Probability & Satitistics: It matters - Lesson 1 - Expected Value
 

From reading GFY and some other boards, I don't think too many webmasters have a good grasp of Probability & Statistics. Now, you're probably saying "WTF should I care about that crap? I didn't pay attention in school, so I ain't gonna give a crap about some asshole preaching it to me now." Well, it's of utmost imporatance if you want to make money in this business, because it will effect all of the decisions you make in where to send your traffic, how to run your sites, etc.

The first and most important concept is Expected Value. In probability, the expected value (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ("value"). Thus, it represents the average amount one "expects" to win per bet if bets with identical odds are repeated many times. Note that the value itself may not be expected in the general sense, it may be unlikely or even impossible.

Expected value (EV) is a central principle in the theory of probability. It is used for average estimation of some random value. Expected value is similar to a center of gravity assuming that the values of probability are the masses of solid point.

Why should you care about expected value? What does it mean to a webmaster? Well, in a nutshell, you care about it because it doesn't really matter what the potential maximum dollars you can collect from a hit you send somewhere. What really matters is the exected value or, in effect, the expected return you are going to get from sending that hit to a given location.

How do you compute Expected Value? To put it in as simple terms as possible, the EV of any chance event is the average of all possible outcomes. When most people hear the word ?average? they usually think of what mathematicians call the mean; that is, you add up a bunch of numbers and divide by the number of numbers. To calculate the EV, however, we must use a weighted average, not just the mean.

If an event has n different outcomes, probability of each outcome is pi. The expected value of some variable x that takes values xi can be calculated with the next formula:

E(x) = x1p1 + x2p2 + ... + xnpn ,

In case the probabilities of outcomes are equal ( p1=p2=...=pn=1/n ) the expected value equals to arithmetic mean:

E(x) = x1/n+ x2/n + ... + xn/n = (x1 + x2 + ... + xn) / n

Or more bluntly, take the probability of each outcome and multiply it by the benfit of that particular outcome, and then add them all up.

And example from our industry:

You send traffic to thirdworldpimp.com. Let's say the PPS $5 for 3 day trials, they PPS $35 for 1 month signups, and nothing if there is no sale. Let's also say that 1:100 signs for the 3 day trial and 1:300 signs full. So, you've got (1/100) X $5 + (1/300) X $35 = $0.27 . Or in other words, each click sent there has an expected value return of 27 cents.

A second example:

You send traffic to ebonynasty.com. Let's say the PPS $2 for 3 day trials, they PPS $5 for 1 month signups, and nothing if there is no sale. Let's also say that 1:5 signs for the 3 day trial and 1:10 signs full. So, you've got (1/5) X $2 + (1/10) X $5 = $0.90 . Or in other words, each click sent there has an expected value return of 90 cents.

So, even though the PPS is totally shit on a $ per sign, the expectd value of the second program is 3 times higher. You know what that means? if you're actually looking to maximize your return, you'd actually promote the second prgram over the first.

* note - not to brag, but just for background: the author holds Bachelor of Science and Professional Master of Engineering Degrees in Operations Research from Cornell University.

Wow, down to 3 minute editing! that should have been $15 PPS for trials in the first example

This thread is too complicated for this board