Crime and Punishment in America: 1999

Policy Reports | Crime

No. 229
Friday, October 01, 1999
by Morgan O. Reynolds

Calculating Expected Punishment

Figure VII - The Crime Funnel for Burglars

"Between 1990 and 1997, expected punishment for serious crimes more than doubled."

It is virtually impossible to prevent people outside of prison from committing crimes. Since criminals do not knowingly commit crimes in front of the police, the police rarely catch them in the act. The criminal justice system relies on punishments imposed afterward. In effect, the system constructs a list of prices (expected punishments) for various criminal acts, and criminals decide whether they are willing to pay, just as many of us decide whether to risk parking or speeding tickets.

Viewed this way, the expected prison sentences are the prices we charge for various crimes. Thus, the price of murder is three years in prison after we factor in the odds of getting away with it, the price of burglary is about nine days and the price of auto theft is two days.

Expected punishment as a measure of the cost of committing a crime also captures the effectiveness of the criminal justice system in a single number. Expected punishment is not the same as the length of time criminals stay in prison. Rather, expected punishment is calculated by multiplying four probabilities - of being arrested for a crime after it is committed, of being prosecuted if arrested, of being convicted if prosecuted and of going to prison if convicted - and then multiplying that product by the median prison time served for an offense.15

Example: Expected Punishment for Burglary. Consider the details for burglary. As shown in Figure VII:

  • For every 100 burglaries committed, about 50 will be reported to the police.
  • FBI data show that about 13.8 percent of reported burglaries will be cleared by arrest, or about 6.9 burglaries out of the 50 reported.
  • The tracking data on offenders [see Table I] show that about nine out of every 10 arrests for burglary will be prosecuted, or 6.2 out of 6.9.
  • Two-thirds of the resulting 6.2 prosecutions will result in felony convictions, or 4.2 felony convictions out of every 100 burglaries.16
  • Of these convictions, 1.9 felons will be sent to prison while the remaining 2.3 will receive some combination of probation, fines or jail time.

Thus, this approach shows that the overall probability of doing any prison time for committing a burglary is only 1.9 percent.

Once in prison, a burglar will stay there for a median time of about 18.5 months. In 1997 an estimated 1.7 of every 100 burglaries reported to the police resulted in prison time (41,099 court commitments to prison of 2,466,100 reported burglaries), so the median prison term per act of burglary is only 9.4 days (1.7 percent x 18.5 months x 30 days per month). While this may seem like a short time, it is a sharp increase over the expected punishment of 4.8 days in 1990.17

Table I - The Criminal Justice Process for Index Crimes in the 1990s

On average then, a potential criminal can expect to spend nine days in prison for an act of burglary. This expectation of prison time per crime is, of course, heavily influenced by the chances of getting away with it. However, on the average, a rational, risk-neutral criminal should find burglary profitable so long as what is stolen is worth more than nine days behind bars.18

"There is a 39.9 percent probability of serving prison time for a murder."

Expected Punishment for Other Crimes. Table I displays the 1997 probabilities of arrest, the 1990 probabilities of prosecution, and the 1994 probabilities of conviction and imprisonment for the other FBI index crimes as well.19 Multiplying these probabilities together results in probabilities of prison time ranging from 1.4 percent for motor vehicle theft to 39.9 percent for murder. Table II shows how the clearance (that is, the solving) of serious crimes by arrest has declined since 1950. In 1950, for example, 94 percent of murders were cleared by an arrest but only 66 percent of murders in 1997 were (i.e., the chance of getting away with murder rose from 6 percent to 34 percent). Similar declines in arrest clearance ratios occurred for the remaining crimes.

Expected punishment for five serious crimes for selected years is shown in Table III. In 1950 expected punishment for murder and nonnegligent manslaughter was 2.3 years. This had dropped to 1.1 years by 1970, but increased to 3.4 years by 1997. Capital punishment was a more serious concern for murderers in the late 1940s and early 1950s, when over 100 prisoners were executed each year after relatively short stays on death row. This compares to 39 executions per year in the 1990s after death row stays averaging nine to 10 years. In 1950 the chance of a murderer being executed was 1 in 67 murders and in 1997 only 1 in 246 murders, one-quarter of the 1950 risk. Eighteen states executed 68 prisoners in 1998, with Texas in the lead with 20 executions, followed by Virginia with 13 and South Carolina with 7. Executions in 1999 may top 100, the highest total since 1951.

Table II - Percent of Crimes Solved by Arrest

As can be seen from Table III, expected punishments for the four crimes other than murder follow the same U-shaped pattern as murder over time, with punishment falling for the first few decades and then rising in the 1980s and 1990s. In 1997 expected punishment continued to increase, rising 20 percent for aggravated assault, 13 percent each for murder and robbery and negligible amounts for rape and burglary compared to 1996.

Table IV shows the probability of prison time and median months served for the five serious crimes combined. This is perhaps the best overall index of the effectiveness of the criminal justice system, as well as a measure of the threat posed by the system to criminals. The probability of prison declined steeply between 1950 and 1970 and then slowly recovered, yet it is only half that of 1950. Median months served have recovered to more than two years but still fall short of the 32 months served in 1950. Expected punishment has recovered to 83 percent of what it was in 1960 (25 days versus 30 days).

Table III - Expected Prison Time per Serious Crime in Texas%2C 1950-1997

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