In online marketing, we have always wanted to make the best possible predictions of metrics such as the traffic, number of orders, number of new customers or even revenue from spending budget and data in hand. With 5 years of experiences in online marketing in South East Asia, I have been asked countless times how much revenue a company would generate after spending “X” amount in the following month. In this article, I would like to share with you my personal method I use to predict revenue.

1. Efficiency Function: Online Marketing and Analytics
In online marketing, we have always wanted to make the best possible predictions of metrics such as the traffic, number
of orders, number of new customers or even revenue from spending budget and data in hand. With 5 years of
experiences in online marketing in South East Asia, I have been asked countless times how much revenue a company
would generate after spending “X” amount in the following month. In this article, I would like to share with you my
personal method I use to predict revenue.
Simple Efficiency Function
𝑺𝑬𝒇𝒇(𝑺 𝒙) (Simple Efficiency Function) is the function of spending proportion or “𝑆 𝑥” which is returning how efficient
campaigns are running comparing to previous periods. Where spending proportion or “𝑆 𝑥” is the proportion between
your budget and average amount of spending in previous periods.
Note: 𝑺𝑬𝒇𝒇(𝑺 𝒙) is time independent (see Assumption 4)
𝑺𝑬𝒇𝒇(𝑺 𝒙) = 𝑺 𝒙
−𝒃
, 𝒘𝒉𝒆𝒓𝒆 𝒃 𝝐 𝑹+
𝑺𝑬𝒇𝒇(𝑹 𝒙, 𝑺 𝒙) =
𝑹 𝒙
𝑺 𝒙
𝒘𝒉𝒆𝒓𝒆 𝑹 𝒙 =
𝑹 𝒏𝒆𝒘
𝑹̅ 𝒐𝒍𝒅
⁄ 𝒂𝒏𝒅 𝑺 𝒙 =
𝑺 𝒏𝒆𝒘
𝑺̅ 𝒐𝒍𝒅
⁄
Example of Simple Efficiency Function
𝑪𝑬𝒇𝒇(𝑺 𝒙) (Complex Efficiency Function) is the product of Simple Efficiency function and optimization-function 𝑶(𝒕)
where 𝑶(𝒕) is time dependent, which means for complex efficiency function, it could perform better (or worse) if we
have run data before. However, I would like to neglect 𝑶(𝒕) for this article and assume it to be “one”.
𝑪𝑬𝒇𝒇(𝑺 𝒙, 𝒕) = 𝑺𝑬𝒇𝒇(𝑺 𝒙) × 𝑶(𝒕)
𝑹 is the result that you would like to predict, 𝑹 could be Revenue (which is what we are going through in this article),
#clicks, #orders, #new-customer or #app-install. Please note that the process, concept, and computation are the same.
Whereas before going further to the computation, I would like to state some assumption to you first. Hence, we can
align on the same page. (maybe use the sentence below)
Before we go into the details of the calculations, allow me to state all the assumptions made.
Assumption 1: Simple Efficiency function is a decreasing function
Every campaign that you are running can either be defined as 1. A bad campaign 2. An average campaign or 3. A good
campaign.

2. If I ask you to lower your spending budget, which type of campaigns will you turn off… a good one? Of-course not, you
will definitely turn off the bad ones (if there is no other constrains).
Now you can probably see that in an ideal case, if we lower our spending, our efficiency (or our performance) will always
be better and vice versa.
Assumption 2: 𝐥𝐢𝐦
𝑺 𝒙→𝟎
𝑺𝑬𝒇𝒇( 𝑺 𝒙) = ∞
Some of you may already be aware that even if you stop spending, you still get clicks, orders and revenue. In online
marketing, it would be because of website cookies, and offline would be resulted from your branding effort. When there
are sales or orders without any spending, we say that the efficiency is “∞”
Assumption 3: 𝐥𝐢𝐦
𝑺 𝒙→∞
𝑺𝑬𝒇𝒇( 𝑺 𝒙) = 𝟎
Assume that you spent X amount this week on your marketing campaigns and must send 100X next week. Your
efficiency will drop dramatically and sink right into the ground.
Assumtion 4: 𝑺𝑬𝒇𝒇(𝟏) = 𝟏
This assumption states that the Simple Efficiency fuction is independent of time, sesonal, economic and political factors.
This is implying that, if my spending for this month is equal to that in the previous month, I will get the same amount of
revenue I made last month. (Of-course, as mentioned previously, there will be optimization-function to compute
complex-efficiency function’s value)
Based on the 4 assumptions made, Simple Efficiency function is as follow,

