The technique itself is straight out of media buying from the 1950s. Given some number of n alternative advertising options (e.g., magazines), which set of size k will reach the most readers and be seen the most often? Unduplicated reach is the primary goal because we want everyone in the target audience to see the ad. In addition, it was believed that seeing the ad more than once would make the ad more effective (that is, until wearout), which is why frequency is a component. When TURF is used to create product lines (e.g., flavors of ice cream to carry given limited freezer space), frequency tends to be downplayed and the focus placed on reaching the largest percentage of potential customers. All this seems simple enough until one looks carefully at the details, and then one realizes that we are interpreting random variation.
The R package turfR includes an example showing how to use their turf() function by setting n to 10 and letting k range from 3 to 6.
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This code produces a considerable amount of output. I will show only the first 10 best triplets from the 120 possible sets of three that can be formed from 10 alternatives. The rchX columns tells the weighted proportion of the 180 individuals in the dataset that would buy one of the 10 products listed in the columns labeled with integers from 1 to 10. Thus, according to the first row, 99.9% would buy something if Items 8, 9, and 10 were offered for sale.
combo

rchX

frqX

1

2

3

4

5

6

7

8

9

10


1

120

0.998673

2.448993

0

0

0

0

0

0

0

1

1

1

2

119

0.998673

2.431064

0

0

0

0

0

0

1

0

1

1

3

99

0.995773

1.984364

0

0

0

1

0

0

0

1

0

1

4

110

0.992894

2.185398

0

0

0

0

1

0

0

0

1

1

5

64

0.991567

1.898693

0

1

0

0

0

0

0

0

1

1

6

109

0.990983

2.106944

0

0

0

0

1

0

0

1

0

1

7

97

0.99085

1.966436

0

0

0

1

0

0

1

0

0

1

8

116

0.989552

2.341179

0

0

0

0

0

1

0

0

1

1

9

85

0.989552

2.042792

0

0

1

0

0

0

0

0

1

1

10

36

0.989552

1.800407

1

0

0

0

0

0

0

0

1

1

The sales pitch for TURF depends on showing only the "best" solution for 3 through 6. Once we look down the list, we find that there are lots of equally good combinations with different products (e.g., the combination in the 7th position yields 99.1% reach with products 4, 7 and 10). With a sample size of 180, I do not need to run a bootstrap to know that the drop from 99.9% to 99.1% reflects random variation or error.
Of course, the data from turfR is simulated, but I have worked with many clients and many different datasets across a range of categories and I have never found anything but random differences among the top solutions. I have seen solutions where the top several hundred combinations cannot be distinguished based on reach, which is reasonable given that the number of combinations increases rapidly with n and k (e.g., the R function choose(30,5) indicates that there are 142,506 possible combinations of 30 things in sets of 5). You can find an example of what I see over and over again by visiting the TURF website for XLSTAT software.
Obviously, there is no single best item combination that dominates all others. It could have been otherwise. For example, it is possible that the market consists of distinct segments with each wanting one and only one item.
With no overlapping in this Venn diagram, it is clear that vanilla is the best single item, followed by vanilla and chocolate as the best pair, and so on had there been more flavors separated in this manner.
However, consumer segments are seldom defined by individual offerings in the market. You do not stop buying toothpaste because your brand has been discontinued. TURF asks the wrong question because consumer segmentation is not itembased.
As a quick example, we can think about credit card reward programs with its categories covering airlines, cash back, gas rebates, hotel, points, shopping and travel. Each category could contain multiple reward offers. A TURF analysis would seek the best individual rewards ignoring the categories. Yet, comparison websites use categories to organize searches because consumer segments are structured around the benefits offered by each category.
The TURF Analysis procedure from XLSTAT allows you to download an Excel file with purchase intention ratings for 27 items from 185 respondents. A TURF analysis would require that we set a cutoff score to transform the 1 through 5 ratings into a 0/1 binary measure. I prefer to maintain the 5point scale and treat purchase intent as an intensity score after subtracting one so that the scale now ranges from 0=not at all to 4=quite sure. A nonnegative matrix factorization (NMF) reveals that the 27 items in the columns fall into 8 separable row categories marked by the red indicating a high probability of membership and yellow with values close to zero showing the categories where the product does not belong.
The above heatmap displays the coefficients for each of the 27 products, as the original Excel file names them. Unfortunately, we have only the numbers and no description of the 27 products. Still, it is clear that interest has an underlying structure and that perhaps we ought to consider grouping the products based on shared features, benefits or usages. For example, what do Products 5, 6 and 17 clustered together at the end of this heatmap have in common? Understand, we are looking for stable effects that can be found in the data and in the market where purchases are actually made.
The right question asks about consumer heterogeneity and whether it supports product differentiation. Different product offerings are only needed when the market contains segments seeking different benefits. Those advocating TURF analysis often use ice cream flavors as their example, as I did in the above Venn diagram. What if the benefit driving sales of less common flavors was not the flavor itself but the variety associated with a new flavor or a special occasion when one wants to deviate from their norm? A segmentation, whether NMF or another clustering procedure, would uncover a group interested in less typical flavors (probably many such flavors). This is what I found from the purchase history of whiskey drinkers, a number of segments each buying one of the major brands and a special occasion or variety seeking segment buying many niche brands. All of this is missed by a TURF analysis that gives us instead a bad answer to the wrong question.
Appendix with R Code needed to generate the heatmap:
First, download the Excel file, convert it to csv format, and set the working directory to the location of the data file.
test<read.csv("demoTurf.csv")
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