Court Uses Math!

Today's opinion in Barber v. Thomas poses a math problem as well as an interpretive problem. Federal prisoners who behave well in prison are eligible to receive "good time" credits toward service of their sentence. But when exactly should they be released?

The relevant statute says that a prisoner serving a term of more than one year may receive a credit "of up to 54 days at the end of each year of the prisoner’s term of imprisonment," and that "credit for the last year or portion of a year of the term of imprisonment shall be prorated." So if a prisoner is receiving prorated credit while serving the last year of his sentence, how do you calculate the release date?

The appendix to the Supreme Court's opinion actually contains algebra! Having concluded that the provision for prorated credit means that the prisoner should continue to earn credit at the rate of 54 days per 365 days served, the Court works out the necessary equations. I would do it this way: assuming a sentence of y years, let x be the number of days the prisoner actually needs to serve. Then we have:

x + (54/365) x = y.

So, (419/365) x = y.

And therefore, x = (365/419) y, which is about .871y. So for a 10-year sentence, a prisoner who got maximum good-time credits would have to serve .871 * (10 *365) = 3179 days, or 8 years 260 days. The Court did it a little differently but got to the same result.

Cool to see some actual math, even easy math, in a Supreme Court opinion.

But is this the lawful method of calculating credit? That was the interpretive question. The prisoners wanted slighlty more credit, and the dissent argued that a prisoner's credit for each year should shorten the next "year" for which the prisoner could earn credit. Thus, if a prisoner earned 54 days of credit in his first year, that would be credited against his next 365-day year, so he could earn another 54 days of credit in the next 311 days.

I think the Court's opinion makes more sense. The statute provides for up to 54 days of credit "at the end of each year of the prisoner’s term of imprisonment." That sounds like the prisoner must serve 365 days, not 311, to earn 54 days of credit.