In his speech today, Ken Clarke said this:
"Sentencing should not be based on cost, but on principles of retribution, reflection of public anger and the effective prevention of further crime."
He then went on to say something slightly different:
"I believe in intelligent sentencing, which will seek to give better value for money and the effective protection that people want."
While the former includes the notion of punishment, the latter does not. It is a contradiction that goes to the heart of much public concern about prison and sentencing policy.
The British public seems convinced that prison works, not necessarily on a strict cost-benefit analysis, but as a practical demonstration of how criminals should be treated.
A poll by Ipsos MORI a few years ago found that 57% of Brits were opposed to putting fewer criminals behind bars and 74% wanted more prisons.
When asked more recently about how to save money in the criminal justice system, the most popular answer for 38% of people was to cut education programmes in jails.
This is pretty much the exact opposite of what the government is intending. Ken Clarke's argument is that what the tax-paying public really want is "reduced reoffending, fewer victims and value for money".
Researchers from the international consultancy Matrix Knowledge recently did some number-crunching to estimate the cost-effectiveness of alternatives to prison. Some of the results are startling.
They calculated that sending a heroin-addicted offender for residential treatment rather than jail makes them 43% less likely to reoffend - saving the taxpayer in the long term an estimated £88,000. The figures rise to almost £203,000 if you include an estimate of the savings from having fewer potential victims.
Using a surveillance programme like the current intensive supervision programme is likely to lead to 31% less reoffending - saving between £57,000 and £130,000.
Curiously, using surveillance as well as non-residential drug treatment is less cost effective than surveillance alone, it appears. Still an improvement on prison when it comes to re-offending, but only 14% better with savings of £41,000 up to £61,000.
However, community sentences for tagged juvenile offenders make them just 3% less likely to reoffend, saving only £3,000 against the cost of locking them up.
The researchers also looked at the impact of programmes in prison. Treating a sex offender behind bars saves £35,000 to £130,000. Drug treatment in jail saves £31,000 to £115,000. But psychological therapy, they calculated, saves just £400 up to £17,000.
If you are Justice Secretary Ken Clarke trying to save 25% of your budget, these are just the kind of numbers you want to read.
But when I looked at the formula Matrix Knowledge used to calculate effectiveness, I noted that there was something missing.
Nowhere in the arithmetic is there a value for punishment, for retribution, for what Mr Clarke calls the "reflection of public anger".
It would be difficult but I think it would be worth trying to do the calculation because only then can the public get a true sense of the "price of punishment".