Jump to ContentJump to Main Navigation
Explaining Criminal CareersImplications for Justice Policy$

John F. MacLeod, Peter Grove, and David Farrington

Print publication date: 2012

Print ISBN-13: 9780199697243

Published to Oxford Scholarship Online: January 2014

DOI: 10.1093/acprof:oso/9780199697243.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 25 September 2021

Criminal Careers of Serious, Less Serious, and Trivial Offenders

Criminal Careers of Serious, Less Serious, and Trivial Offenders

Chapter:
(p.75) 4 Criminal Careers of Serious, Less Serious, and Trivial Offenders
Source:
Explaining Criminal Careers
Author(s):

John F. Macleod

Peter G. Grove

David P. Farrington

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199697243.003.0004

Abstract and Keywords

The theory is applied to subsets of offenders based on the seriousness of their offending. Offenders with custody at their first conviction are found to be a random sample (4.5%) of all OI offenders, and 11.5% of offenders with at least one custodial sentence (defined as serious offenders). The serious offenders are shown to fall into just two categories leading to a simplified gamma distribution based model which is shown to fit age/custody profiles up to the seventh incarceration. An analysis of offence type specialisation indicates that offenders tend be versatile rather than specialised and that the variety of offence types increases in proportion to the logarithm of the career offence count. Trivial offenders, those committing non-standard-list summary offences, are shown to comprise only one category. A simple model for the age conviction profile is derived and, the population size, recidivism and frequency parameter values for trivial offenders are estimated.

Keywords:   Offence specialisation, seriousness, custody, age/conviction profile, serious offenders, trivial offenders

Orientation

In Chapter 2, we proposed a theory that there are three categories of offenders: high-risk/high-rate, high-risk/low-rate, and low-risk/low-rate. Both the risk of reconviction and the rate of offending are constant over age. In Chapter 3 we applied this theory to predict independent criminal career data, including the age–crime curve. In order to explain the increase in the aggregate offending rate before the peak age of offending, we postulated that the probability of being charged and convicted after being caught increased with age during the juvenile years. We also estimated that there were about 100,000 prolific offenders in England and Wales at any one time.

In this chapter we investigate more serious offending, offences leading to custodial sentences, and the criminal careers of serious offenders. We show how an approximate two category model adequately explains particularly serious offences and approximately fits all offences. We then explore the offending patterns of serious offenders, those with at least one custodial sentence in their careers, and compare them with the offending patterns of less serious offenders, those without any custodial sentences in their criminal careers. We then look briefly at offenders who commit mainly summary offences, ranging from regulatory offences, vagrancy, and drunkenness to offences against the bird protection act and of course minor motoring offences.

Introduction

Examining serious offences first raises the question of what constitutes a serious offence. The data from the Offenders Index (OI) that we have examined so far includes all convictions for standard list (p.76) offences. In the main these are offences which are potentially triable in the Crown Court, although some (‘either way’) offences may be tried in the magistrates’ court with the agreement of the defendant. There are also a small number of the more serious summary offences included in the standard list. Offences in the standard list range from minor assaults to murder and from petty theft and shoplifting to armed robbery. We clearly need to distinguish between petty offenders and serious criminals. One measure of seriousness could be the imposition of a custodial sentence. But even here, for the same offence seriousness, offenders with several previous convictions are more likely to receive custody than offenders with a short or no criminal history. To control for this we first looked at a subset of offenders who received a custodial sentence at their first court appearance and then at the subset of serious offenders 1 with at least one custodial sentence in their careers.

Offenders with Custody at First Court Appearance

For this analysis we used the 1958 cohort sample from the Offenders Index, which is the largest of the cohort samples and includes offenders up to age 35. In this sample some 20 per cent of male offenders receive a custodial sentence at some point in their criminal career, but less than 5 per cent of male offenders fall into the subset of offenders with a custodial sentence at the first court appearance. In the custody at first appearance subset we can be reasonably sure that the level of minimum seriousness for the offence is set at the higher end of the seriousness spectrum.

Repeating the risk/rate analysis of Chapter 2 on this subset provided goodness of fit statistics comparable to those obtained for the whole male sample data. Table 4.1 shows the parameter estimates obtained for both the whole sample and the custody at first appearance subset.

It can be seen from Table 4.1 that the parameter estimates for the subset are very close to those for the whole sample. There are some differences. A smaller proportion of offenders in the custody at first appearance subset are at high-risk of recidivism, 38 per cent compared to 42 per cent in the whole sample. In part, this is because (p.77)

Table 4.1 Comparison of parameter estimates for the risk and rate models for male offenders in the 1958 cohort, whole sample and custody at first appearance subsets

1958 cohort

N

α

ph

pl

B

b

λh

λl

All male offenders

10,077

0.42

0.80

0.25

19049

0.52 ± 0.02

1.01 ± 0.03

0.33 ± 0.01

Male offenders with custody at first court appearance

465

0.38

0.80

0.17

766

0.55 ± 0.08

0.96 ± 0.08

0.37 ± 0.03

Where:

N’ is the total number of male offenders in the cohort with at least one conviction,

α’ is the proportion of offenders in the high-risk (of reconviction) category,

ph’ is the high-risk probability and

pl’ is the low-risk probability.

B’ is the total number of inter-conviction times in the data,

λh’and ‘λl’ are the mean numbers of convictions per year for the high-rate and low-rate categories respectively and

b’ is the proportion of inter-conviction times attributed to the high-rate category.

high-risk offenders are more likely to be convicted at an early age and hence receive more lenient treatment at their first appearance, despite the seriousness of the offence. The probability of recidivism in the low-risk category is lower in the subset than in the whole sample, 0.17 compared with 0.25, so perhaps custody is a greater deterrent for offenders in the low-risk category. The rate parameters are even closer with two of the three having overlapping confidence intervals and the third parameter’s confidence intervals touching. From this evidence it would be hard to argue that these characteristics are meaningfully different between the whole sample and the custody at first appearance subset.

From the risk/rate analysis we can calculate the numbers of offenders in each of the risk/rate categories (see the Appendix which reconciles the risk/rate categories). Table 4.2 shows the allocation of offenders to the categories, for both the whole sample and the custody at first appearance subset. With a null hypothesis that these serious first offenders occur randomly among the offender categories, we can test the 3 by 2 contingency table, highlighted in Table 4.2, for random (in proportion to the marginal totals) allocation of offenders to the risk/rate categories. (p.78)

Table 4.2 Allocation of offenders to the risk/rate categories

1958 cohort male offenders

N

High-risk/high-rate

High-risk/low-rate

Low-risk/low-rate

Whole sample

10077

2479

1753

5845

Custody at first appearance subset

465

106

71

288

The null hypothesis cannot be rejected: Chi2 = 3.2 on 2 df, p = 0.8. This gives support to the proposition that these serious offenders do indeed occur randomly across the offender categories, at least for the custody at first appearance subset. However, some 20 per cent of male offenders in the 1958 cohort receive one or more custodial sentences at some point in their criminal career. If we define these individuals as serious offenders then the custody at first appearance subset includes less than a quarter of them.

