Crime and Punishment in Texas in the 1990s

Policy Reports | Crime

No. 237
Thursday, November 30, 2000
by Morgan O. Reynolds

How Prison Capacity Affects Expected Punishment

Table II - Calculating Expected Punishment

"For many people, the benefits of committing a crime outweigh the cost."

Most crimes are not heedless, irrational acts. Instead, they are committed by people who respond to incentives and at least implicitly compare the expected benefits with the expected costs, including the costs of being caught and punished. The reason we have so much crime is that, for many people, the benefits outweigh the costs - making crime more attractive than other career options.

It is virtually impossible to prevent people from committing crimes. What the criminal justice system does is construct a list of "prices" or disincentives (expected punishments) for various criminal acts. People commit crimes as long as they are willing to risk paying the possible price society might charge, just as many of us might risk a parking or speeding ticket by disobeying traffic laws.

Because criminals and potential criminals rarely have accurate information about the probabilities of arrest, conviction and imprisonment, their personal assessments of the expected punishments vary widely. Some overestimate their probability of success, while others underestimate it. More experienced and intelligent criminals face better odds of getting away with their crimes. Despite the element of subjectivity, if crime becomes cheaper (the expected cost of crime to perpetrators falls), crime increases and vice versa.23 This theory is consistent with public opinion24 and with the perceptions of potential criminals.25 And it is supported by considerable statistical evidence.26

How Expected Punishment Is Calculated. Four adverse events must occur before a criminal ends up in prison.27 The criminal must be arrested, prosecuted, convicted and sentenced to prison. As a result, the expected punishment for crime depends on a number of conditional probabilities: the probability of the crime coming to the attention of the police, the probability of being arrested for a crime after it is committed, the probability of being prosecuted after an arrest, the probability of pleading guilty or being convicted if prosecuted and the probability of going to prison if convicted.

Figure IV - Violent and Property Crime Arrests per 100 Crimes%2C Adult Drug Arrests per 10%2C000 Adults

"Expected punishment is not the length of time convicted criminals actually stay in prison."

As Table II shows, expected punishment is the result of multiplying these four probabilities and then multiplying by the average or median time served. Even if each of the separate probabilities is reasonably high, their product can be quite low. Suppose, for example, that each is one-half. In other words, one-half of all crimes result in an arrest, one-half of all arrests lead to prosecution, one-half of all prosecutions produce a conviction and one-half of all convictions mean a prison sentence. The overall probability that a criminal will spend time in prison is only 6.25 percent (0.5 x 0.5 x 0.5 x 0.5 = 0.0625).

"It is the average time spent in prison per crime committed in the state."

Expected punishment is not the length of time convicted criminals actually stay in prison; nonviolent Texas offenders released in 1998 served an average of three years and aggravated violent offenders released in 1998 served an average of seven years.28 To reiterate, expected punishment has to do with probabilities in addition to time served and takes into account that 98 percent of all index crimes in Texas do not result in any prison time.29 Expected punishment shows the imprisonment odds and anticipated time served by criminals, just as an actuarial table might show mortality rates for a population (probabilities of death) and be used by an insurance company to calculate expected losses from paying off its policies.30

"The probability of arrest for violent crimes went from 39 percent to 43 percent during the decade."

The Probability of Arrest. Figure IV shows arrest rates for violent, property and drug crimes in Texas during the 1990s.31 Arrests for violent crimes rose slightly relative to the number of violent crimes reported to the police, from 39 percent to 43 percent during the decade, worsening the odds for violent criminals.32 Arrests for index property crimes, on the other hand, stayed relatively constant at about 20 percent of reported property crimes. The adult drug arrest rate per 10,000 adults rose a robust one-third, suggesting more drug distribution and use, dumber drug offenders who got caught more often and/or increased police resources devoted to the war on drugs.

Table III - Expected Prison Time per Serious Crime in Texas%2C 1960-99

The Probability of Going to Prison. The probability of going to prison or a state jail after arrest for a serious crime increased during the 1990s. For violent crimes, 36 percent of arrests resulted in a prison admission in 1998, up from only 30 percent in 1990. Still, police in Texas arrested 28,000 people for violent crimes in 1998, while only 10,094 - 36 percent of those arrested - went to prison. That means 64 out of every 100 people arrested for crimes of violence served no time in a state lockup.33 Police made a total of 206,481 arrests on all violent, property and drug charges combined in 1998, resulting in prison and state jail admissions of 46,550, an overall imprisonment rate of 22.5 percent of arrests, up from 20.0 percent in 1990. Net result? More people arrested for major crimes today go to prison and stay there longer, boosting expected punishment dramatically.

"The expected punishment for murder is 9.1 years."

Expected Punishment in Texas. A comparison of Figure II and Table III shows by offense the differences between the median time actually served in prison and the expected punishment at the time a crime is committed:34

  • Murderers in prison spend a median time of 13.4 years there, but expected punishment for someone who commits a murder is 9.1 years (because the probability of prison is 67.6 percent times 161 median months served).
  • The median time served by rapists is an estimated 12.4 years, while expected punishment for committing rape is two years (the probability of prison, 16.4 percent, times 149 median months served).
  • The median time served for robbery is 7.5 years, but expected punishment is only 7.1 months (the probability of prison, 7.9 percent, times 90 months served).
  • The median time served for aggravated assault is 3.4 years, but expected punishment is only 52 days (the probability of prison, 4.2 percent, times 3.38 years).
  • The median time served for burglary is 26.3 months, but expected punishment is 14 days (the probability of prison, 1.8 percent, times 26.3 months).

If some of these numbers seem low, they are. For this reason, crime still pays for many criminals. Nonetheless, the expected cost of crime to criminals is higher than it was in the early 1990s.

Figure V %26 VI

"The expected punishment for murder is 9.1 years."

The Change in Expected Punishment over Time. Increasing the prison time served several-fold has had a dramatic effect on expected punishment for every type of crime in Texas. As Table III shows:

  • During the nine-year period 1990 to 1999, expected punishment rose 213 percent for murder and 243 percent for rape.
  • It rose 300 percent for aggravated assault and 189 percent for robbery.
  • It rose 40 percent for burglary.

"The greatest increase in expected punishment was for murder."

On the average, the crimes with the longest expected prison terms (violent index crimes of murder, rape, robbery and aggravated assault) are the crimes least frequently committed, comprising only about 11 percent of all index crimes in Texas. The remaining 89 percent of index (property) crimes carry an expected prison term of only a few days.

Expected Punishment and the Crime Rate. Figures V & VI, VII & VIII, and Figures IX & X show the relationship between expected punishment and various Texas crime rates over the past four decades. As the figures indicate:

  • Both crime and expected punishments were low in 1960, and expected punishments failed to rise to meet the steep increases in crime during the 1960s and 1970s.
  • Although crime rates continued their ascent during the 1980s, the rate of increase moderated (except for aggravated assault) as expected punishment increased modestly.
  • Expected punishment rose steeply in the 1990s to unprecedented heights, and crime rates fell.

The conclusion? Since 1991 a drastic increase in expected punishment has coincided with a major decline in crime.35

Table IV shows the calculation of aggregate expected punishment for violent crimes and burglary. The path of expected punishment overall resembles the pattern for each crime, with a mild decline in prison days per crime from the '60s into the early '80s, then a moderate rise and finally a sharp increase in the '90s. Table III, discussed above, shows the path of expected punishment for each of the five serious index crimes (also expected punishment for Figures V & VI, Figures VII & VIII, and Figures IX & X).

Figure VII %26 VIII

Figure IX %26 X

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