Working as an affiliate depends on balancing many issues. This article gives an affiliate some mathematical tools to help make decisions about the mix of merchant links on a site.

The Mix of Success

A farmer looks out across his field at sunset and wonders, "should I plant the back field in alfalfa this year?" In his kitchen, he works on his computer using several spreadsheets showing alternatives for planting crops, adding more dairy cows, borrowing more money for new machinery, or alternate actions. He cannot predict the weather, nor can he know precisely the prices he will get at the market. He has finite resources, time, and energy, and he knows that with each choice, he bypasses other courses of action that might yield better results.

Like a farmer weighing alternatives, a Web affiliate has many choices about how to invest resources and must take risks in order to succeed. The affiliate's web site is like a farm with possible fields (pages) yielding possible crops (impressions, click-throughs, and sales). The options have outcomes that are unknown and depend on many, changing, and interacting factors.

Seeing the Big Picture

The mechanisms involved in affiliate relationships is a chain of events. A user of the World Wide Web may follow a link, use search engine, or enter a URL in a Web browser to access an affiliate's Web site. The user viewing a page yields impressions of merchant links on that page. The users who chooses to click on a merchant link produces a click-through, and those click-throughs lead to possible sales and earnings from sales commissions. This whole process is summed up in a simple formula:

E = ICS

In this formula, I is the number of impressions. An impression is when a merchant link is displayed in the user's Web browser. C is the probability that a user will click-through a link given that the link impression occured. S is the expected sales commission per click-through. S is broken down as:

S = PS * AS * CS

In this formula for S, PS is the probability of a sale given that the user clicked the merchant link. AS is the average sale (the total sales amount divided by the number of sales). CS is the commission rate for the sale based on the affiliate agreement.

For example, an affiliate might have a merchant link on a page that gets 2,000 impressions (I) over the course of a week. If there were 200 click-throughs during this time, the probability of a click-through for each impression, C, is 200/2,000 or 0.10. If two sales for this link occurred during the week, the probability of a sale for each click-through, PS, is 2/200 or 0.01. If the two sales were for $10 and $30, and the affiliate earned 5% commission on the sales, S is calculated as:

S = 0.01 * $20 * 0.05 = $0.01

So we can calculate earnings, E, as:

E = ICS = 2,000 * 0.10 * $0.01 = $2

The benefit of this formula is that it gives you insight into the components of affiliate income and gives you a way to analyze possible allocation of your resources. The actual earnings, of course, would be reported on the affiliate network reports after they have been earned. We'll see how we can apply this formula in a variety of ways to gain insight into affiliate performance.

You can apply the E = ICS formula at various levels of detail. We just used it to calculate the earnings for a single merchant link. An affiliate's web site may contain many different merchant links and different placements of the same link on different pages. If we use the notation (l, i) after variable names to indicate the instance i of that merchant link l, we can create a general formula to capture the entire Web site's earnings. The entire earnings, E, of the affiliate's web, is the summation over all the merchant links and the instances of each:

E = ∑_l ∑_i [I(l, i) * C(l, i) * S(l, i)]

In this formula, the sums for each of the I, C, and S quantities are taken over all links (l) and all instances of those links (i) on the Web site.

Of course, this E does not represent total profit for the affiliate. The affiliate's costs for development, technical operation of the web, promotion, taxes, and all other costs (including opportunity costs) should be taken into consideration. Overall, the goal of an affiliate is to choose a set of merchant links and place instances of these links on Web pages in such a way as to gain the most earnings while controlling costs.

Considering Your Options

As an affiliate, you can approach the E = ICS formula by considering how you can increase each factor.

The increase in I, the number of impressions, is a big dream of most Web publishers. More visitors means more impressions. To increase the number of visitors, you can consider promotional ideas such as placement of your Web's URL in directories of Web sites or in advertisements. Your total impressions can also rise if each of your visitors access more pages on your site. You might draw your reader into accessing more pages by placing more content at your site.

Increasing, C, the probability of a click-through, is a bit more complex. A click-through depends on many factors, including the placement and type of merchant link and user choice. For example, you might have a merchant link on the bottom of a page that is doing fairly well. By moving this link to the top of a page, you may increase its click-through rate. Other locations for placing the merchant link--on the left or right side, for example--may yield different results.

