# Total Unduplicated Reach and Frequency (TURF)

TURF, which stands for Total Unduplicated Reach and Frequency, is a tool for understanding the portfolio of alternatives (products or medias) which will maximize reach (i.e., penetration). It is used for selecting combinations of flavors and product variants (e.g., what are the best five flavors of ice cream for a manufacturer to offer?).

## Q 4.8.6 and Later

For Q 4.8.6 or later, a TURF analysis is conducted by running a QScript: Marketing - TURF (Total Unduplicated Reach and Frequency). An explanation of the terms and concepts used in TURF is provided below:

### Alternatives and Portfolios

A TURF analysis contains a set of alternatives which represent products (or medias), from which subsets of alternatives are selected to construct portfolios. In Q, alternatives are selected from variables in Pick Any or Pick Any - Grid questions. The objective of a TURF analysis is to find the portfolios with the highest reach. If two portfolios have the same reach, then the one with a higher frequency is assigned a higher ranking. The analysis returns the top portfolios for each portfolio size within a specified range of portfolio sizes.

### Reach and the Minimum Alternatives Per Case

The reach is a percentage representing the "coverage" of a portfolio. This is commonly calculated as the (weighted) proportion of respondents in a survey who have provided a positive response to one or more alternatives in the portfolio. Therefore the reach is intended to represent the proportion of the population that would be interested in at least one of the alternatives, although this does not necessarily have to be case. An option called the minimum alternatives per case, also known as depth of reach, specifies the number of alternatives that each respondent has to respond positively to in order to be counted in the reach. This number is commonly one, but may be a whole number up to the maximum portfolio size.

Importantly, the Minimum Alternatives Per Case option is applied within each portfolio for the purpose of computing the Reach percentage. So if the minimum alternatives is set as 3, and the size of a portfolio is 4, only people who have 3 or 4 of selections from the options in that portfolio are counted towards the calculation of the % of reach.

### Frequency

The total (weighted) number of positive responses received for all the alternatives in a portfolio. This measure is used to differentiate two portfolios with the same reach, where the one with a higher frequency is assigned a higher ranking.

### Minimum Proportion of Positive Responses

An option to specify the minimum (weighted) proportion of positive responses that alternatives must have in order to be included in portfolios. The purpose of this is to exclude alternatives are likely to contribute the least to the reach, which reduces the size of the search space and hence the computation time, although this will only be noticeable for analyses with a large number of alternatives. The minimum proportion is set to zero by default, which means that no alternatives are excluded.

### Forced Alternatives

An option that allows a subset of alternatives to be specified to be present in all portfolios. Such alternatives are often core products and the objective of the TURF analysis becomes one of choosing the remaining non-core products to add that maximise the reach. By forcing alternatives, the size of the search space is reduced.

### Mutually Exclusive Alternatives

An option to specify one or more sets of alternatives where the alternatives in each set must not appear in the same portfolio. The purpose is to avoid considering portfolios with two or more almost-identical alternatives, as these alternatives often receive similar responses and therefore are unlikely to appear in portfolios that maximise reach. By specifying mutually exclusive alternatives, the size of the search space is reduced.

### Minimum Portfolio Size

An option to specify the smallest portfolio size for which TURF optimization is conducted. This number must be at least the number of forced alternatives, at least the minimum alternatives per case and at least one. Specifying a higher minimum reduces the size of the search space.

### Maximum Portfolio Size

An option to specify the largest portfolio size for which TURF optimization is conducted. This number must be no more than the total number of alternatives but may be lower depending which alternatives have been excluded and which alternatives are mutually exclusive. Specifying a lower maximum reduces the size of the search space.

### Number of Top Portfolios to Display

An option to specify how many top portfolios to show, i.e. if this number is n, then the top portfolio until the nth ranked portfolio will be shown in the results. This number does not significantly affect the computation time but a large number may make the output results longer and more difficult to navigate. The default is one, meaning that only the top portfolio is shown.

