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TURF Analysis

Portfolio tool

Choose the set that reaches the most people, not the set with the highest individual scores. The three most popular items often appeal to the very same customers.

👨‍🏫 Professor Mode: Guided Learning Experience

New to TURF? Professor Mode walks you through the case where the three favourites all talk to one audience.

OVERVIEW & WHAT THIS TOOL SOLVES

When you can only put 3 flavors in a freezer case or bundle 4 features into a subscription tier, picking the top-scoring items from a survey is a classic product-line mistake: the #1, #2, and #3 favorites often appeal to the exact same mainstream buyers while leaving a huge niche segment empty-handed. TURF (Total Unduplicated Reach and Frequency) searches every possible item combination of size k to find the portfolio that reaches the maximum number of unique customers at least once.

🎯 Questions It Answers

  • Which combination of k items (flavors, SKUs, ad channels, or features) maximizes total unduplicated customer reach?
  • How many percentage points of audience reach do we lose if we naively launch the k individually most popular items?
  • How much incremental reach does each added item bring on the sequential expansion ladder, and what if an item is locked in or excluded?

📂 What Data You Need

  • Respondent × Item Matrix: Survey or purchase rows where each column records a respondent's interest/rating for an item
  • Reach Threshold Rule: Binary 0/1 indicator or rating cutoff (e.g., Top-2-Box ≥ 4 on a 5-point scale)
  • Portfolio Size & Constraints: Target line size k, plus optional must-include locks or must-exclude bans

💡 What You'll Discover

  • Optimal vs. Popular Portfolio Gap: Exact unduplicated reach and average frequency of the TURF winner vs. the naive top-k set
  • Incremental Reach Ladder & Shapley Credit: Step-by-step reach expansion from 1 to k items and fair Shapley attribution
  • Segment & Constraint Diagnostics: How the winning line performs across customer tiers and what locking a boss's pet SKU costs
🔍 Key Nuances & Common Traps to Watch For
  • Why Individual Popularity Fails at Portfolio Design: If Chocolate (55%) and Fudge Brownie (50%) are loved by the exact same chocoholics, launching both adds almost zero new shoppers—whereas Mango Sorbet (28%) may bring in an entirely distinct audience.
  • Reach vs. Frequency Trade-Off: Customer acquisition and shelf space usually prioritize Reach (attracting at least one buy from as many shoppers as possible), whereas variety packs for existing loyalists care more about Frequency (how many options each reached shopper likes).
  • Check Near-Tied Portfolios: Often the #1 and #2 portfolios differ by less than 0.5 percentage points of reach; inspect the Top Portfolios table so supply-chain cost or margin can break statistical ties.
Try this: Load the first case study, compare the TURF-optimal line against the Most-popular line at k = 3, and check which favorite got swapped out to bring in new shoppers.
📐 Under the Hood: Model Equations & Variable Definitions

1. Unduplicated Portfolio Reach & Average Frequency

\[ \text{Reach}(S) = \frac{1}{N} \sum_{i=1}^{N} w_i \cdot \mathbb{I}\!\left( \sum_{j \in S} a_{ij} \ge 1 \right), \qquad \text{Freq}(S) = \frac{\sum_{i=1}^{N} w_i \sum_{j \in S} a_{ij}}{\sum_{i=1}^{N} w_i \cdot \mathbb{I}\!\left( \sum_{j \in S} a_{ij} \ge 1 \right)} \]

💬 Read it in plain English: A customer i is counted as "reached" (indicator = 1) if they like at least one item in portfolio S—no matter whether they like 1 item or all k items—while Frequency averages how many items in S each reached customer likes.

S, k
Candidate Portfolio & SizeYOUR DATA ⓘ
Subset of items S with cardinality |S| = k evaluated by the combinatorial search.
N, wi
Sample Size & Respondent WeightYOUR DATA ⓘ
Total respondents N and sampling weight w_i (defaults to 1, normalized over N).
aij
Binary Appeal IndicatorYOUR DATA ⓘ
Equals 1 if respondent i’s score on item j meets the appeal threshold τ, and 0 otherwise.
Reach(S)
Unduplicated Portfolio ReachOUTPUT ⓘ
Proportion of the audience that finds at least one appealing item in portfolio S.
Freq(S)
Average Reached FrequencyOUTPUT ⓘ
Mean number of appealing items in S per reached respondent.