Graphics may also enhance visibility. If the merchant link is text, you might consider choosing a graphic link. Graphics and color contrast might draw a visitor's eye and therefore possibly produce more click-throughs. However, if your visitors aren't all that interested in the merchant link in the first place, or if the page is cluttered with many visuals, these bigger or brighter graphics might not make much of a difference.

Increasing, S, the expected sales commission as a result of a click-through, is a bit more difficult, as much of this final stage of a user's action relies on the merchant's Web site. One factor of S is PS, the probability of a sale given a click-through. You can improve this by making sure that the merchant links you choose closely relate to the interests of your visitors. The idea here is that the closer the merchant link relates to the topic of the Web page on which it is placed, the more likely the visitor will click a link and buy a product.

The other component of S is AS, the average sale. Simply put, larger sales amounts per order increase your earnings. An overall approach is to make sure that you provide content to decision-makers who plan to spend money on products.

The final factor of S, commission on sales, is fixed by your affiliate agreement, but your agreement might include a raise in commission rate if you accomplish a certain volume of sales. You might take advantage of this if you have several different affiliate programs to choose from. Once you reach the volume of sales required for the higher commissions for one affiliate program, you might place more links from this affiliate program on your site.

Taken together, your efforts to increase I, C, and S, may lead to larger earnings. However, realize that these factors vary as a product. For example, say you have an initial state of your web in which you measure earnings:

E₀ = I₀ C₀ S₀

Then you make an effort to increase I, C, and S each by a certain factor. For example, say you double your impressions. Your resulting impressions, I, are twice the initial impressions I₀:

I = 2 * I₀

If we use the notation F_I to stand in general for the factor of change on your impressions, and F_C and F_S to stand for the changes in your C and S values respectively, we can express the results of your efforts as:

E = (F_I I₀) * (F_C C₀) * (F_S S₀)
  = F_I F_C F_S (I₀ C₀ S₀)

You can see that your efforts have a common factor of I₀ C₀ S₀ with your initial state. We can express the change in earnings, ΔE, as:

ΔE = E - E₀
   = (I₀ C₀ S₀) * (F_I F_C F_S) - (I₀ C₀ S₀)
   = (I₀ C₀ S₀) (F_I F_C F_S - 1)

The important point is to see how the product F_I F_C F_S works in this equation.

You might have a F_I = 2 (doubling your impressions) and no change in S (F_S = 1), but you might experience a drop in your clickthrough rate by half (F_C = 0.5), so your change in earnings is:

ΔE = I₀ C₀ S₀ (2 * 0.5 * 1 - 1)
   = I₀ C₀ S₀ (0)
   = 0

Your change in earnings is 0! This is because your hard work to increase your impressions was wiped out by a drop in your click-through rate, resulting in a change of 0. This is often the explanation for slowing sales--click-through rates drop as users become used to merchant links and ignore them.

Notice also that if you double impressions, and your click-through rate falls to (F_C = 0.2):

ΔE = I₀ C₀ S₀ (2 * 0.2 * 1 - 1)
   = -0.6 * I 0 C 0 S 0

You'd have a drop in earnings over your original effort. In general, you can see from the formula that if:

F_I F_C F_S < 1

you will have a drop in earnings. This is one of the key implications of the E = ICS formula.

On the good side, if you were able to double your impressions, click-through rate, and expected sales commisions all at the same time, you'd have F_I = F_C = F_S = 2, and:

ΔE = I₀ C₀ S₀ (2 * 2 * 2 - 1)
   = 7 * I₀ C₀ S₀

Your earnings would increase seven-fold. Keep these factors in mind as you work to increase your affiliate earnings.

In practice, you may find that the clickthrough factor F_C tends to be less than one over time as your Web site visitors get used to the links at your site--a fatigue factor seems to come into play. The result is that you'll need to make sure that your impression factor F_I stays above 1 to compensate.

Keeping Track of Your Efforts

Your affiliate network will give you many ways to obtain reports on your work, but you still may want to create your own spreadsheet. You will usually have several different merchant links in a variety of places on your site. You may also work with several different merchants in an affiliate network and even several different affiliate networks. To integrate all these figures to see your entire site's performance, you can use a spreadsheet. For example, here is a simple table (made very simple for brevity, with numbers rounded to nearest two decimal places) of the efforts of an affiliate over a week's time:

