What a dog food label
does not tell you.

The problem

Two labels, no way to compare them.

One label says 26% protein. Another says 9%. The second is not a third of the first, it is mostly water. Dry matter removes the water but not the energy density, and a dog is fed calories rather than kilograms. Everything therefore converts to grams per 1,000 kilocalories, the basis the AAFCO profiles are written on and the only one on which a kibble, a can and a fresh diet sit in one column.

grams per 1,000 kcal = (nutrient % as fed × 10,000) ÷ kcal per kg

Both inputs come off the label. But the first one is a promise. A guaranteed analysis states a minimum for crude protein and crude fat, and a maximum for crude fiber, moisture and ash. The real food is normally on the other side of those numbers, and the label never says by how far. Converting a printed 26% into a single figure is false precision. The honest output is a range, and that range has to be measured.

Method

Defining a margin.

For one product, the margin is the ratio of its typical or measured content to its own printed guarantee, same product, both as fed.

margin = typical % ÷ guaranteed %

A ratio rather than a difference in percentage points, so the figure transfers between products of different nutrient density. Margins on minima come out above 1.00, margins on maxima below it. Each is reported as the 10th, 50th and 90th percentile of the observed distribution rather than the observed minimum and maximum, so one atypical product cannot set the bounds for an entire format.

This was tested rather than assumed. The ratio model was compared against an additive percentage-point model on every format-by-nutrient cell by coefficient of variation, and won on all but one: kibble protein 0.06 against 0.76, kibble fat 0.13 against 1.24, canned fat 0.31 against 0.94. In the canned fat cell the difference model produces a negative 10th percentile, which is unpublishable. The single exception is canned crude fiber, discussed under limits.

Results

The margins.

122 usable paired observations from 155 recorded. Multipliers applied to the printed guarantee. Minima are floored at 1.00 and maxima capped at 1.00.

Fresh and semi-moist carry no fiber margin: too few paired observations.

Semi-moist has no ash figure at all, so carbohydrate is withheld for that food type rather than borrowing another type's ash.

The load-bearing finding

The calorie denominator does not move.

The conversion divides nutrient percentage by the label's stated calorie density, so it matters whether inflating the numerator should also inflate the denominator. It should not. AAFCO Model Regulation PF9 requires a calculated calorie statement to be derived from average values, with fiber, moisture and ash determined in the same manner. The printed calorie figure therefore already reflects the real protein and fat.

This was verified empirically on 40 products across Purina and Hill's. Typical values reproduced the printed kcal/kg in every case, to within 0.2 to 2%. Guaranteed values came out 7 to 15% low on kibble and 19 to 47% low on cans, and won zero times. The margin is applied to the numerator alone. Getting this wrong returns 59.7 to 78.5 grams per 1,000 kcal on a 26/16 kibble at 3,800 kcal/kg, where the correct answer is 68.4 to 80.3.

Two derivations

Recovering what labels omit.

Ash back-solve

Ash is rarely stated on a label and is needed to derive carbohydrate by difference. Because the calorie statement is computed by modified Atwater from typical values, the identity can be inverted:

ash = 100 − CP − CF − crude fiber − moisture − [(kcal/kg ÷ 10) − 3.5·CP − 8.5·CF] ÷ 3.5

This reproduced Hill's own published ash on all 27 SKUs where it could be checked, to within 0.06 percentage points. It doubles as a pairing test: a row that back-solves to an impossible ash figure is a guarantee and a typical table taken from different formulations, and was excluded.

As-fed recovery

Hill's publishes average nutrient content on a dry-matter basis only, with no typical moisture figure. Inverting the calorie statement recovers it: the dry-matter fraction is the stated as-fed kcal/kg divided by the kcal/kg the dry-matter table implies. This recovers typical moisture exactly rather than assuming a value.

Decisions

Three choices, and why.

Pooling at equal weight

Two independent populations were used: manufacturer-published typical analysis paired with the same SKU's guarantee, and single-lot proximate assays published by state feed-control laboratories. They differ materially and significantly. Therapeutic and premium canned products run about 1.34 times their protein minimum where mass-market grocery cans run about 1.14 times. Pooling by raw sample count would make the published percentile an artefact of how many rows each source happened to yield, so the two populations are pooled at equal weight as a stated rule.

