Two Numbers, One Herd: Michigan's Reporting Gap

Ask how many deer Michigan hunters killed in 2022 and there are two correct-looking answers: 303,054 and 258,906. The first is the state's mandatory harvest registration; the second is its hunter-survey estimate. They describe the same herd, in the same year, from the same agency. And they differ by more than forty-four thousand deer. In 2023 the same two instruments landed within six thousand of each other. Two numbers, one herd, a gap that is enormous one year and small the next: this is a paper about which number to trust, and about why the honest answer is to refuse to blend them.

Most of what people call "the harvest number" is really the output of one measurement instrument, and Michigan runs two of them. The first is mandatory harvest registration: hunters are required to report the deer they take, and the state tallies those reports into a county-level count. The second is a hunter-survey estimate: after the season, a sample of license holders is surveyed about their success, and the responses are expanded statistically into a statewide-and-regional estimate. Both are legitimate; neither is the herd itself. Registration captures what hunters actually reported: complete in principle, but subject to non-compliance and reporting error. The survey estimates what hunters did: robust to individual reporting gaps, but carrying sampling error and modeling assumptions. Ask the two instruments the same question and, unsurprisingly, they give two answers.

Michigan's mandatory registration is recent, so there are three seasons where both instruments report the same herd side by side. The contrast is the whole paper. In 2022 registration counted 303,054 deer against a survey estimate of 258,906: a gap of 44,148, or 17.1%. That is not a rounding difference; it is a small county's worth of deer, the distance between a good year and a mediocre one, riding entirely on which instrument you read. Then in 2023 the two nearly converged: 274,282 vs 268,177, a gap of 6,105, or 2.3%. And in 2024, 299,492 vs 291,994: 7,498, or 2.6%. The instruments agree well in two years and diverge sharply in the third, and nothing on the face of the numbers tells you in advance which kind of year you are in.

Two official numbers for the same deer herd, from the same agency, in the same year. They disagree by up to seventeen percent. The honest move is not to average them.

The intuitive fix (split the difference, report the average) is the one thing the data forbids. Averaging two instruments assumes they are two noisy reads of the same quantity that will cancel out, and that is not what these are. They cover different geographies (83 registered counties versus roughly 60 modeled units), carry different and non-independent error structures, and behave differently from year to year, as the swing from a 17% gap to a 2% gap shows. A blend would manufacture a third number that no measurement produced, hide the disagreement that is itself the useful signal, and quietly change its own meaning whenever the gap moved. Worse, it would break comparability: a figure that is 50% registration in one year and effectively 50% of a much closer survey in the next is not a consistent series. When two instruments disagree materially and inconsistently, the disciplined response is to pick one for a given purpose, state which, and carry the other alongside it, never inside it.

The right number depends on the question. For a county-level read (how a specific county fared, how neighbors compare) the mandatory registration is the instrument with real county grain, and FDR uses a single preferred registration-based row per county-year. For a long historical trend, the survey estimate is the instrument with the deep back-series, and it should be read as its own continuous line, not spliced onto the newer registration. The rule underneath both choices is the same: never present one instrument as the other, and never pool them. A hunter or analyst using Michigan data should always know which of the two numbers they are holding — because in a year like 2022, the choice is worth forty-four thousand deer. Two numbers, one herd. The literacy is in keeping them two.