Custody Rates

For the discussions which follow, we need to define three types of custody rate, the overall custody rate, the custody rate at particular appearance numbers and the individual custody rate. The overall custody rate is defined as the proportion of convictions resulting in a custodial sentence. We consider all court appearances of male offenders in the 1958 cohort and find that the overall custody rate is 14.2 per cent. But the custody rate is not the same at all appearance numbers. At first appearances only 4.6 per cent of offenders receive a custodial sentence. The custody rate then increases with each subsequent appearance number to 20 per cent at the fourth and 40 per cent at the eleventh appearances. Custody rates at appearance numbers above the eleventh show considerable variation but with an average of 40 per cent and no discernible trend.

There are several possible explanations for the relationship between custody rate and appearance number. The most likely explanation is a progressive lowering of the seriousness threshold for custodial sentences, and certainly previous convictions are an aggravating factor in sentencing decisions. A second possible explanation is an escalation of offence seriousness as the criminal career progresses. To explore the second possibility we need to look (p.79) at individual custody rates, ie the proportion of an individual’s convictions that result in a custodial sentence. We will return to this issue in the next section where we consider serious offenders in more detail.

Serious Offenders

The serious offenders subset (offenders with one or more custodial sentences up to age 35) does not exhibit the same statistical structure as the cohort sample overall (see the recidivism plot in Figure 4.1). The initial slope, the solid line on the graph, represents a recidivism probability for serious offenders of 0.865 which is significantly higher than the 0.80 (dotted line on the graph) estimated for the high-risk category of the whole sample. For the data, points on the graph, the slope appears to get steeper with higher appearance numbers suggesting reducing recidivism probability as the career progresses. However, the incremental recidivism probability2 of the serious offenders’ subset is consistently higher than that of the high-risk category of the whole male offender sample.

From the analysis of the custody at first appearance subset there appeared to be a higher proportion of low-risk offenders than in

Criminal Careers of Serious, Less Serious, and Trivial Offenders

Figure 4.1 Recidivism of serious offenders

Source: 1958 cohort Offenders Index.

(p.80) the whole sample, but these low-risk, custody at first appearance, serious offenders represent less than 11.5 per cent of all serious offenders and the effect of their lower recidivism is masked by the much greater number of high-risk category offenders in the serious offenders subset.

The above custody at first appearance analysis also suggests that serious offenders might be just like offenders in general. However, if we examine the individual custody rate, that is the proportion of an individual’s convictions resulting in custody, for offenders in the whole serious offenders subset, we find that the mean custody rate does not increase significantly with career conviction count. In fact, the highest individual custody rates occur for serious offenders with only one or two convictions (see Figure 4.2). The average individual custody rate initially falls to a low of 26 per cent, for serious offenders with six convictions (up to age 35), and then increases gradually to an average of 45 per cent for serious offenders with 24 convictions. The average individual custody rate for serious offenders with three or more convictions is 30 per cent, so some 70 per cent of their offences fall below the custodial threshold, despite the threshold reducing as the career progresses. For these persistent serious offenders, the median custody rate is 27 per cent, with an inter-quartile range from 18.5 per cent to 38.5 per cent.

Criminal Careers of Serious, Less Serious, and Trivial Offenders

Figure 4.2 Average individual custody rate plotted against career conviction count

Source: 1958 cohort (Male Serious Offenders), Offenders Index.

(p.81) To summarize, using custody as an indicator of offence seriousness leads us to classify some 20 per cent of male offenders as serious offenders. These individuals are versatile in the seriousness of their offending, and on average only 30 per cent of their convictions result in custody. Among these serious offenders the high-risk of recidivism category are over-represented, despite them being under-represented in the custody at first appearance subset. The over-representation of high-risk offenders among serious offenders is, in part, due to the increased probability of a custodial sentence for offenders with several previous convictions. As a corollary, offenders in the low-risk category who receive custody are very likely to have committed very serious offences and hence attract long sentences, which provides a possible explanation for the lower recidivism rates observed for offenders released from sentences of over six years compared with those released from sentences of under six years.

We have seen from the custody at first appearance analysis that serious first offenders appear to be a random sample from the risk/rate categories identified in the whole cohort, inasmuch as they exhibit similar recidivism probability and reconviction time distributions. But a custodial sentence at a first conviction is a relatively rare occurrence, with only 4.6 per cent of male offenders overall and 23 per cent of serious offenders sent to prison at their first court appearance. The majority of serious offenders exhibit very different characteristics with higher recidivism probabilities and a disproportionate number of custodial convictions.

Less Serious Offenders

The subset of less serious offenders, with no custodial convictions up to age 35, exhibits the same statistical structure as the whole sample but, again, with very different parameter values. The proportions in the risk categories are 58 per cent and 42 per cent for high and low-risk categories respectively, apparently the reverse of the whole sample values. As explained in Chapter 2 the unequivocal allocation of offenders to specific risk/rate categories is problematic and the removal of serious offenders from the sample blurs the distinction between risk categories so that low-risk offenders with more convictions and high-risk offenders with fewer appear to be more similar. The probabilities of reconviction for the high and low-risk less serious offenders are 0.58 and 0.10 respectively, (p.82) which are very much less than the corresponding values for the whole sample of 0.8 and 0.25. As we saw with the male and female subsets in Chapter 2, parameter estimates are dependent on the conditioning of the sample and are in fact characteristics of the sample population rather than of the individuals within it. The removal of serious offenders leaves behind sub-categories of offenders who not only commit less serious offences but who, as a group, also have lower recidivism probabilities.

Serious Offences

We can now turn our attention to serious offending and examine the subset of the serious offenders’ convictions which resulted in custodial sentences and look at custodial recidivism and inter-imprisonment times. We begin by following the procedure described in Chapter 2 to obtain the custodial values for the ‘λ’s, ‘p’s and the allocation of offenders to the risk/rate categories (see Table 4.3 for the results obtained from the 1953 cohort).

