Randomization failure: the 1969 draft lottery

During the early part of the Vietnam war, males could be exempt from serving in the military (and being sent to war) by attending college. Eventually this practice was ruled unfair (to people who couldn't afford college), so the college exemption was eliminated.

In 1969 the Selective Service organized a lottery to decide which boys would be drafted into the military . They decided to draft people by randomly selecting people by their birthdates as follows:

  1. A piece of paper with each calendar day was put it in a capsule, and the capsule was dropped into a large bin set up like a hamster treadmill.

  2. The Head of the Selective Service stuck his hand into the bin and mixed things up for a few seconds, and then the bin was spun around for a few minutes.

  3. Blind-folded, the Selective Service Head reached in and pulled out a capsule--that date was assigned draft number #1, the next date was draft #2, until the last one was draft #366 (they included leap days).
These numbers determined the order in which people would be drafted, and it was projected that about 10% of the males would be sent to Vietnam immediately after bootcamp and that another 10% would go to Vietnam within their period of enlistment.

What do you see wrong with this procedure ? (type answer in the box)

"So what WERE the problems?"

The Challenge

Some individuals (probably those with low numbers) noticed that those people with low numbers tended to be people born in the latter months of the year. In fact, the correlation between day of birth (1-366) and draft number was - .28. A random process would have produced a correlation around zero. Because this correlation was statistically significant, the lottery was challenged in court as being unfair.

Do you think the lottery was unfair (to those born late in the year)?

NO      Yes

The legal outcome

Despite the statistical evidence and the plausible flaws you hopefully identified, the judge ruled the lottery to be fair and refused to have it redone. However, the military did correct these flaws in subsequent years.

Addendum: the author of this exercise was drafted that year. Because he was born early in the year, he got a high number, thereby avoiding Vietnam and surviving long enough to write this exercise. So maybe you can blame the Selective Service for your having to do this web exercise!





By putting the birthdays into the bin in sequence and by insufficiently mixing them up, they increased the likelihood that the last days put in were most likely to be the first ones grabbed.

Even if the Selective Service Head intentionally tried to select capsules from the bottom, his hand probably pushed the top capsules down into the pile as he plunged it in'

Because of friction and/or static electricity, spinning the capsules around did not mix them up sufficiently.