Common mistake 1 with TURF - reach of a product line

Assuming the highest-reaching item belongs in the line. It often does not, and the sample here demonstrates it.

Common mistake 2 with TURF - reach of a product line

Comparing reach figures across studies with different thresholds. They are not comparable at all.

Common mistake 3 with TURF - reach of a product line

Reading a 90% reach as 90% market share. It is the share of respondents who said they would buy something - a ceiling on interest, not a forecast.

Common mistake 4 with TURF - reach of a product line

Searching over many line sizes and reporting the best. The maximum of many combinations is biased upward - with twelve items there are 220 three-item lines, and the best of them is partly the best sample draw.

EconStatsCraft › TURF - reach of a product line

TURF - reach of a product line

Which combination of items satisfies the most people. A preference ranking says which item is best; this says which three together reach furthest, and the answers differ whenever tastes overlap - the second-best item is often redundant.

What it needs

Respondent
Item
Would buy (0/1) - Threshold a rating first if that is what you have.

The intuition

Total unduplicated reach and frequency asks which small set of products reaches the most DIFFERENT people. It is not a ranking exercise: the best individual item is often absent from the best bundle, because the people it reaches are already covered by cheaper companions. What matters is not how good an item is but how much of the population it adds that nothing else in the line covers.

When to use it

Assortment and range decisions: which flavours to stock, which SKUs to keep, which package of benefits to offer. Any question where you can only offer a few things and want to leave as few people out as possible.

Where the estimator comes from

Let R_{ij}=1 if respondent i would buy item j. The reach of a set S is \text{Reach}(S)=\frac{1}{n}\sum_i \mathbf{1}\!\left[\textstyle\bigcup_{j\in S}R_{ij}=1\right], the share covered by AT LEAST one member. Maximising this over sets of size k is the maximum coverage problem, which is NP-hard, so exhaustive search is only feasible for small k and modest item counts - \binom{20}{4} is 4,845 and fine, \binom{50}{6} is 15.9 million and not. The greedy algorithm - repeatedly add whichever item adds the most new reach - is guaranteed to reach at least 1-1/e\approx63\% of the optimum (Nemhauser, Wolsey and Fisher, 1978), and in practice much closer, but it is NOT optimal.

The model

\text{reach}(S)=\frac{1}{n}\sum_{r=1}^{n}\mathbf{1}\!\left[\exists\, i\in S:\ y_{ri}=1\right]

What it assumes

A binary "would buy" per respondent per item, which means you chose a threshold. A top-two-box definition reaches more people than a top-one-box definition and can reorder the line, so the threshold is a decision to report.
That reach is the objective. It counts people, not volume, margin or the cost of making one more variant - a line optimised on reach alone tends to sprawl.
That everyone reached is worth the same. They are usually not.
That the items in the line do not change how respondents feel about each other. Reach is computed by unioning individual answers, which assumes adding a second flavour neither cannibalises nor enhances demand for the first.

Statistical properties

Reach is submodular: each additional item adds less than the one before, because the uncovered population shrinks. That diminishing return is what produces the characteristic flattening curve and what justifies stopping at a small line.
The greedy path and the optimal set genuinely differ. Greedy commits to the best first item and cannot undo it, while the optimal set may contain no item that would have been chosen first.
TURF ignores volume entirely. A line reaching 90% of people who each buy one unit is worse business than one reaching 60% who buy ten, and nothing in the method knows that.
The reach definition drives everything. "Would buy" from a survey is a stated intention, and shifting the threshold to "top-two box" changes the answer as much as changing the algorithm.
It assumes the items are substitutes drawn from one budget. Cannibalisation within the line is captured; the possibility that an extra flavour grows total category demand is not.
With many items and a large k the search must be heuristic. Report which algorithm was used, because exhaustive and greedy give different lines.

How to read the output

The incremental column is the point. The gap between an item’s own reach and what it ADDS is duplication - people it appeals to who are already covered.
Once the incremental reach flattens, further items are buying almost nothing. That is the natural stopping point for a range.
The best line and the greedy build can differ, and the module says which method was used. Greedy picks the biggest item first and can be beaten - in the sample here it reaches 89.6% while the exhaustive best line reaches 90.2% without that item at all.
Reach is a ceiling, not a forecast. It counts everyone who said yes to at least one item, with no allowance for distribution, price, awareness or the fact that stated intention overstates purchase.

A worked reading

Twelve flavours, 500 respondents. Mango has the single largest reach at 62.4% - run the MaxDiff module on the same data and it also ranks first on preference share - and yet the best three-flavour line is Coffee, Strawberry and Vanilla at 90.2%, with Mango nowhere in it. The greedy build shows the mechanism: taking Mango first (62.4%) then Coffee adds 22.6 points of INCREMENTAL reach for 29.2% of its own, and Lemon then adds only 4.6 more, ending at 89.6%. The optimising search finds 90.2% by giving up the strongest single item for three that overlap less. That is the whole lesson of TURF and the reason a ranking cannot be read as a shortlist: the second item is chosen for who it reaches that the first does not, so an item can be everyone's second favourite and still earn its place ahead of the winner.

Symptom → diagnosis → what to do

If you see this	It means	Do this
The top-scoring item missing from the best line	Correct and the central insight	Its buyers are covered by others
Reach flattening after three items	Submodularity	The natural place to stop the line
Greedy and exhaustive disagreeing	Expected; greedy is not optimal	Use exhaustive where the combinatorics allow
Reach near 100% with few items	The reach threshold is too generous	Tighten it to a top-box definition
Every combination scoring alike	Preferences are undifferentiated	TURF has nothing to find here
A high-volume item excluded	TURF counts people, not units	Weight by expected volume if that is the goal

Common mistakes

Assuming the highest-reaching item belongs in the line. It often does not, and the sample here demonstrates it.
Comparing reach figures across studies with different thresholds. They are not comparable at all.
Reading a 90% reach as 90% market share. It is the share of respondents who said they would buy something - a ceiling on interest, not a forecast.
Searching over many line sizes and reporting the best. The maximum of many combinations is biased upward - with twelve items there are 220 three-item lines, and the best of them is partly the best sample draw.

Where to read this properly

Nemhauser, Wolsey and Fisher (1978), "An Analysis of Approximations for Maximizing Submodular Set Functions", Mathematical Programming 14(1).
Miaoulis, Parsons and Free (1990), "Turf: A New Planning Approach", Marketing Research 2(1).
Krause and Golovin (2014), "Submodular Function Maximization", in Tractability.

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Conjoint analysis · MaxDiff (best–worst scaling) · Price sensitivity (Van Westendorp) · Market basket analysis · Perceptual map · Scale reliability (Cronbach’s alpha) · Key driver analysis

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TURF - reach of a product line

What it needs

The intuition

When to use it

Where the estimator comes from

The model

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

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