We can see from Table 4.3 that the high-risk/low-rate category has apparently disappeared, leaving just two categories. We now propose a model with ‘high’ and ‘low’ categories only, where the high and low categories are substantially equivalent to the high-risk/high-rate and low-risk/low-rate categories of Chapter 2 respectively. We will also introduce a simpler approach to the modelling of assumption 5 of Chapter 3. In order, to account for the apparent rise in crime during adolescence, we will assume that one or more

Table 4.3 Allocation of serious male offenders to the risk/rate categories for the 1953 cohort

Offenders

Total

High-risk of re-incarceration ph = 0.681

Low-risk of re-incarceration pl = 0.136

Offenders

High-rate of incarceration λh = 0.451

58%

58%

Low-rate of incarceration λl = 0.129

42%

42%

Total

58%

42%

(p.83) early custodial opportunities3 are dealt with either informally or by other CJS disposals.

Simplified Modelling of Convictions for Serious Offences

We show in the Appendix that if the offending rate is constant over age and the time to the next offence is distributed as a negative exponential then, from any point in time, the time to the second offence (committed after that point in time) is distributed as a gamma distribution with shape parameter 2, and to the nth offence as a gamma distribution4 with shape parameter n.

Equation 4.1 gives the general form of the gamma distribution.

y ( t ) = A λ ( λ t ) n 1 Γ ( n ) e λ t
(4.1)

Where:

  • x(t) is the number offending in unit time at time t from the chosen point in time,

  • α is the total number of future offenders at the chosen point in time,

  • λ is the rate parameter,

  • n is the gamma distribution shape parameter,

  • Γ(n) is, for integer n, equivalent to factorial (n 1).

In order to model age at first custody we can make the assumption that one or more of the initial custodial opportunities result in non-custodial disposals. So the observed age at first custodial conviction curve is in fact the age to the second, third, or fourth custodial opportunity. This would result in a weighted sum of gamma distributions with shape parameters (ci) where (ci 1) is the number of custodial opportunities ignored prior to the first custodial conviction for the ith section of offenders and the weight wi is the proportion of offenders in that section. For computational convenience (p.84) we will simply divide our offenders into two sections. For one we will ignore only the first custodial opportunity and for the second we will ignore one additional custodial opportunity. In this instance if we assume that the two sections are of equal size then we can say that we have ignored 1.5 custodial opportunities to arrive at our first actual custody.

Our motivation for these simplifications is to provide a basis for forecasting the prison population up to ten years ahead, which we will describe more fully in Chapter 7. The mathematical model implementing our theory had to be easily programmed to permit the direct computation of the age profiles for each imprisonment or conviction number. We also need a parameterization of the model based on all the data available which provides a satisfactory fit over the period up to 1993 and beyond. We begin by following the procedure described in Chapter 2 to obtain the custodial values for λ and p for the high and low categories aggregated over all the cohorts. The results are given in Table 4.4.

In fitting the rate of custodial conviction (λ), we must consider the time offenders have been in prison and subtract this from the inter-incarceration times. As it turns out we get a very similar value for λ if the time spent in custody is ignored. This is because the majority of ‘times served’ are relatively short and often a proportion of this time is served on remand prior to the conviction date. Also, the slopes of the graphs constructed in Chapter 2, which give us the conviction rate, are not greatly changed by adding on this extra time, which merely moves the entire graph to the right by an amount equivalent to the average time served under sentence.

The next step was to try to fit the age–imprisonment curve for various values of the proportion who are criminal (q). The fitting was done against each separate imprisonment, first, second, third, etc. Because the ‘high’ category has a higher recidivism probability it will dominate the high custody number graphs. This allows the high category parameters to be set before moving to the low category.5 As well as q it is also possible to estimate the first age at which (p.85)

Table 4.4 The aggregated parameters obtained for offenders convicted of offences for which they were imprisoned before 1993

Table 4.4a: Male

‘High’ category

‘Low’ category

Imprisonment rate λ (years)-1

0.50 +/− 0.05

0.20 +/− 0.05

Re-incarceration probability p

0.67 +/− 0.03

0.18 +/− 0.02

Proportion of criminal population q

0.55 +/− 0.03

0.45 +/− 0.03

Criminality c

0.073 +/− 0.004

Temporal adjustment δ years

-0.6

Number of custodial opportunities ignored

1

Age of first imprisonment (years)

15

Table 4.4b: Female

‘High’ category

‘Low’ category

Imprisonment rate λ (years)-1

0.35 +/− 0.05

0.09 +/− 0.01

Re-incarceration probability p

0.67 +/− 0.05

0.15 +/− 0.02

Proportion of criminal population q

0.3 +/− 0.1

0.7 +/− 0.1

Criminality c

0.0040 +/− 0.0001

Temporal adjustment δ years

−0.6

Number of custodial opportunities ignored

1

Age of first imprisonment (years)

15

someone is likely to be imprisoned and the number of custodial opportunities ignored before actual imprisonment occurs. The best fitting parameter values, for males and females separately and aggregated over all cohorts, are shown in Table 4.4a and 4.4b. (p.86) The table includes a ‘temporal adjustment’ parameter θ which we will consider in some detail later.

Figures 4.3a and 4.3b show the results of the simplified model compared to the actual age-custody data from the 1958 cohort from the Offenders Index. The lines on the graphs show the predictions of the model for the annual numbers imprisoned or otherwise detained at a given age. The first four imprisonments are shown, on one graph, Figure 4.3a, and the fourth to the seventh imprisonments are shown on separate graphs in Figure 4.3b. The annual data for the 1958 cohort from the Offenders Index is shown as points on the graphs. There are no data points over the age of 34 as members of the 1958 cohort were under 35 at the time the sample was extracted from the Offenders Index.

As we can see the results are quite good for such a simple model. Although the three category model derived in Chapters 2 and 3 does fit the data better, the computational advantages of this (gamma distribution based) model outweigh the marginal reduction in fit. This simple two category model provides an explicit formula for the age/custody curve at each custody number, greatly facilitating practical applications of the theory. Clearly this model is not describing everything that is going on, and there are no doubt many second order effects which are important. It should also be remembered that custody rates did in fact change over the period.

Criminal Careers of Serious, Less Serious, and Trivial Offenders

Figure 4.3a The predictions of the two group age-custody model compared with data from the Offenders Index (custodies 1 to 4)

Note: 1958 cohort offenders who were incarcerated before 1992.

