Price per unit analysis: how to normalize units and compare packs

Convert every pack to total quantity in the category’s one unit before dividing. Total quantity is count times size each. The factors below come from the NIST conversion tables.

Multipacks, variety packs and combination packs

• Multipack of one product. Total quantity is count times size each. Twelve 12 fl oz cans are 144 fl oz.
• Variety pack of one size. Flavors of the same size and brand are one pack, with one unit price.
• Combination pack of different products. A shampoo-and-conditioner set has no single unit price. NIST notes the uniform unit pricing regulation exempts variety and combination packages. Leave them out of unit-price comparisons or compare each component.
• Ambiguous sizes. A range, an “up to” claim, or a title such as “2 x 24 ct” that can be read two ways should go to review, not to a guess.

When a per-use unit changes the answer

Per ounce favors a dilute product. A concentrate has fewer ounces and the same number of uses, so a per-ounce comparison between the two is misleading. Add a per-use measure, labeled as a second metric, and show both.

“The average price per ounce” names at least three different numbers. Each answers a different question.

• Mean of the unit prices. Treats every pack as equal. It answers: what does a typical pack cost per ounce?
• Total dollars over total ounces (a ratio of sums). Weights each pack by what was sold. It answers: what did a typical ounce cost?
• Median. The middle value, of the packs or of the units sold. It resists outliers and moves in steps.

Take two packs at fixed prices: the 12 oz at $4.80 (40.0¢ per oz) and the 64 oz at $16.00 (25.0¢). In one period the 12 oz sells 900 units and the 64 oz sells 100. In the next the mix shifts to 700 and 300. No price changes.

What a shelf snapshot cannot tell you

A price list has no sales weights. From a catalog or a shelf scan you can compute the mean and the median of pack points and the median by brand. You cannot compute a ratio of sums, and any figure that looks like a market price per ounce is not one. Say “median across pack points” and give the count.

The median trap

A median of pack points counts packs, not ounces or purchases. It reflects how many sizes exist at each price. Take eight pack points: 5 small packs at 40¢ per ounce and 3 large ones at 25¢. The median is 40.0¢, though the large packs hold most of the ounces. Delist two of the small packs and the median falls to 32.5¢, a move of −18.8% with no price change. Compare at matched sizes, or report medians per size band, so assortment breadth does not move the result.

How small a sample can be

No standard sets a minimum. This is our own working rule: print the count next to every median, do not report a median from fewer than five pack points, and add the range when there are fewer than ten. Here is why. Five pack points have unit prices of 22, 25, 27, 30, 41 cents per ounce, with a median of 27.

Two prices exist for one pack. Regular price is the price without any deal. Shelf price is what a shopper pays today: the deal price when there is one, otherwise the regular price. Use regular price to judge structure, since a one-week deal should not look like a pricing mistake. Use shelf price to describe what shoppers pay now. Never put both in one average.

Brands: match the size, then state the direction

Compare two brands at the same total size and format, with the same price type. The gap between them has two correct values depending on which brand is the base. Say which.

Sizes: use the curve, not a straight line

Brands rarely sell the same sizes. Compare a pack with what packs of its size cost in the category by reading both from a fitted curve of unit price against size. Pack price ladders shows how to draw it.

Retailers and time

• Retailers. Compare the same unit, the same price type and the same day. Tag unit prices can differ across chains because of unit choice and rounding, so recompute from the pack price and size.
• Time. Track the same pack points over time. Do not compare an average over a set of packs that changed. A new size entering the set moves an average with no price change.

NIST SP 1181 recommends showing unit prices at or above $1.00 to the nearest cent. Below $1.00, round to the nearest cent or to the nearest tenth of a cent, and use one method, not both. For analysis, keep full precision and round only when the number is shown, as the toilet roll example showed. Define your display rule once. In this article cents per ounce show one decimal in tables, so 6.250¢ per fl oz shows as 6.3¢.

Keep the raw quantities and derive the unit price, so every number can be audited. A column for total quantity in the base unit, then one division. The two averages differ by one line of SQL.

-- one row per pack point; flavors of a size are averaged first
SELECT brand, subsegment, total_oz,
       AVG(regular_price)             AS regular_price,
       AVG(regular_price) / total_oz  AS price_per_oz
FROM   products
WHERE  regular_price IS NOT NULL
GROUP  BY brand, subsegment, total_oz;

-- ratio of sums (needs units sold) against a mean of ratios
SELECT SUM(units * price) / SUM(units * oz) AS dollars_over_ounces,
       AVG(price / oz)                      AS mean_of_unit_prices
FROM   sales;

In a spreadsheet, the same rule is SUMPRODUCT(units, price) / SUMPRODUCT(units, ounces) for the first and AVERAGE of a unit-price column for the second. Put the unit in the column header, and put the price type (regular or shelf) in it too.

1. Choose one unit per category from the packs on the shelf. Record the choice.
2. Convert each pack to total quantity in that unit. Send ambiguous sizes to review.
3. Leave combination packs out. Treat variety packs of one size as one pack.
4. Choose regular or shelf price and label every number with it.
5. Name the average: mean of pack points, ratio of sums, or median. Print the count.
6. Compare at matched sizes. State the base of every gap.
7. Compute at full precision. Round at display with one rule.

1. Comparing fluid ounces with ounces.
2. Comparing pack prices when count, size or sheets per roll differ. The CMA found one retailer’s branded and store-brand fish fingers both came in packs of 30, but the store-brand pack weighed about 7% more, so a gap of 11% on pack price was 19% per unit.
3. Averaging unit prices without weights and calling the result the market price.
4. Mixing regular and deal prices in one average.
5. Trusting a shelf tag’s unit price across chains that round or choose units differently.
6. Treating a variety or combination pack as comparable.
7. Using per serving when manufacturers define servings differently. Show per ounce and per serving separately.
8. Ignoring concentration. Per ounce favors dilute products in laundry and cleaning.
9. Reading unit price as value. A smaller pack can be the right buy for storage, waste or budget. The CMA says that not every shopper can trade up.
10. Parsing sizes from titles without validation.

• Mixed dimensions. A category sold by both weight and volume has no single honest unit. Split it, or use count.
• Density. Converting volume to weight needs the product’s density. A fluid ounce of water weighs about 1.04 oz, and the figure changes with every liquid.
• Pack size is not use. Concentrates, cups per bag and loads per bottle break a per-ounce comparison. Add a per-use view.
• Stock-up economics. A lower unit price helps only if the shopper can store and use the quantity.
• Thin samples. Under five pack points a median is a single pack’s price in disguise.
• Snapshots. The CMA notes that its own examples may not hold over time. The same is true of a shelf scan.

Shelfprice converts each Kroger group pack to one unit per category, rolls flavors up to brand, subsegment and total size, and keeps regular price and shelf price apart. It has shelf prices and sizes but no sales, so it reports medians and counts, not ratios of sums. The price tracking page describes the product.