2. Marginal Reach Lift (Removal Loss) & Combinatorial Objective

\[ S^* = \arg\max_{|S| = k} \text{Reach}(S), \qquad \Delta \text{Reach}(j \mid S) = \text{Reach}(S) - \text{Reach}(S \setminus \{j\}) \]

💬 Read it in plain English: TURF finds the k-item subset S* that maximizes unduplicated reach, and measures each item's unique contribution ΔReach(j | S) by how much reach drops if item j is removed from the portfolio.

S*
Optimal TURF PortfolioOUTPUT ⓘ
The size-k combination achieving the highest unduplicated reach (ties broken by frequency).
ΔReach(j | S)
Unique Removal Loss of Item jINFERENCE ⓘ
Share of respondents who like item j and no other item in portfolio S.

Step 1 DATA SOURCE

Each case study is a real portfolio decision with a fixed number of slots. Start with Frost & Fold Creamery if this is your first time — twelve flavors, three freezer slots, and a clear overlap trap. Or upload your own survey: one row per respondent, one column per item.

📚

Use a Case Study

📤

Upload Your Data

Drag & Drop raw data file (.csv, .tsv, .txt)

One row per respondent, one column per item. Accepts MaxDiff scores (score_ columns, continuous/ratio 0–100 per respondent), ordinal rating scales (e.g., 1–5 or 1–10 Likert), or binary 0/1 acceptance. Optional weight and categorical segment columns are picked up if present.

Clean or reshape in Import Wizard →
No file uploaded.

Step 2 How many can you offer?

Two decisions, and the second one matters more than it looks. Portfolio size is how many slots you actually have. What counts as reached is where you draw the line between “would buy” and “merely does not hate it” — and moving that line can change which set wins. Decide it on business grounds before you look at the answer, not after.

The number of items you can actually launch. Shelf space, budget or contract terms usually decide this before the analysis starts.

This is a modelling decision, not a detail. Settle it before you look at the answer.

Constraints — lock items in or rule them out

A contract, a supply limit or a brand rule can decide part of the set before the data does. Reach can only fall when you force a choice; that drop is what the constraint costs. Each item shows its solo popularity rank and acceptance rate.

Step 3 Read the answer

Start with the box below, which says in one sentence which set to launch and what it buys you over the obvious choice. Everything after it is the evidence: which items earn their slot, how much is left to gain, and whether a different judgement call would have given you a different answer.

Reach of the best set
—
What the swap buys you
—

Most popular vs. widest reach

Two sets of the same size, side by side. Popular is what you get by ranking items and taking the top few. Widest reach is the set TURF chose. The length of each bar is the share of people who would take at least one item from that set — and in stacked mode each slice shows how many new people the 1st, 2nd and 3rd item brought in.

📊 How to Read This Chart
  • Watch the 2nd and 3rd slices in the Popular bar. When popular items share the same fans, the first item grabs a big slice and the 2nd and 3rd items add tiny slivers.
  • Watch the swapped items in the Widest-reach bar. An item with a lower solo rank earns its slot by adding a thick slice of customers the first item missed.
  • Almost no gap is a real and useful result too. It means the popular items already reach distinct audiences, and ranking would have served you fine. Report that rather than inventing a story.
  • The bars count people, not purchases. Somebody who would take four of your items still counts once.

Individual item appeal vs. portfolio selection

Every candidate ranked from most popular to least popular on its own. Notice which items are dropped from the popular top-3 because their fans are already covered, and which lower-ranked items jump into the winning TURF set because they reach a distinct crowd.

📊 How to Read This Chart & Full Item Table
  • ★ Chosen + Popular (Blue): High individual appeal and part of the reach-optimal portfolio (usually the #1 anchor item).
  • ▲ TURF Swap-In (Teal): Lower individual rank, but chosen by TURF because its fans do not overlap with the anchor item.
  • ✕ Popular but Redundant (Amber): In the top-3 individually, but dropped by TURF because most of its fans already accept another chosen item.
Solo Rank Item Solo Reach Portfolio Role

What to watch

    Top portfolios

    The best combinations, ranked by reach. Look at the top few rows together, not just the first one. If several sets land within the sampling margin of each other they are effectively tied, and the choice between them belongs to supply, operations or brand fit rather than to this table. Click any row to compare its breakdown against #1.