(p.87)
Criminal Careers of Serious, Less Serious, and Trivial Offenders

Figure 4.3b The predictions of the two group age-custody model compared with data from the Offenders Index (custodies 4 to 7)

(p.88) Simplified Modelling of all Convictions

The two category model can also be applied to all standard list convictions, not only those leading to imprisonment. The results are shown in Figure 4.4 and Table 4.5. Figure 4.4 shows the modelled age curves for the first four conviction numbers (lines on the graph) and the corresponding numbers of offenders at each age/conviction number from the 1958 cohort (points on the graph). Again the fit is reasonable, but as ever there are other things going on. We have seen in Chapter 3 that a three category model can produce a better fit to the age–crime curves, both for individual conviction numbers and overall. The two category fit for early ages is quite poor. However this model is very simple and we would not expect an ‘ignore the first two conviction opportunities or so’ model to accurately reflect the complex processes involved in dealing with young offenders.

As we saw in Chapter 2 there is evidence of a category of offenders with a high recidivism probability and a low rate of offending. These offenders will in general have long careers and still be offending when other high (recidivism) risk offenders have given up. Their influence has been to reduce the value of λ for the high category in the two category model. The high category is in fact an amalgamation of both high-rate and low-rate offenders, in the ratio 70:30, which reduces the high-rate parameter from well over 0.85 (see the estimates in Table 2.2) to 0.63 (see Table 4.5a). This reduction in

Criminal Careers of Serious, Less Serious, and Trivial Offenders

Figure 4.4 The predictions of the two group standard list conviction model compared with data from the Offenders Index

Source: 1958 cohort, Offenders Index.

(p.89)

Table 4.5 The parameters obtained for the two category model for offenders convicted of standard list offences before 1993

Table 4.5a: Male

‘High’ category

‘Low’ category

Conviction rate λ (convictions per year)

0.63 +/- 0.08

0.22 +/- 0.02

Reconviction probability p

0.82 +/- 0.03

0.29 +/- 0.02

Proportion of criminal category q

0.40 +/- 0.05

0.60 +/- 0.05

Criminality c

0.33 +/- 0.02

Temporal adjustment δ years

-0.6

Number of conviction opportunities ignored g

2.4*

1.4*

Age of first conviction (years)

11

Table 4.5b: Female

‘High’ category

‘Low’ category

Conviction rate λ (convictions per year)

0.58 +/− 0.08

0.27 +/- 0.05

Reconviction probability p

0.78 +/− 0.04

0.21 +/- 0.02

Proportion of criminal category q

0.10 +/− 0.05

0.90 +/- 0.05

Criminality c

0.087 +/− 0.003

Temporal adjustment

−0.6

Number of conviction opportunities ignored g

2.8*

1.8*

Age of first conviction (years)

11

(*) Where N.n means a fraction (1–0.n) have N informal convictions and 0.n have N + 1.

λ necessitates the introduction of the temporal adjustment (δ) of −0.6 years into the mathematical representation of the two category model. The temporal adjustment is needed to bring the peaks of the age–conviction (custody) curves in line with the observed data for each conviction (custody) number. To achieve this, the gamma distribution model is modified as follows:
y ( t ) = A λ ( λ ( t δ ( n 1 ) ) ) n + f i r s t 2 Γ ( n ) e λ ( t δ ( n 1 ) )
(4.2)

Where:

  • y(t) is the number offending in unit time at time t from the earliest conviction/custody age,

  • (p.90) A is the total number of offenders in the category,

  • λ is the rate parameter,

  • n is the actual conviction/custody number,

  • first is the number of the conviction/custodial opportunity resulting in actual conviction/custody,

  • Γ(n) is, for integer n, equivalent to factorial (n − 1),

  • d is the temporal adjustment.

This approximation of the theory into two offender categories provides us with a very simple mathematical model which adequately fits the data for both custodial and all convictions before 1993. In particular the similarity between the predicted and actual curves for those incarcerated suggests that the two category model is an excellent description of the age profile of those receiving custodial sentences in this period.

An important point to notice is that, the proportion of ‘high’ category offenders is greater for male custodial convictions (0.55) compared with all male convictions (0.4). Similarly, although there are many fewer offenders who are imprisoned in their lifetimes (as measured by the criminality parameter) the imprisonment rate λ is only very slightly less than the conviction rate (0.5 per year as opposed to 0.6 for the high category and almost identical for the low category). This result reinforces the conclusion that serious offending is not simply a random sample of standard list offending, as suggested by the analysis of the custody at first conviction subset, because overall serious offenders disproportionately commit the more serious offences. The ‘high’ category dominates among serious offenders. We can calculate for example that more than three quarters of the receptions into prison can be attributed to members of the ‘high’ population.

We need to be a little careful here. A member of the high offending category will appear before the courts a number of times (on average five). The higher imprisonment rate of the high category may simply be because they are recidivists. This means that although there will be many more of the high category in prison, the low category will be disproportionately represented amongst those who have committed very serious offences, and therefore have very long sentences.

Versatility or Specialization in Offending

As illustrated in Figure 4.2, serious offenders do not in general specialize wholly in serious offences. With very few exceptions, (p.91) only serious offenders with just one or two convictions in their criminal careers have individual custody rates much greater than 40 per cent. Serious offenders may however exhibit some specialization by offence type. To investigate the level of specialization we can look at the transition matrices from one offence type to another. Table 4.6 is a transition matrix for serious offenders given a custodial sentence for the column offence whose previous custodial sentence was for the row offence. The cell entries are the counts of offenders making each transition and the percentages are of the row total.

If all offenders were complete specialists then only the leading diagonal (violence to violence, rape to rape etc) highlighted in bold, would have non-zero cell values. The off-diagonal entries therefore suggest a degree of versatility in offending. Examination of the leading diagonal shows that only the burglary to burglary transition exceeds 50 per cent; thus for all other offences the next custodial sentence is more likely to be for a different offence type. Complete versatility on the other hand would result in cell entries being in direct proportion to the product of row and column totals, the familiar null-hypothesis estimator for contingency tables. The complete versatility hypothesis can be tested using the (one tailed) Chi2 test, and this hypothesis was rejected (Chi2 = 735 with 64 df., critical value at p = 0.001 is 104). Thus serious offenders are neither completely specialist nor completely versatile. The degree of specialization or versatility can be measured using the Forward Specialization Coefficient proposed by Farrington (1986; see also Farrington, Snyder, and Finnegan 1988). The FSC can be calculated directly from Table 4.6 using Equation 4.3:

F S C = ( O E ) ( R E )
(4.3)

Where:

O is the observed (diagonal table entry)

E = R C N
  • R is the row total.