### Optimization Methods

There are two optimization methods used in TURF, exhaustive and stochastic. The exhaustive method searches through all possible portfolios and is used for all cases, except when the search space so large that it would typically take more than a few seconds to run. In such a situation an option is provided to use the stochastic method instead, which is highly likely but not guaranteed to provide the exact list of optimal portfolios. This is because the stochastic method relies on randomly chosen starting points at which to begin the search. However, as the random seed is kept constant, the same results will be returned each time if the input options are unchanged.

The error rate of the stochastic method is very low. Tests have been conducted on real-world problems with 30 alternatives, for a range of portfolio sizes, both with and without forced and mutually exclusive alternatives. For each configuration, the stochastic method was repeated 1000 times (with a different seed) on the sample problem, with the resulting top 20 portfolios being correct in all 1000 runs.

### TURF Output Example

The output below was copied (without formatting) from the results of a TURF analysis on chewing gum flavors. There were 16 alternatives (flavors), with Spearmint chosen as a forced alternative and Strong Peppermint and Peppermint chosen as the first set of mutually exclusive alternatives and Eucalyptus and Menthol chosen as the second set of mutually exclusive alternatives. The minimum proportion was specified to be 20%, which meant that White Fruit was excluded. The minimum portfolio size was 3 and the maximum portfolio size was 5. The filter called Filter: Eat Gum Monthly+ and the weight called Weight: Days Chewing Gum Per Year were applied to the input data.

TURF Summary: Best Portfolios for Each Size
Size     Reach     Frequency
---------------------------------------------------------------------------  -----  --------  ------------
Peppermint OR Spearmint OR Strawberry                                            3    93.88%       334,201
---------------------------------------------------------------------------  -----  --------  ------------
Green Apple OR Peppermint OR Spearmint OR Strawberry                             4    96.61%       406,762
---------------------------------------------------------------------------  -----  --------  ------------
Green Apple OR Menthol OR Peppermint OR Spearmint OR Strawberry                  5    97.87%       484,720
---------------------------------------------------------------------------  -----  --------  ------------

Best Portfolios of Size 3
Rank     Reach     Frequency
---------------------------------------------------------------------------  -----  --------  ------------
Peppermint OR Spearmint OR Strawberry                                            1    93.88%       334,201
---------------------------------------------------------------------------  -----  --------  ------------
Fruit OR Peppermint OR Spearmint                                                 2    92.95%       319,214
---------------------------------------------------------------------------  -----  --------  ------------
Green Apple OR Peppermint OR Spearmint                                           3    92.91%       322,452
---------------------------------------------------------------------------  -----  --------  ------------

Best Portfolios of Size 4
Rank     Reach     Frequency
---------------------------------------------------------------------------  -----  --------  ------------
Green Apple OR Peppermint OR Spearmint OR Strawberry                             1    96.61%       406,762
---------------------------------------------------------------------------  -----  --------  ------------
Lemon OR Peppermint OR Spearmint OR Strawberry                                   2    96.44%       414,414
---------------------------------------------------------------------------  -----  --------  ------------
Orange OR Peppermint OR Spearmint OR Strawberry                                  3    96.17%       408,536
---------------------------------------------------------------------------  -----  --------  ------------

Best Portfolios of Size 5
Rank     Reach     Frequency
---------------------------------------------------------------------------  -----  --------  ------------
Green Apple OR Menthol OR Peppermint OR Spearmint OR Strawberry                  1    97.87%       484,720
---------------------------------------------------------------------------  -----  --------  ------------
Green Apple OR Lemon OR Peppermint OR Spearmint OR Strawberry                    2    97.71%       486,976
---------------------------------------------------------------------------  -----  --------  ------------
Eucalyptus OR Green Apple OR Peppermint OR Spearmint OR Strawberry               3    97.64%       467,480
---------------------------------------------------------------------------  -----  --------  ------------

