## In Barber v. Thomas, Justice Breyer Upgraded from Balancing Tests to “Elementary Algebra”

June 7th, 2010

Take a look at the Appendix to Barber v. Thomas (p. 18). Justice Breyer, in an attempt to explain the intricacies of calculating Good Time Credits for federal sentences, relies on a page and a half of algebra. “Elementary algebra” he calls it. This much math in a SCOTUS opinion makes me cringe.

As I’ve said before, I became a lawyer because I hate math.

The defendant is sentenced to 10 years’ imprisonment.As a prisoner he exhibits exemplary behavior and isawarded the maximum credit of 54 days at the end of eachyear served in prison. At the end of Year 8, the prisoner has 2 years remaining in his sentence and has accumu-lated 432 days of good time credit.
Because the difference between the time remaining in his sentence and theamount of accumulated credit (i.e., 730 – 432) is less than ayear (298 days), Year 9 is the last year he will spend in prison. (Year 10 has been completely offset by 365 of the432 days of accumulated credit.) Further, Year 9 will be a partial year of 298 days (the other 67 days of the yearbeing offset by the remainder of the accumulated credit).
Here is where the elementary algebra comes in. We know that x, the good time, plus y, the remaining time served, must add up to 298. This gives us our first equa-tion: x + y = 298.
We also know that the ratio of good time earned in the portion of the final year to the amount of time served inthat year must equal the ratio of a full year’s good time credit to the amount of time served in a full year. The latter ratio is 54/365 or .148. Thus, we know that x/y = .148, or to put it another way, x = .148y. Because we know the value of x in terms of y, we can make a substitu-tion in our first equation to get .148y + y = 298. We then add the two y terms together (1.148y = 298), and we solve for y, which gives us y = 260. Now we can plug that value into our first equation to solve for x (the good time credit). If we subtract 260 from 298, we find that x = 38.
The offender will have to serve 260 days in prison inYear 9, and he will receive 38 days additional good time credit for that time served. The prisoner’s total good time is 470 days (432 + 38 = 470). His total time served is 3180 days.
Say what?
Justice Kennedy, who dissented in an odd alignment with Justice Ginsburg and Stevens, wrote a pithy conclusion:
The straightforward interpretation urged here accordswith the purpose of the statute, which is to give prisoners incentive for good behavior and dignity from its promised reward. Prisoners can add 54 days to each year. And when they do so, they have something tangible. In placeof that simple calculation, of clear meaning, of a calendarthat can be marked, the Court insists on something differ-ent. It advocates an interpretation that uses differentdefinitions for the same phrase in the same sentence; denies prisoners the benefit of the rule of lenity; and caps off its decision with an appendix that contains an algebraic formula to hang on a cell wall.
If only Justice Kennedy would stop using fuzzy math in his national consensus 8th amendment opinions.