.
Source: https://habr.com/ru/post/151212/
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