Clamping at 1.00

Margins on minima are floored at 1.00 and on maxima capped at 1.00. Unclamped, kibble protein p10 was 0.983 and fat p10 was 0.934. The clamp is evidenced rather than cosmetic: zero of the 28 manufacturer typical protein values and zero of the 22 fat values fall below their own guarantee. The entire sub-1.00 tail comes from single-lot assays, most of it inside AAFCO's own analytical variation, which tolerates a compliant protein sample down to about 0.97 times and fat to about 0.90 times. That tail is measurement error plus a small number of genuine misbranding cases. Neither is what this models.

Kibble moisture follows the retail bag

This is the one cell not taken from the equal-weight pool. Manufacturer typical moisture runs about 0.75 of the guaranteed maximum because it is measured at production. Regulatory assays of retail bags run about 0.55, and Hill et al. 2009 gives 0.59 across 750 dry samples. The divergence is mechanical: a bag equilibrates downward in distribution while a sealed can cannot, which is why canned moisture shows no such split. The quantity that matters is the moisture in the bag someone actually owns, so the assay evidence wins. Each percentile traces to one named source: p10 is the regulatory-assay p10 (n=20), p50 is Hill et al. 2009 (n=750), p90 is the manufacturer-typical p90 (n=22).

Data

Every source, named.

No Wynwood product is in the dataset. Royal Canin canned rows were dropped: their printed calorie statement does not reproduce under modified Atwater, so the pairing could not be verified. Treats and biscuits were excluded, as were repeat lots, calorie-mismatched pairings, and products printing both a minimum and a maximum fat.

Validation

Checked against the largest study in the field.

Hill RC et al., JAVMA 2009;234(3):347-351, reports 2,208 paired guarantee-and-assay observations from 204 manufacturers, split by form. It was used for validation only and contributed no rows. The kibble and canned margins derived here reproduce it. The fresh and semi-moist rows are thin, are marked low confidence, and are not validated against it.

Limits

What this does not support.

• Dry moisture is the weakest cell, even though kibble is the best-evidenced format. The guaranteed maximum barely predicts actual moisture in dry products, R squared 0.23, because nearly every kibble guarantees 10 to 12% while actuals range 4 to 9% independently of that.
• Canned fiber is the least trustworthy number here. It rests on manufacturer data alone, because the Connecticut laboratory reports canned crude fiber rounded to 1.0%, a reporting floor rather than a measurement, and it is the one cell where the additive model beat the ratio model.
• Canned fat is very wide, and the width is real. Wet guarantees are set very low, a 1.0 to 2.5% fat minimum on a stew being routine, so a can printing 2.5% can genuinely hold 5.4%.
• One band per format is a simplification. Overage shrinks as the guarantee rises, consistently. Branching on the size of the printed guarantee is the obvious next version.
• The fresh row rests on six products. Fat in the underlying studies was determined by acid hydrolysis and fiber as total dietary fiber, neither being the method the guarantee is legally defined against, so the fresh fat multiplier is biased slightly high.
• The semi-moist row is not a diet-grade figure. Every contributing observation is a soft chew, roll or semi-moist treat. No complete semi-moist dog food with a published typical analysis could be found.
• Amino acids, vitamins and trace minerals are not on labels, so nothing here speaks to them.
• A guaranteed analysis says nothing about digestibility, ingredient quality, or whether the diet was ever fed to a dog. This compares what is declared. It does not compare foods.

Worked example

A 26% protein kibble at 3,800 kcal/kg.

The calorie figure is not adjusted. The printed calories already reflect the real protein and fat.

References

Works cited.

1. Association of American Feed Control Officials. Model Regulation PF9, calorie content statements.
2. Hill RC, Choate CJ, Scott KC, Molenberghs G. Comparison of the guaranteed analysis with the measured nutrient composition of commercial pet foods. J Am Vet Med Assoc. 2009;234(3):347-351.
3. Oba PM, Utterback PL, Parsons CM, Swanson KS. Chemical composition, true nutrient digestibility, and true metabolizable energy of chicken-based ingredients differing by processing method using the precision-fed cecectomized rooster assay. Transl Anim Sci. 2021;5(3):txab071.
4. Oba PM et al. Transl Anim Sci. 2024;txae163.
5. Vecchiato CG et al. Nutritional and microbiological quality of commercial raw meat-based diets for dogs. Animals. 2022;12(18):2395.
6. South Dakota Department of Agriculture and Natural Resources. Commercial Feeds annual reports, 2020-2024.
7. New Jersey Department of Agriculture. Analytical Report, commercial feeds, 2014-2015.
8. Connecticut Agricultural Experiment Station. Technical Bulletins TB24, TB43, TB45.