    # Items Reach Frequency Gap vs #1 Notes

    Frequency is the average number of these items a reached respondent would take. It is averaged over reached respondents only, so it never falls below 1.

    Would a different rule change the answer?

    You had to decide what counts as “would buy”, and that was a judgement call. This re-runs everything under the neighbouring rules. If the same set wins throughout, your answer is robust and you can say so. If the winner moves, your recommendation depends on a line you drew — and that belongs in the write-up rather than hidden in a footnote.

    Rule Best set under that rule Reach Same answer?

    What each item adds

    A cumulative waterfall showing the new people each item brings in on top of everything chosen before it, building up to the total portfolio reach. A tall first step and shorter ones after it is normal: the first item has the whole market to win, and every later item can only pick up whoever is left.

    Items are added in the order that grows reach fastest, so each step is what that item contributed on top of the ones before it, not its reach on its own.

    📊 How to Read This Chart
    • A near-zero bar means little additional reach at this position in the ladder. Use removal loss above to judge what the full portfolio would lose by dropping this item.
    • Order matters. An item looks weak here partly because of what came before it. Swap the order and the same item could look strong, which is why you judge the set, not the ranking.
    • This is the chart to use when someone asks “why is that in the lineup?” — the bar is the answer.

    How many do you need?

    Reach as you allow yourself more slots. The elbow is the decision. Before it, each extra item is still winning new customers; after it, you are mostly paying to sell more to people you already reach. The vertical line marks your current portfolio size k = 3.

    Where the line flattens, extra items stop buying new people and start buying frequency from people you already had.

    📊 How to Read This Chart
    • Find where the line bends and compare it with the number of slots you actually have. If the bend is below your budget, you can launch fewer items and lose almost nothing.
    • The dashed ceiling line at the top shows the maximum possible reach if you offered every item on the list (100% minus the unreached share).
    • The curve can never go down. Adding an item cannot take a customer away, so a flat stretch means “no new people”, not “worse”.

    Who overlaps with whom

    This is the chart that explains why the popular set loses. A dark cell means the two items are chasing the same people, so putting both in your lineup buys you very little. A pale cell means they appeal to different crowds — which is exactly the pairing that grows reach. Items in the winning set are marked with ★.

    Each cell reads: of the people who accept the row item, what share also accept the column item. It is deliberately asymmetric, because a small item can sit entirely inside a large one without the reverse being true.

    📊 How to Read This Chart
    • Read along a row: “of everyone who likes this row item, what share also likes that column item?”
    • The grid is not symmetric, and that is the point. A niche item can be almost entirely contained inside a popular one — 90% one way, 15% the other. Only the first number means “this item is redundant”.
    • Look for a pale row. An item that overlaps with nothing has an audience all of its own, and it will usually appear in the winning set even with an unremarkable score.

    Methods and results

    Managerial interpretation

    Take it with you

    Exploratory questions

    All of these are answerable with the controls above. The last two are the ones worth arguing about in class.

    1. How much does popularity cost you? With Frost & Fold at three slots, compare the reach of the best set against the reach of the most popular. Multiply that gap by a market of 50,000 shoppers. How many people is it?
    2. Which item is carrying the set? Compare What each item adds (the sequential ladder) with What does each selected item contribute? (Shapley credit and removal loss). Why does the first item in the ladder look larger than its removal loss?
    3. When should you stop? Use How many do you need? to find the elbow. If each extra flavor costs $40,000 a year in production, where would you stop, and what reach would you be giving up?
    4. Does the answer survive your judgement call? Change what counts as reached from a 4-or-5 to a 5-only. Does the winning set change? What would you tell a client who asks which rule is “correct”?
    5. Is a tie really a tie? Find two portfolios within half a point of each other in Top portfolios. On what grounds would you choose between them, given the data cannot?
    6. Who are you leaving out? Load CivicPulse and look at Does it work for everyone? A set can reach most of the population and still miss a group badly. When is the highest-reach set the wrong recommendation?