  • C is the column total excluding the ‘first custody’ row, and

  • N is the sum of the observations. (p.92)

    Table 4.6 Transition matrix for custodial sentences of 1958 cohort male offenders

    Previous Custody

    Violence

    Rape

    Sex

    Burglary

    Robbery

    Theft

    Fraud

    Drugs

    Other

    Total

    Violence

    64

    2

    1

    67

    11

    65

    11

    8

    23

    253

    25.30%

    0.79%

    0.40%

    26.48%

    4.35%

    25.69%

    4.35%

    3.16%

    9.09%

    Rape

    1

    0

    0

    2

    0

    3

    0

    0

    0

    6

    16.67%

    0.00%

    0.00%

    33.33%

    0.00%

    50.00%

    0.00%

    0.00%

    0.00%

    Sex

    1

    2

    5

    5

    1

    4

    1

    0

    1

    20

    5.00%

    10.00%

    25.00%

    25.00%

    5.00%

    20.00%

    5.00%

    0.00%

    5.00%

    Burglary

    83

    4

    8

    575

    64

    264

    47

    18

    42

    1106

    7.50%

    0.36%

    0.72%

    51.99%

    5.79%

    23.87%

    4.25%

    1.63%

    3.80%

    Robbery

    15

    0

    2

    46

    10

    27

    1

    1

    6

    108

    13.89%

    0.00%

    1.85%

    42.59%

    9.26%

    25.00%

    0.93%

    0.93%

    5.56%

    Theft

    84

    4

    8

    258

    35

    365

    48

    17

    51

    870

    9.66%

    0.46%

    0.92%

    29.66%

    4.02%

    41.95%

    5.52%

    1.95%

    5.86%

    Fraud

    18

    0

    1

    36

    1

    31

    18

    2

    9

    117

    15.38%

    0.00%

    0.85%

    30.77%

    0.85%

    26.50%

    15.38%

    1.71%

    7.69%

    Drugs

    3

    0

    0

    10

    1

    5

    1

    17

    1

    38

    7.89%

    0.00%

    0.00%

    26.32%

    2.63%

    13.16%

    2.63%

    44.74%

    2.63%

    Other

    18

    0

    1

    33

    3

    40

    5

    2

    17

    119

    15.13%

    0.00%

    0.84%

    27.73%

    2.52%

    33.61%

    4.20%

    1.68%

    14.29%

    First Custody

    309

    24

    25

    612

    97

    598

    140

    104

    111

    2022

    15.28%

    1.19%

    1.24%

    30.27%

    4.80%

    29.57%

    6.92%

    5.14%

    5.49%

    All Offence types

    596

    36

    51

    1644

    223

    1402

    272

    169

    261

    4659

(p.93) Table 4.7 shows the FSCs for serious offenders in the 1958 cohort. We now need to interpret the FSC. Stander et al (1989) suggested that specialization was in evidence if the FSC was significantly different from zero. In Table 4.7 all the same offence transitions meet this criterion, with the exception of the transition from rape to rape, but in that case the cell entry in Table 4.6 is zero and only six previous custodial sentences were for rape. Alternatively it could be argued that versatile offending is in evidence if the FSC is significantly different from 1. Again all FSCs in Table 4.7 meet that criterion. The FSC therefore needs to be interpreted as a measure of versatility versus specialization. Perfect versatility is indicated by FSC = zero and perfect specialization by FSC = 1. The most specialized serious offenders would appear to be involved in the more serious drugs offences but even there the FSC suggests a marked degree of versatility. For all offence types the tendency is towards versatility rather than specialization.

The next question is, do serious offenders become more or less specialized as the career progresses? We therefore need to explore whether transition probabilities change as the custody number increases. We followed the procedure outlined in Stander et al (1989). This procedure involves the construction of intermediate matrices for each previous offence type in which the rows represent the custody number from two to five, the columns represent the offence types at the corresponding custody number, and the cell

Table 4.7 Forward Specialization Coefficients for each of the offence types

Offence type

Forward specialization coefficient

Violence to Violence

0.16

Rape to Rape

0.00

Sex to Sex

0.24

Burglary to Burglary

0.21

Robbery to Robbery

0.05

Theft to Theft

0.16

Fraud to Fraud

0.11

Drugs to Drugs

0.43

Other to Other

0.09

(p.94) entries are the counts of offenders making that transition. The analysis was restricted to the first four transitions to maintain the total transition count at each custody number to more than 200. Chi2 was calculated for each intermediate matrix and summed over the nine matrices. Since Chi2 = 154 on 167 df. (the critical value at p = 0.05 is 198), the null hypothesis, that the transition probabilities were the same at each custody number, could not be rejected. Similarly the Chi2s for the four intermediate matrices were all non-significant, replicating Stander et al’s findings. It should be noted here that for some of the transitions where the number of offenders involved was low, both expected and actual counts were zero and these cells were not included in the degrees of freedom calculations.

The analysis of offence type transitions above has concentrated on custodial convictions only. We now look at all convictions of both serious offenders and offenders with no custodial sentences, the less serious offenders. Table 4.8 replicates Table 4.7 with the addition of the FSCs for the conviction transitions of serious offenders with at least one custodial sentence; less serious offenders with no custodial sentences up to age 35; and the whole 1958 cohort sample.

Table 4.8 Forward Specialization Coefficients for various subsets of the 1958 cohort

Offence type

Serious offenders custodial only

Serious offenders all convictions

Less serious offenders

All offenders

Violence to Violence

0.16

0.16

0.18

0.17

Sex to Sex

0.24

0.21

0.22

0.21

Burglary to Burglary

0.21

0.19

0.14

0.19

Robbery to Robbery

0.05

0.06

0.00

0.05

Theft to Theft

0.16

0.13

0.14

0.14

Fraud to Fraud

0.11

0.09

0.08

0.09

Drugs to Drugs

0.43

0.37

0.40

0.38

Other to Other

0.09

0.14

0.15

0.14

(p.95) The Rape to Rape transition has been omitted from Table 4.8 as only one offender in the 1958 cohort was convicted of a second rape. Also, rape was a relatively rare offence in the 1958 cohort with only 40 convictions for rape out of a total of 32,803 convictions overall. It can be seen from Table 4.8 that variations in the FSCs, for the same offence transitions, between the various subsets of offenders are very small. Even between the two disjoint subsets, serious offenders (all convictions) and less serious offenders, the differences are small. Serious offenders appear to be marginally more specialized in burglary and robbery and marginally less specialized in all other offence types.

Specialization in the sense used above is about the likelihood of an offender being convicted of the same offence on consecutive court appearances. We now look at the distribution of offence types over all convictions and compare the distribution for serious offenders (those with one or more custodial sentences in their careers up to age 35) with the distribution of offence types for less serious offenders (those without any custodial convictions up to age 35).

