I will point out the reasons why this equation reduces to one single variable; it reduces to revenue from the social media channel. If you don’t want to follow this you can see it in action by going to valueofalike and moving the number of likes (top button) back and forth and then noting the value on the bottom; the “value of a like” doesn’t move. That’s right, the “value of a like” doesn’t change at the bottom of the page. This means you can remove that input (and much more); Their recommendation? : “Get more likes”, even though more followers won’t “add value”.

It’s clear that it doesn’t make sense to calculate the average value of a like without having the number of likes be a part of the formula.

To see this without reducing just set all variables in the equation equal to one except likes:

L/1 * 1/L *1*1 = VOAL

Setting L = 1 gives a value of 1 as does setting L = 1 million. Likes don’t factor in.

If our average sale price is a dollar, and all else is set equal to 1. We get $1.00 (modulated by some other units). If our average sale price is $1million and likes = 1 we get $1million. All this equation does is modulate the dollar value , which we already know from measuring sales from the social media channel visits, by ratios of other numbers. This is the incorrect way to model the well-known “value of a network” problems scientists have been modeling for years.

One can also tell by the way the equation is written that something is “not right” but I decided to see what it really reduces to since it came from Harvard Business Review. I was surprised to see HBR publish this type of article which is clearly just posing as being “mathematical”. I didn’t realize they were now publishing advertorials. After all, no one will really pay attention if you just publish a simple formula right? Here is the “formula” that attempts to calculate the “value of a like” (VOAL):

(1) L/(UpM) * (LpD*30) (C/L)*CR*(ACR) = VOAL.

Should just be written as: (L*LpD*C*CR*ACR*30)/ (L*UpM) = VOAL

The L’s (number of people that like your page) cancel because you have an L in the numerator and an L in the denominator. This means that the number of people that like your business page doesn’t matter. Let’s see if this makes sense.

He also thought it useful to multiply the number of links per day (Lpd) by 30 to express in terms of months (he should haver just used LpU (links per month) but maybe it looks better to put a 30 in the equation? Not sure. Therefore it is ok, since we are using averages, to cancel the implied 30 in the denominator, unlikes-per-month (UpM). This could give you a daily value. At any rate, it doesn’t really matter. The term CR is conversion rate and they claim it doesn’t matter if the conversion rate is calculated from your overall website or the social media traffic from which the formula is modeling. In fact, it would matter if we are trying to calculate a “value” for the network. Now this formula reduces to:

(2) (C*CR*ACR*LpD)/U

If you look at the term C*CR (clicks times conversion rate) we don’t need these terms either because this is total sales! There is a U (unlikes) in denominator so if you aren’t getting unliked, at some rate, this is zero. You can’t divide by zero so the default must be assumed to be one. Theoretically this could mean that if you aren’t getting unliked (unliked = 1), and since Likes don’t appear in the equation, you don’t even need a Facebook page to get the value from Facebook likes? Businesses should be happy to be getting an infinite return form doing nothing.

Now the formula reduces to this:

(3) SocialMediaRevenue*LpD/U

“SocialMediaRevenue” ( I just renamed his “ACR” to SocialMediaRevenue ) is just sales from the social media channel we are tracking. Since we are just producing an absolute number we could just use equation 3. The value of the number really doesn’t matter. You would have to compare the number to another set of data to see if it was “better” or get some relative meaning from it.

Also notice in eq. 3 that LPD/U is not useful because it just modulates, at a daily rate, the value of our average sales from the social media channel we are measuring. So let’s just get rid of that term. We also need to add back in the number of likes to our page. Since he was trying to calculate the average value of a like AVOAL (but named the formula and didn’t include likes in the denominator) let’s divide it by L by putting the L back in the equation where it belongs. The formula published mathematically reduces to:

(4) SocialMediaRevenue/L = AVOAL.

Or, in summary, this formula gives us no new information. The equation just says: “If you get a lot of sales from a social network then it’s valuable. Calculate the total sales form that channel to get a number”. Except L wasn’t included in the denominator.

As was pointed out in the past: “selling out science is a profitable business model”.

If you are interested in formulas related to social computing and calculating value from social networks there are plenty of papers and research articles being published to build from. This attempt to quantify the value of a like isn’t even solving the already classified “Network Value of a Customer” problem. If we can measure the dollar amount of our customer visits from a network we don’t need to modulate it with other ratios of values. What we want to know is the value of network followers including the secondary viral effects from users seeing brand pages etc. Modeling the value of these effects typically includes using Markov chains and other probabilistic models and should include the network effort for obtaining followings. The formula doesn’t add any value to the information we already have.

We also discussed a two dimensional problem and showed how to expand a machine learning problem to infinite dimensions.

Lecture Notes

Slides for Lect 8.

Some useful links.
Google’s n-grams data
Text REtreival conference
A corpus of twitter data:Tweets2011

Here are the slides from lecture 6