How were draft lottery numbers assigned and what statistical method determined fairness in 1969?
Executive summary
The 1969 draft lottery assigned each of the 366 calendar dates to a draft order by physically drawing capsules containing dates from a large container; September 14 was drawn first and thus assigned number 1 [1] [2]. Statisticians quickly tested the outcome and found patterns—especially unusually low (i.e., early) draft numbers for late-year birthdays—using nonparametric rankings and Monte Carlo–style permutation tests, concluding the drawing procedure was unlikely to be purely random [3] [4] [5].
1. How the lottery was run: an urn, capsules and public draws
The Selective Service prepared 366 small slips (one per calendar date including Feb. 29), placed them in blue plastic capsules, put the capsules into a large glass container, and publicly drew them one-by-one on December 1, 1969; each draw’s date received the next draft number (September 14 was drawn first) [6] [1] [2]. The event was covered on radio and TV, and the first 195 assigned numbers later became the pool actually called in 1970 [1] [2].
2. What “fairness” meant to contemporaries: equal chance by birthday
Contemporary and later commentators defined fairness as each of the 365 (or 366) birthdays being equally likely to be ranked first, second, third, etc.; in other words, a person’s birthdate should not predict draft probability [7]. The Selective Service framed the exercise as an effort to reduce earlier bias that had favored older men [1] [8].
3. Early statistical alarms: months clustered toward low numbers
Within weeks statisticians and journalists noticed a systematic pattern: dates late in the year tended to have lower (more dangerous) draft numbers, implying those born in later months were more likely to be called [5] [4]. The New York Times reported statisticians’ charges that the selection “did not produce a truly random result” and noted that imperfect mixing of the capsules could explain month-level trends [5].
4. The statistical methods used to test randomness
Analysts used nonparametric ranking tests and permutation/Monte Carlo simulations: they grouped dates by month, computed average draft ranks for each month, converted those to month ranks, and measured total distance or deviation from what would be expected under uniform randomness; then they simulated many random permutations to estimate how often a deviation at least as extreme would appear by chance [3] [9]. Studies reported extremely low probabilities (e.g., about 0.1% in one reanalysis) that the observed monthly ranking pattern would occur under a properly mixed random draw [3].
5. What the tests actually found—and their limits
Quantitative work showed a pronounced ordering of months that was unlikely under pure randomness: late-year birthdays were disproportionately assigned low draft numbers [3] [4]. However, statistical significance here speaks to departure from a specific null model of complete random permutation of dates; it does not by itself prove malicious intent or that every individual board acted unfairly. Analysts also cautioned that imperfections in physical mixing (a plausible mechanical explanation) could produce the observed pattern [5] [6].
6. Official response and subsequent lotteries
Government officials defended the process as “as fair as possible” while acknowledging efforts at mixing; they also did not re-run or alter the 1969 results despite the critiques [5]. Later lotteries (1970 onward) used revised methods and are generally assessed as better randomized in follow-up analyses [10] [3].
7. Broader context and consequences
The controversy amplified public distrust of the draft and fed the antiwar movement; critics also noted that the lottery did not eliminate inequities tied to deferments and local board practices [8] [11]. Statisticians’ challenges prompted broader lessons about using rigorous randomization procedures (e.g., computerized random numbers or thoroughly controlled physical randomization) for high‑stakes policy actions [3] [10].
8. Bottom line for readers
The 1969 lottery was run as a classic physical “ball-and-urn” draw and then scrutinized with nonparametric rank comparisons and permutation/Monte Carlo tests that found the month-by-month pattern highly unlikely under perfect randomness [6] [3] [5]. Available sources document the statistical findings and offer mechanical explanations (imperfect mixing), but they do not present evidence in the cited material that the result was deliberately engineered [5] [6].