Figures 4.5a and 4.5b show the offence type distributions for the two subsets respectively. The percentages shown on the histograms are the proportions that each offence type is of the total convictions sustained by serious and less serious offenders. Table 4.9 presents the proportions of convictions for each offence type committed by these two offender subsets.

In the 1958 cohort there are a total of 12,417 offenders (male and female), 2,164 (17.4 per cent) of whom fall into the serious

Criminal Careers of Serious, Less Serious, and Trivial Offenders

Figure 4.5a Offences of serious offenders

Note: Offenders with one or more custodial sentences up to age 35.

(p.96)
Criminal Careers of Serious, Less Serious, and Trivial Offenders

Figure 4.5b Offences of less serious offenders

Source: 1958 Cohort Offenders Index.

Note: Offenders with no custodial sentences up to age 35.

offender
subset. Collectively serious offenders were responsible for 45.7 per cent of convictions and disproportionately responsible for convictions in all offence types. It is perhaps not surprising that these offenders are over-represented in offence types with a high probability of custodial sentences (rape, robbery, and burglary) but their over-representation in all offence types suggests that in general they are more prolific and more versatile as well as committing

Table 4.9 Numbers and proportions of convictions for each offence type attributable to the Serious and Less Serious Offender subsets

Type of offence

Serious offender subset

Less serious offender subset

Total convictions

Violence

1765

41.60%

2478

58.40%

4243

Rape

37

92.50%

3

7.50%

40

Sex

134

34.63%

253

65.37%

387

Burglary

3922

64.45%

2163

35.55%

6085

Robbery

275

85.67%

46

14.33%

321

Theft

5881

40.85%

8516

59.15%

14397

Fraud

1236

36.44%

2156

63.56%

3392

Drugs

543

44.54%

676

55.46%

1219

Other

1156

43.97%

1473

56.03%

2629

All Offences

14949

45.70%

17764

54.30%

32713

(p.97) the more serious offences. Among serious offenders, 26.3 per cent of them had more than ten convictions in their careers up to age 35 and the highest career conviction count was 38. For the 10,236 less serious offenders, less than 0.5 per cent sustained more than ten convictions up to age 35 and the highest career conviction count was only 15.

Finally we explore versatility of offending in relation to career conviction counts. For each count we calculated the average number of different offence types (maximum 9) committed during the career. Figure 4.6 shows how the average type count increases as the number of convictions increases for both the serious and less serious offenders, circles and plusses on the graph respectively. The solid line on the graph is a logarithmic fit to the combined data suggesting that the variety of offence types is proportional to the log of the number of offences committed.

In interpreting this graph it must be remembered that offender numbers diminish as the career conviction count increases. Only one less serious offender reached a career conviction count of 15, but 210 serious offenders had 15 or more convictions. Figure 4.7 shows the distribution of offence type counts for the serious and less serious offender subsets. The x axis is the proportion of the subset with the given offence type count. One-fifth of serious offenders have just one offence type, but over two-thirds of this 20 per cent, 14.5 per cent of serious offenders, have only one conviction. The

Criminal Careers of Serious, Less Serious, and Trivial Offenders

Figure 4.6 Plot of the average number of different offence types against career conviction count

Source: 1958 cohort, Offenders Index.

(p.98)
Criminal Careers of Serious, Less Serious, and Trivial Offenders

Figure 4.7 Proportions of serious and less serious offender groups against the count of offence types

Source: 1958 cohort, Offenders Index.

proportion then increases slightly with offence type count to 25 per cent at three offence types, and then falls back to 19 per cent at four, 10 per cent at five and less than 3 per cent with six or more and only seven offenders convicted of seven different offence types. The decline in the proportion reflects the diminishing numbers of offenders with higher career conviction counts. Less serious offenders show a different pattern; 75 per cent have just one offence type but 65 per cent have only one conviction. The proportion of less serious offenders at each type count diminishes rapidly as the type count increases reflecting the lower recidivism probability of this subset and the smaller number of offenders with more than six convictions.

Despite the very real differences in the distribution of offence type counts between the two categories, the relationship between type count and career conviction count is very similar for serious and less serious offenders, circles and plusses on the graph in Figure 4.6 respectively. Offenders without custodial sentences up to age 35 may appear more specialized but only because their career conviction counts are much lower.

Trivial Offenders

The analysis presented so far has concentrated on those (standard list) offences recorded in the Offenders Index. There are many less (p.99) serious offences tried exclusively in the magistrates’ courts which are not recorded on the Offenders Index. These offences include various forms of antisocial behaviour, drunkenness, disturbing the peace, minor assaults, motoring offences, breach of regulations governing trade and other activities, etc. All breaches of the criminal law, rather than the civil law, are technically crimes and non-standard list summary convictions constitute the majority of criminal convictions recorded in England and Wales. Because these offences were not recorded on the OI there is little information available regarding the offenders and in particular there is no criminal history information available.

Data on convictions for non-standard list offences were however available from the ‘Court Appearance’ computer system, run by the Research, Development and Statistics Directorate of the Home Office. This system collected information from all courts in England and Wales. The records for standard list convictions were copied to the Offenders Index and retained but records on the Court Appearance system were not retained longer than was necessary for the compilation of Criminal Statistics publications. We were able to extract magistrates’ court data from the 1996 court appearance data set. Although all convictions (court appearances) are included, the age information for a little under half of the offenders convicted and sentenced during that year was not recorded by the courts. About one third of the convictions were for standard list offences, many of which would have been committed for trial in the Crown Court and would include the serious offences analysed above. The remaining summary offences are investigated below. Male offenders are again considerably more numerous than females and we have restricted our analysis to males.

The missing age data on well over half of the non-standard list conviction records causes problems for the analysis. However it was possible, by making some reasonable assumptions, to investigate the characteristics of the offenders committing less serious offences. Missing age is recorded with a date of birth as 01/01/1971 in the 1996 raw data. To correct for this we have, as a first step, replaced the recorded count of convictions at age 25, circa 360,000, with 20,500, the average conviction count for ages 24 and 26. Figure 4.8 shows the age profiles obtained from the raw data with that adjustment.

It can be seen from Figure 4.8 that the standard list convictions exhibit the familiar age–conviction curve first encountered in (p.100)

Criminal Careers of Serious, Less Serious, and Trivial Offenders

Figure 4.8 Age profiles for offenders appearing in the magistrates’ court in 1996

Source: 1996 Home Office court appearance data.

