Like math? You better learn to.

Which option?

  • Option A

    Votes: 230 24.2%

  • Option B

    Votes: 408 42.9%

  • Option C

    Votes: 122 12.8%

  • Just tell me, I'm too stupid to figure it out.

    Votes: 192 20.2%
  • Total voters
    952
Solution proposal assignment 7:
A quick intro to probability notation:
Pr(x|i) means the probability of x given i.
Pr(x & i) means the probability of x and i occuring together.
Pr(x) means the unconditional probability of x occuring.

Now let's solve the problem at hand:

Apriori:
Pr(g|H) = 0.6
Pr(b|H) = 0.4
Pr(g|L) = 0.1
Pr(b|L) = 0.9

Needed for later:
Pr(H & g) = Pr(H) * Pr(g|H) = 0.4 * 0.6 = 0.24
Pr(H & b) = Pr(H) * Pr(b|H) = 0.4 * 0.4 = 0.16
Pr(L & g) = Pr(L) * Pr(g|L) = 0.6 * 0.1 = 0.06
Pr(L & b) = Pr(L) * Pr(b|L) = 0.6 * 0.9 = 0.54
Pr(g) = Pr(H & g) + Pr(L & g) = 0.30
Pr(b) = Pr(H & b) + Pr(L & b) = 0.70

Aposteriori probabilities:
Pr(H|g) = Pr(H & g)/Pr(g) = 0.24/0.30 = 0.8
Pr(H|b) = Pr(H & b)/Pr(b) = 0.16/0.70 ~= 0.229
Pr(L|g) = Pr(L & g)/Pr(g) = 0.06/0.30 = 0.2
Pr(L|b) = Pr(L & b)/Pr(b) = 0.54/0.70 ~= 0.771

Optimal choices based on expected profits:
Apriori:
Marketing the product yields expected profits: 0.4 * 35 000 + 0.6 * 5 000 = 17 000
Not marketing yields: 15 000
Thus you choose to market apriori.

Aposteriori:
Expected profits if indication is g:
If marketing: Pr(H|g) * 35 000 + Pr(L|g) * 10 000 = 29 000
If not marketing: 15 000
You choose marketing.

Expected profits if indication is b:
If marketing: Pr(H|b) * 35 000 + Pr(L|b) * 15 000 = 11 870
If not marketing: 15 000
You choose not marketing.

Value of testing = Pr(g) * 29 000 + Pr(b) * 15 000 - 17 000 = 2 200
 


knukk said:
Solution proposal assignment 7:
A quick intro to probability notation:
Pr(x|i) means the probability of x given i.
Pr(x & i) means the probability of x and i occuring together.
Pr(x) means the unconditional probability of x occuring.

Now let's solve the problem at hand:

Apriori:
Pr(g|H) = 0.6
Pr(b|H) = 0.4
Pr(g|L) = 0.1
Pr(b|L) = 0.9

Needed for later:
Pr(H & g) = Pr(H) * Pr(g|H) = 0.4 * 0.6 = 0.24
Pr(H & b) = Pr(H) * Pr(b|H) = 0.4 * 0.4 = 0.16
Pr(L & g) = Pr(L) * Pr(g|L) = 0.6 * 0.1 = 0.06
Pr(L & b) = Pr(L) * Pr(b|L) = 0.6 * 0.9 = 0.54
Pr(g) = Pr(H & g) + Pr(L & g) = 0.30
Pr(b) = Pr(H & b) + Pr(L & b) = 0.70

Aposteriori probabilities:
Pr(H|g) = Pr(H & g)/Pr(g) = 0.24/0.30 = 0.8
Pr(H|b) = Pr(H & b)/Pr(b) = 0.16/0.70 ~= 0.229
Pr(L|g) = Pr(L & g)/Pr(g) = 0.06/0.30 = 0.2
Pr(L|b) = Pr(L & b)/Pr(b) = 0.54/0.70 ~= 0.771

Optimal choices based on expected profits:
Apriori:
Marketing the product yields expected profits: 0.4 * 35 000 + 0.6 * 5 000 = 17 000
Not marketing yields: 15 000
Thus you choose to market apriori.

Aposteriori:
Expected profits if indication is g:
If marketing: Pr(H|g) * 35 000 + Pr(L|g) * 10 000 = 29 000
If not marketing: 15 000
You choose marketing.

Expected profits if indication is b:
If marketing: Pr(H|b) * 35 000 + Pr(L|b) * 15 000 = 11 870
If not marketing: 15 000
You choose not marketing.

Value of testing = Pr(g) * 29 000 + Pr(b) * 15 000 - 17 000 = 2 200
Click to expand...

Ummmm...yeah. Sounds about right :confused:
 
SEO_Mike said:
Ummmm...yeah. Sounds about right :confused:
Click to expand...

I added som explanatory notes:

Solution proposal assignment 7:

A quick intro to probability notation:
Pr(x|i) means the probability of x given i.
Pr(x & i) means the probability of x and i occuring together.
Pr(x) means the unconditional probability of x occuring.

Now let's solve the problem at hand:

Apriori:
A priori probabilities are the probabilities we have at hand before we conduct the PPC testing (from which we get a indication/response/signal/message):
Pr(g|H) = 0.6
Pr(b|H) = 0.4
Pr(g|L) = 0.1
Pr(b|L) = 0.9

So, e.g. Pr(g|H) is the probability of a good signal, given that the demand is high.