List of All 16 Alternatives from Q22. Preferred flavour
%    Population
----------------------------------------------------------------------------------  --------  ------------
Strong peppermint                                                                     49.86%        89,070
----------------------------------------------------------------------------------  --------  ------------
Eucalyptus                                                                            33.99%        60,718
----------------------------------------------------------------------------------  --------  ------------
Fruit                                                                                 38.81%        69,324
----------------------------------------------------------------------------------  --------  ------------
Green Apple                                                                           40.62%        72,562
----------------------------------------------------------------------------------  --------  ------------
Lemon                                                                                 44.90%        80,213
----------------------------------------------------------------------------------  --------  ------------
Menthol                                                                               43.64%        77,958
----------------------------------------------------------------------------------  --------  ------------
Mint and passionfruit                                                                 25.75%        45,994
----------------------------------------------------------------------------------  --------  ------------
Orange                                                                                41.61%        74,335
----------------------------------------------------------------------------------  --------  ------------
Peach                                                                                 22.33%        39,890
----------------------------------------------------------------------------------  --------  ------------
Peppermint                                                                            71.97%       128,561
----------------------------------------------------------------------------------  --------  ------------
Spearmint                                                                             67.92%       121,329
----------------------------------------------------------------------------------  --------  ------------
Strawberry                                                                            47.20%        84,310
----------------------------------------------------------------------------------  --------  ------------
Sweetmint                                                                             36.88%        65,888
----------------------------------------------------------------------------------  --------  ------------
Vanilla                                                                               31.85%        56,899
----------------------------------------------------------------------------------  --------  ------------
Watermelon                                                                            29.27%        52,290
----------------------------------------------------------------------------------  --------  ------------
White Fruit                                                                           12.08%        21,572
----------------------------------------------------------------------------------  --------  ------------

Forced Alternatives

----------------------------------------------------------------------------------
Spearmint
----------------------------------------------------------------------------------

Mutually Exclusive Alternatives 1

----------------------------------------------------------------------------------
Strong peppermint
----------------------------------------------------------------------------------
Peppermint
----------------------------------------------------------------------------------

Mutually Exclusive Alternatives 2

----------------------------------------------------------------------------------
Eucalyptus
----------------------------------------------------------------------------------
Menthol
----------------------------------------------------------------------------------

Excluded Alternatives
Alternatives with % less than 20%

----------------------------------------------------------------------------------
White Fruit
----------------------------------------------------------------------------------

Note
Portfolios are ranked in terms of highest reach and then highest frequency.
The filter "Filter: Eat Gum Monthly+" has been applied to the TURF analysis.
The weight "Weight: Days Chewing Gum Per Year" has been applied to the TURF analysis.
Base n (unweighted total sample size): 1,230
Base Population (weighted total sample size): 178,632
Missing n (number of observations excluded due to missing data): 9

## Older Versions of Q

For versions of TURF prior to Q 4.8.6, a TURF analysis is run by:

1. Creating a Pick Any question containing the data of interest and selecting it in the blue drop-down menu.
2. Selecting SUMMARY in the brown drop-down menu.
3. Selecting the cells that containing the data to be compared (see the figure below).
4. Pressing (alpha) and scrolling through the outputs until you find the TURF Analysis section.

The first output produced is a TURF Summary. This shows the optimal alternatives (products or media) for a given portfolio size. For example, the table below shows that of the flavors in the analysis, if only 1 alternative was available, then Peppermint maximizes the reach with a reach of 66%, while if two alternatives are available, reach is maximized by offering both Strawberry and Peppermint, and the resulting reach for these two alternatives is 84.89%, etc.

In this example, only six alternatives have been included in the analysis so Q only shows reach for up to six alternatives. The more alternatives included in the TURF analysis, the more portfolios that need to be tested. For example, where there are 20 alternatives, then there are

• 20 portfolios involving 1 alternative (i.e., each alternative on its own)
• 190 portfolios involving different pairs of alternatives
• 1,140 portfolios offering different triples of alternatives
• 184,756 portfolios involving ten alternatives.

To avoid situations where users inadvertently request a TURF that will take too long time to compute, Q only examines portfolio sizes that will involve less than 1,000,000 combinations of alternatives. In practice, this means that Q does not evaluate larger portfolios when there are more than 22 alternatives (e.g., with 23 alternatives, Q only examines portfolios of size 9 or less; with 24 alternatives, 8 or less, etc.).

In addition to the TURF Summary, Q computes the top portfolios for each of the portfolio sizes. Where the portfolio size consists of more than 100 combinations of alternatives, only the top 100 are shown (additional portfolios of interest can be created using Create NET.