Note: Raw data corrected at age 25.

Chapter 3, which is not surprising as the OI has been derived from the same basic data source. The non-standard list convictions however do not at first sight conform to the profile. They peak at age 20, the rise in convictions is steeper and delayed to the late teenage years, and it then drops to nearly half the peak at age 21. Also, although non-standard list convictions account for two-thirds of the annual total, due to the missing age data the profile shows fewer non-standard list convictions at almost every age, compared to standard list convictions. The steeper rise in the late teenage years is because many summary offences, regulatory offences in particular, are not available to juveniles, or to other offences being routinely dealt with outside the court system when committed by juveniles. The apparent rapid decline at age 21 is entirely due to the missing age data.

Correcting for missing data for summary offences is problematic as we have no firm information on why age is recorded for some convictions and not for others. In the courts, for many offences, it is quite important to identify juveniles and young adults but much less important to record the age of adults. The main exceptions to this are the less serious motoring offences and we will return to these later. Examination of the standard list convictions from the OI suggests that missing age data occurs randomly over offence types and does not appear to distort the age–conviction curve at ages other than 25. For simplicity we have assumed that, for the standard list offences, non-recording of age after age 20 is (p.101)

Criminal Careers of Serious, Less Serious, and Trivial Offenders

Figure 4.9 Standard list age–conviction curve (with and without missing data adjustment)

Source: 1996 Home Office court appearance data.

Note: For the solid line the outlier data points represent the total number of standard list convictions in 1996 at the age shown in one-year increments of age. The outlier at age 25 has been replaced by the average of age 24 and 26 and the surplus distributed pro-rata over all ages ≥ 21.

random, and we have therefore spread the excess count from age 25, pro rata, over the 21+ data points. Figure 4.9 shows the results of this adjustment; the circles on the graph are the raw data points and the line is the corrected profile, using a logarithmic x axis. The corrected profile is not very different from the original data ignoring the age 25 outlier.

For the non-standard list (non-SL) convictions the corrections needed to be more complicated. Applying the above correction to the non-SL age–conviction curve created a large step increase at age 21 which we believe is unlikely to represent the true situation. Separating motoring offences from the non-SL data shows that the number and proportion of summary motoring offences increase dramatically at age 17, representing nearly two-thirds of all non-SL offences thereafter. For many of these post-17 motoring offences, age would not be of any particular concern to the magistrates and is thus more likely not to be recorded. Non-motoring offences on the other hand are more likely to follow the age recording practices outlined above where age is more important before age 21 than after. We have assumed that the peak age for non-SL offences remains at age 20 and that at age 21 the conviction count is a nominal 6 per cent less than at age 20. All age counts above 21 were then increased in the same proportion, thus eliminating the step decrease (p.102) at age 21. The resulting total number of corrected convictions was then subtracted from the known total non-SL conviction count and the difference added pro-rata over conviction counts for all ages above 16. The corrected profile was then age-weighted to reflect a constant male birth rate of 330,000 over the entire age range.

The result of this procedure is shown in Figure 4.10. On the graph the lower plot is the raw non-SL data, with the outlier (missing age data) at age 25. The upper plot is the corrected age–conviction profile and the straight line is an exponential fit to the corrected profile between ages 20 and 50. The slope of the corrected profile, over the 20 to 50 age range is very similar to the slope derived from the standard list subset (Figure 4.9), suggesting that after age 18 similar processes are at work for both standard list and non-standard list convictions.

Prior to age 18, the profiles are very different. As outlined above many offences are not available to juveniles. However, those that are might be expected to give a similar age profile to the standard list offences already discussed, especially if repeated frequently. What we actually see is very few, non-SL convictions, less than 3 per cent of the peak rate (convictions per one year age band) at and before age 16, jumping to 60 per cent at age 17. For standard list convictions, at age 16 the rate is 45 per cent of the peak and numerically an order of magnitude greater than the non-SL rate.

Criminal Careers of Serious, Less Serious, and Trivial Offenders

Figure 4.10 Male non standard list age–conviction curve

Note: The graph shows raw data and raw data corrected for missing age data and normalised to a 330,000 annual birth rate. The outlier at age 25 in the raw data has been redistribute as described in the text to produce the corrected curve.

(p.103) In the main the non-SL offenders would seem to have a different age–conviction curve from their standard list offender counterparts. This is not to say that there is no overlap between the two; several of the non-SL offences are just less serious versions of indictable offences and, as we have seen, offenders are versatile both in offence type and seriousness. Having said that, the non-SL convictions are far more numerous, for adults, than the standard list convictions and it is unlikely that the same people are wholly responsible for both.

We therefore suggest that there is a group of trivial offenders, living on the margins of legality, who commit the bulk of regulatory offences, unconcerned by the requirements for licences, hygiene, or health and safety regulations, or parking and speeding restrictions, and they may also be involved in minor acts of public disorder and antisocial behaviour. Some of these offences in the extreme could well be included in the standard list. These trivial offenders may also be inclined to evade taxation or defraud the benefit system which again would bring them into the realm of standard list offences and hence contribute significantly to our group of high-risk/low-rate offenders of Chapters 2 and 3 or more generally to the less serious offenders analysed above. Trivial offenders could therefore be characterized as antisocial individuals with a general disregard for others and the law, but who usually stop short of more serious offending.

Grove (2003, pp 95–102), in fitting the simplified model to the male non-SL conviction data, suggested that some 10 per cent of the male population were involved in petty crime with very high recidivism probabilities and conviction frequency (p = 0.955 and λ = 0.85). Approximately one in six of these convictions would be for a less serious standard list offence creating a (trivial) sub-category of the high category offenders in the simplified model of Offenders Index data. Although this simplified high, low, and trivial, model improved the SL fit and was successful in predicting the impact of changes in the re-classification of some summary offences as standard list, the model did not take account of many non-SL convictions with missing age information. In effect Grove did not redistribute all of the ‘missing age’ motoring convictions as was done above; in addition he assumed that the majority of non-SL/non-motoring offences were committed by offenders who occasionally committed SL offences.

(p.104) The lack of detailed information on the criminal careers of non-SL offenders makes the allocation of these convictions to specific offender categories difficult. Below, we take an alternative approach and consider a range of assumptions about the composition of a trivial offender category. The shape of the age–crime curve for non-SL convictions (Figure 4.10) suggests that the behaviour of juveniles in this group is largely overlooked or dealt with in other ways. We therefore assume that non-SL criminal careers start at 17, coinciding with leaving full time education and legally driving motor vehicles. There is also no justification for assuming different capture/conviction probabilities for first and subsequent convictions.