3. (graph is plotted from www.wolframalpha.com)
And the simple efficiency function will be
𝑺𝑬𝒇𝒇(𝑺 𝒙) = 𝑺 𝒙
−𝒃
, 𝒘𝒉𝒆𝒓𝒆 𝒃 𝝐 𝑹+
So
𝒃 = −
𝒍𝒏(𝑺𝑬𝒇𝒇)
𝒍𝒏(𝑺 𝒙)
= 𝐥𝐨𝐠 𝑺 𝒙
𝑺𝑬𝒇𝒇−𝟏
(Note: when b is less than 0, this means we have failed to optimize our campaigns)
And simple efficiency function for revenue projection will be,
𝑺𝑬𝒇𝒇(𝑺 𝒙) =
𝑹 𝒙
𝑺 𝒙
𝒘𝒉𝒆𝒓𝒆 𝑹 𝒙 =
𝑹 𝒏𝒆𝒘
𝑹̅ 𝒐𝒍𝒅
⁄ 𝒂𝒏𝒅 𝑺 𝒙 =
𝑺 𝒏𝒆𝒘
𝑺̅ 𝒐𝒍𝒅
⁄
How I use Simple Efficiency Function in my career
Let’s say I have been running my startup company for 6 months or 24 weeks. I currently have 24 pairs of spending and
revenue data, and will use these data to calculate 𝑺𝑬𝒇𝒇 . Therefore, I have 552 (24×23) datasets to calculate the mean
𝒃̅ , 𝑤ℎ𝑒𝑟𝑒 𝒃̅ 𝝐 𝑹+
Use the mean value of valid data among 552 datasets. Plug it into 𝑺𝑬𝒇𝒇(𝑺 𝒙) = 𝑺 𝒙
−𝒃
, substitute 𝑺 𝒏𝒆𝒘 with my
marketing budget next month, then …
𝑹 𝒏𝒆𝒘 = (
𝑺 𝒏𝒆𝒘
𝑺̅ 𝒐𝒍𝒅
⁄ )
𝟏−𝒃̅
× 𝑹̅ 𝒐𝒍𝒅
As a result, you have the Est. revenue next month from the amount of budget set.
Assumption review: After you have run the campaigns, and you have 𝒓𝒆𝒂𝒍 𝑹 𝒏𝒆𝒘 to calculate 𝒓𝒆𝒂𝒍 𝑺𝑬𝒇𝒇 𝒏𝒆𝒘
Case 1: 𝒓𝒆𝒂𝒍 𝑺𝑬𝒇𝒇 𝒏𝒆𝒘 > 𝑬𝒔𝒕. 𝑺𝑬𝒇𝒇 𝒏𝒆𝒘 then
You have optimized your campaigns better than before!
Case 2: 𝒓𝒆𝒂𝒍 𝑺𝑬𝒇𝒇 𝒏𝒆𝒘 = 𝑬𝒔𝒕. 𝑺𝑬𝒇𝒇 𝒏𝒆𝒘 then
You have optimized your campaigns as equally well as before.
Case 3: 𝒓𝒆𝒂𝒍 𝑺𝑬𝒇𝒇 𝒏𝒆𝒘 < 𝑬𝒔𝒕. 𝑺𝑬𝒇𝒇 𝒏𝒆𝒘 then
You have optimized your campaigns worse than before.
CONCLUSION
We have always wanted to forecast and accurately estimate our revenue from the only controllable factor we have, our
spending budget. With the concept of efficiency function, this can be easily done. Although, a lot more work and study
are required to further develop the optimization-function which is yet to be calculated in a greater depth. However, I
believe that this idea has provided me with a very nice guideline and direction on what to do in my marketing strategy. If
you have any questions, thoughts or comments to give me a wider picture to this analysis, please feel free to leave me a
message below or email me at peerapat.sirichot@gmail.com. Otherwise, send me your data, and I will predict your
future.