Merchant Link	On page	Placed	Impressions (I)	Click-Throughs	Prob of Click-Through (C)	Orders	Total Sales	Comm rate on Sales (CS)	Prob of Sale (PS) given click-through	Ave Sale (AS)	S = PS * AS * CS	E = I * C * S	E / k I
Acme Motors	a.html	Top	8,000	250	0.03	12	$325	5.00%	0.05	$27.08	0.07	$16.25	$2.03
Acme Windows	b.html	Bottom	1,800	110	0.06	10	$800	5.00%	0.09	$80.00	0.36	$40.00	$22.22
Acme Movies	c.html	Bottom	200	20	0.10	0	$0	5.00%	0.00	$0.00	0.00	$0.00	$0.00
Beta Boxes	c.html	Top	200	75	0.38	3	$16	5.00%	0.04	$5.33	0.01	$0.80	$4.00
Beta Motors	a.html	Bottom	8,000	160	0.02	7	$125	5.00%	0.04	$17.86	0.04	$6.25	$0.78
TOTAL			18,200	615		32	$1,266					$63.30	$3.46

This table shows that the affiliate earned a total of $63.30 for the week.

The table's last column is the earnings (E) per thousand (k) impressions (I). This quantity helps bring the link's performance into focus by scaling a link's earnings to the number of impressions it received.

The Acme Windows link produced more earnings as well as dramatically more E/kI. By changing its current placement on the bottom of the b.html page to the top, perhaps even more results could be realized.

The Beta Boxes link on c.html page produced just 80 cents, but its E/kI at $4 is impressive. It produces well given that its page, c.html, didn't get all that many impressions. Perhaps giving the Beta Boxes link on a page with more impressions may give it a chance to earn more.

The Acme Movies link produced nothing, but it was on a page that didn't get all that many visits. You might review if this product fits the audience needs, or give the Acme movies link another chance on a more popular page.

You can see how a spreadsheet like this can help you see the performance of your links and help you make decisions about which merchant links to move, keep, or remove.

Understanding the Complexities

While the fundamental variables of an affiliate's efforts can be expressed by the simple arithmetic of E = ICS, this formula does not operate in isolation. An affiliate's efforts operate within the interplay of user perception and behavior, changing Web traffic, demand for merchant products, and many other factors. In fact, the science of understanding marketing in computer-mediated environments is still developing.

Further, your efforts won't always be toward maximizing earnings (or even profits) at all costs. If you want a long-term relationship with your customers, you'll always work to serve the interests of your customers and not turn them off with overly-intrusive advertising. At the same time, your Web audience should understand that creating Web content costs money, and therefore an audience shouldn't be opposed to you earning a fair return on your effort.

You can deal with this complexity by considering your options based on the formulas derived above and summarized in the Mix Checklist below, keeping records, and making your best decisions with the resources and information you have.

Mix Checklist

1. Your gross earnings as an affiliate result from a chain of events in which a visitor comes to your site, clicks on a link, and orders a product. A simple formula expresses this:

   E = ICS

   I is the number of impressions. C is the probability that a user will click-through a link given that the link impression occured. S is the expected sales commission per click-through that can be broken down as:

   S = PS * AS * CS

   PS is the probability of a sale given that the user clicked the merchant link. AS is the average sale (the total sales amount divided by the number of sales). CS is the commission rate for the sale based on the affiliate agreement. These formulas can be used to analyze your affiliate work at different levels of detail and give you ways to compare link performance.

2. Your profits will depend on your gross earnings minus the costs you have in producing those earnings. Your overall efforts is to chose a mix of merchant links and placement of those links on your pages so as to maximize your earnings, keep costs under control, and build a good relationship with your audience.

3. Your efforts to maximize your gross earnings can focus on increasing I (impressions), C (probability of a click-through), and/or S (expected sales commissions given a click-through). In so doing, the return on your effort depends on all these factors operating together, and your change in earnings, ΔE can be expressed as:

   ΔE = (I₀ C₀ S₀) (F_I F_C F_S - 1)

   where F_I, F_C and F_S are the change factors in your I, C, and S values and I₀, C₀ and S₀ are the initial values of your I, C, and S values.

4. Keep a spreadsheet to track your site's earnings, impressions, click-through probabilities, sales commissions, and other factors. Also calculate the earnings per thousand impressions for each link to compare link performance on pages which have differing numbers of visitors.

5. Understand that formulas and spreadsheets can't predict the future nor entirely capture the complex and dynamic environment of online commerce. These formulas and spreadsheets can be tools in your overall effort to use your best judgement to allocate resources and connect with your audience.