Solving Equation 3.7, without the separate first conviction component, for a single trivial category and differentiating the result gives the following expression for the age profile for age ≥ 17:

y ( t 17 ) = A ( 1 p ) λ e ( 1 p ) λ ( t 17 )
(4.4)

Where:

  • y(t − 17) is the total convictions per year at age t,

  • α is the total number of convictions, over all ages,

  • p is the recidivism probability,

  • λ is the conviction rate parameter (convictions per year).

If p is zero then x(t) represents first offences and α is the trivial offender category size. Thus for non-zero p the ratio of total convictions to trivial offender category size is 1/(1 − p).

We have normalized the non-SL conviction profile to a total male cohort of 330,000 and the normalized total number of convictions is 907,000. It is very unlikely that all males in the population are eventually convicted, so, as a reasonable assumption and even allowing for motoring offences, we have assumed that some 40 per cent of males remain conviction-free throughout their lifetime. This implies that some 60 per cent males in a population cohort will have at least one non-SL conviction giving us an estimate for p of 0.78 for petty offences. This figure provides us with a lower bound for the trivial offender recidivism probability.

We also have an estimate for (1 − p) * λ = 0.097, from the exponential fit in Figure 4.10. The lower bound for λ is thus 0.44 convictions per year. If we exclude all standard list offenders, and assume they are not separately convicted of non-SL offences, we are left with about 20 per cent of males in the trivial offender category. This gives us upper bound estimates, for the trivial offender (p.105) category, of 0.93 for recidivism probability and 1.4 convictions per year for λ. Including the high-risk/low-rate offender category, identified in Chapter 2, in the trivial category reduces the recidivism estimate p to 0.92 and the λ estimate to 1.15 convictions per year. These last estimates for p and λ are probably our best guess but clearly changing the assumptions about the composition of the trivial category changes the estimates.

Conclusion

In this chapter we have examined in some detail the aggregate characteristics of offenders committing the most serious offences, those leading to custody, and compared them with other offenders, who have no custodial sentences up to age 35. Offenders with custody at their first appearance appear to be a small but random sample of offenders as a whole. A large proportion of these offenders are at low-risk of recidivism but will have committed very serious offences. Offenders receiving custodial sentences later in their careers are predominantly drawn from the high-risk of recidivism category, are the most persistent, and are disproportionately convicted of the most serious offences.

We have seen that, by considering only custodial convictions, the high-risk/low-rate category of offenders identified in Chapter 2 did not appear to be represented in the serious offender subset. This observation led to a simplification of the mathematical representation of our theory. An approximate two-group gamma distribution-based model was found to fit the age–custody curve for each custody number. Extending this model to the age–conviction curves of all offenders it was found to approximately fit the data at each conviction count.

Various aspects of specialization versus versatility have also been explored. Offenders in general were found to be neither wholly specialized nor completely versatile. For the serious offenders’ custodial transitions, only burglary to burglary exceeded 50 per cent, and all other custodial sentences were more likely to be preceded by some other custodial offence. Similarly for all convictions the most likely transition from any offence type is to a different type. Using Farrington’s (1986) Forward Specialization Coefficient, we found that there were only small differences in the degree of specialization between serious and other offenders. The highest degree of specialization was in drugs offences followed by sex offences and burglary, (p.106) ranked in that order. The FSCs were marginally higher for custodial transitions but that possibly reflects the fact that those offences were the more serious in the offender’s repertoire.

We explored versatility more directly by counting the number of different offence types in offenders’ careers. We found that on average the variety of offending was proportional to the logarithm of the career conviction count. On average offenders with 12 or more convictions will have been convicted for half of the available types of offences. The tendency for all offenders is towards versatility; over 80 per cent of offenders with more than one conviction have been convicted of more than one offence type. At the other extreme no offenders in the 1958 cohort have been convicted of every offence type and only seven offenders have convictions for seven of the nine offence types. Serious offenders appear more versatile but that is mainly because they have higher career conviction counts.

Turning our attention to the other extreme of seriousness, we examined convictions for non-standard list summary offences. These offences include various forms of antisocial behaviour, drunkenness, disturbing the peace, minor assaults, motoring offences, breach of regulations governing trade and other activities, etc. We discovered that, after correcting for large amounts of missing age data and weighting for age, the age–conviction curve for adults showed similar characteristics to the standard list offenders analysed in previous chapters. Juveniles, however, were significantly under-represented in the non-SL convictions. This under-representation was accounted for in part by many non-SL offences not being available to juveniles and those that are being dealt with informally. We made the assumption that non-SL criminal careers started at age 17 and by applying our theory we were able to estimate upper and lower bounds on the recidivism probability p and conviction rate λ for a proposed category of trivial offenders. Although we believe that there is good evidence for the existence of the trivial offender category, its precise composition is uncertain. This uncertainty can only be resolved by collecting better data on trivial offenders, including better recording of age and criminal history.

Notes:

(1) Throughout this chapter the use of italics for serious offenders, less serious offenders, custody at first appearance, and other offenders refers to subsets of offenders as defined in the text where the italics are first used.

(2) The incremental recidivism probability is that value of p for which the number of offenders with n convictions is given by N * p n.

(3) A custodial opportunity is a cleared-up offence which could have resulted in a custodial sentence had the offender been older or had had a number of previous convictions.

(4) This formulation of time to a subsequent conviction number can also be derived directly from the solution of differential equations assuming a constant rate of conviction (see the Appendix).

(5) The reader might wonder why a more algorithmic approach was not used, for example some form of maximum likelihood approach. The authors are proponents of the ‘likelihood school’ of statistics as described by Edwards (1972). However, it is important to remember that likelihood (and in particular maximum likelihood) estimation can only act as guide to the expert judgement of the analyst. The standard example is that of a coin taken from the pocket, thrown in the air and landing heads. The most likely hypothesis regarding the coin is that it has two heads. On the basis of his theory of the world the analyst may consider it more probable that the coin has a tail on the other side. In addition a likelihood analysis can only be carried out where one has a good idea of the error structure and inherent variability of the data. True, here one will have near-Gaussian counting errors, but there will also be unknown effects due to criminal justice system changes in the period and an approximation of unknown accuracy in the treatment of early offences. Also the model being used in this instance is a further approximation of a large scale theory. Even if one were to attempt to put together a likelihood function for this situation, expert judgement on the basis of how well the graph was seen to fit by eye would have to guide the analysis. In this case it seems more honest simply to admit that the fits were ‘judged by expert opinion’.