Needed for later:
Pr(H & g) = Pr(H) * Pr(g|H) = 0.4 * 0.6 = 0.24
Pr(H & b) = Pr(H) * Pr(b|H) = 0.4 * 0.4 = 0.16
Pr(L & g) = Pr(L) * Pr(g|L) = 0.6 * 0.1 = 0.06
Pr(L & b) = Pr(L) * Pr(b|L) = 0.6 * 0.9 = 0.54
Pr(g) = Pr(H & g) + Pr(L & g) = 0.30
Pr(b) = Pr(H & b) + Pr(L & b) = 0.70

Aposteriori probabilities:
These are the probabilities for a state of demand, given a signal response from the PPC testing. E.g., Pr(H|g) is the probability of high demand, given a good signal (g).
Pr(H|g) = Pr(H & g)/Pr(g) = 0.24/0.30 = 0.8
Pr(H|b) = Pr(H & b)/Pr(b) = 0.16/0.70 ~= 0.229
Pr(L|g) = Pr(L & g)/Pr(g) = 0.06/0.30 = 0.2
Pr(L|b) = Pr(L & b)/Pr(b) = 0.54/0.70 ~= 0.771

Optimal choices based on expected profits:
In this stage we figure out what our optimal choices are (to market or not to market), under our different possible situations. First we find out what our optimal responses are before we have a signal from testing, i.e. a priori.
Apriori:
Marketing the product yields expected profits: 0.4 * 35 000 + 0.6 * 5 000 = 17 000
Not marketing yields: 15 000
Thus you choose to market apriori, because it has higher expected profits.

Aposteriori:
This is where we check what actions are the most profitable if we conduct PPC testing and receive the different signals (good or bad indication).
Expected profits if indication is g:
If we choose marketing after a good signal from testing: Pr(H|g) * 35 000 + Pr(L|g) * 10 000 = 29 000
If not marketing: 15 000
You choose marketing.

Expected profits if indication is b:
If marketing after a bad indication: Pr(H|b) * 35 000 + Pr(L|b) * 15 000 = 11 870
If not marketing: 15 000
You choose not marketing.

Value of testing = What you are willing to spend to get the result = Difference in expected profits a posteriori and a priori = Probability of a good signal * Expected profits from our optimal choice given that signal + Probability of a bad signal * Expected profits from our optimal choice given that signal - expected profits from optimal choice a priori = Pr(g) * 29 000 + Pr(b) * 15 000 - 17 000 = 2 200
 
Just get Marketing Experiments Fundamentals of Online Testing I learned all the math about this stuff from there...

And no it's not the same type of math you learn in school.
 
jbartinla said:
#7 is pretty slick, but you seem to be pulling a couple numbers our of the air in your equations like PPC spend, revenue and profitability.
Click to expand...

Whether I pull them out of the air or not is not important. In fact it doesn't change anything. The whole point of such an assignment is to understand the tools you have your disposal to solve for a solution suggestion. The idea is to provide a set of information and assumptions that can be applied to solving the problem at hand. In real life investment decisions projects are also evaluated beforehand and predictions are made to calculate the projects' values. You can think of #7 as what you do after you have predicted what the relevant variables' values will be.
 
Assignment 8

You are about to launch a project that will give $ 100 000 of revenues for sure.
To be able to generate revenues you need to invest in a technology.

Technology A costs $ 30 000 in present value over the years with a capital cost of 10 %. Technology B costs you $ 20 000 (present value) in total over the years with a capital cost of 15 %.

The project lasts 5 years. There are no other costs to consider. There are no taxes.

What are the equivalent annual cost for each of the two technologies? Which technology do you choose for your project and why?
 
Option C is not directly comparable

A way to do it is to see your EPC.

Your EPC should be $20 times 4%=$.80

Option A cost $.40 epc
Option B cost $.20 epc so it is the best

What does cpm means? Cost per million? $.35 per million impression>?

SEO_Mike said:
For the math retards out there and people that claim to hate math, you need to get on the ball. If you want to make money in this industry, math is the single most important skill available. Yes simple math. Not coding, not design work, not even content building but plain old math.

Here's why:

You have $500 to spend and you're considering different places to spend it. The offer you are promoting pays $20, and the CPA company claims that it converts at 4%

Option "A" - Banner that gets 5,000,000 impressions monthly, costs $500, and has an average CTR (according to the site owner) of 0.025%

Option "B" - PPC campaign where the clicks will cost $0.20 each

Option "C" - CPM banner on a popular site, costs $0.35 CPM. Over the course of one month, you can expect to get a maximum of 1,000,000 impressions

So, what are some of the numbers you need to know to make an informed decision?

Also, which option is the best?

I'll post the answer later today.
Click to expand...
 
Wait a minute. That option C is still not comparable. So for 1000 impression you pay .35

In one month you would pay $350 right because you get 1 million impression.

The thing is you don't know your clickthrough. So you don't know how many people click your links? So how do you compare? Test and try I guess.
 
You earn a total of $1000 from option A. Minus the cost of $500. Your profits are $500.

Option B you earn $2000 and minus the $500 cost, you earn $1500

Option C you earn $800,000 minus $350, you earn $799,650

Hope my maths is correct.
 
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