TURF stands for "Total Unduplicated Reach and Frequency." It is an optimization approach for finding a subset of items that "reach" the maximum number of respondents possible. For example, the classic problem is one of choosing which flavors of ice cream to stock in the freezer at a grocery store. The grocer may decide that he/she has limited space and can only include up to 8 flavors of ice cream (out of 30 possible flavors). The grocer wants to maximize the chance that shoppers will find a flavor that they like enough to buy in the freezer (the "Threshold" criterion). For example, if a flavor achieves a score of either "4" or "5" on a 5-point Likert scale ("top two box"), one might decide to count the respondent as "reached." The problem isn't as simple as including the eight most preferred flavors on average across the sample. Niche flavors that appeal to segments of the population (and that can increase total reach) would be overlooked.

For the ice cream example outlined above, the TURF procedure examines all possible subsets of 8 flavors of ice cream (out of 30 total flavors), and for each set counts how many respondents are "reached." The top sets of 8 flavors that maximize "reach" are listed in the output with the percent of respondents reached shown next to each.

One challenge with TURF is that many solutions typically yield essentially equal reach. However, this could be viewed as an opportunity rather than a problem. You can bring other information to bear on the decision (such as expert opinion) to help decide which set is best to solve the business problem. For example, if the grocer knew that one particular flavor (that appears in many of the top sets) tends to spoil more quickly than others, such solutions would be avoided in favor of other similar-reach solutions.

## Reach Methods

Weighted by Probability (Standard MaxDiff Scores):

We compute reach as the probability that the respondent will choose at least one of the items in the portfolio instead of other items of average utility.

To illustrate our approach, we begin with the formula for computing the likelihood of selecting an item from a set of items (of average utility) equal in size to that shown in the MaxDiff questionnaire. We zero-center the raw HB scores such that the average item has a score of 0. Since e0 is equal to 1, the likelihood of selecting item i from a set involving a - 1 other items of average desirability is:

Pi = eUi / (eUi + a - 1)

It is easy to expand this equation to include more items. For example, the likelihood that a portfolio containing items i, j, and k reaches the respondent is:

Pijk = (eUi + eUj + eUk) / (eUi + eUj + eUk + a - 1)

Weighted by Probability (Anchored MaxDiff Scores):

We compute reach as the probability that the respondent will choose at least one of the items in the portfolio when given the option to pick among those items versus the anchor.

To illustrate, let's consider a portfolio with a single item i. The likelihood that item i will be chosen instead of the anchor (where the anchor has a score of 0 and e0 is equal to 1) is:

Pi = eUi / (eUi + 1)

It is easy to expand this equation to include more items. For example, the likelihood that a portfolio containing items i, j, and k would be chosen instead of the anchor is:

Pijk = (eUi + eUj + eUk) / (eUi + eUj + eUk + 1)

First Choice:

A respondent is counted as "reached" if the subset of items contains his/her top item (the item with the highest raw score or value). This option also reports a "Frequency." If a respondent has multiple top items (multiple items with the same highest raw score or value) then each top item will count as a partial "reach" (the "reach" value will be 1 / n where n is the number of top items). The "Frequency" is the number of top items in the set. Note: if you are excluding items from the analysis, then first choice considers whether the portfolio includes the respondent’s highest utility score item among only those items included in the analysis.

Threshold:

The analyst supplies a value, indicating a threshold above which a respondent is counted as "reached." If any of the items' Probability of Choice in the set exceed the supplied threshold, the respondent is considered "reached." This option also reports a "Frequency." The "Frequency" is the number of items in the set that exceed the supplied threshold. If two sets have equal reach, the set with higher frequency should be preferred.