Abstract Purpose: The current study examines significant variations in criminal achievement across sex offenders. To examine the "successful" sex offender, the study proposes a concept of achievement in sexual offending defined as the ability to maximize the payoffs of a crime opportunity while minimizing the costs. Methods: The study is based on a sample of convicted adult male sex offenders using retrospective longitudinal data. Results: The study findings show a wide variation in criminal achievement, a variation that is not correlated with the severity of sentences meted out or the actuarial risk scores obtained by these offenders. Those offenders who specialize in sex crimes were shown to be the most productive and least detected offenders. Two types of successful offenders emerge, the first relying on his conventional background in targeting a victim that can be repeatedly abused for a long period without detection. The second is a younger offender that is successful in the sense of being able to complete aggressions on multiple victims. Conclusions: Results suggest that the successful sex offender is not "detected" once he enters the criminal justice system, nor is he handled in a way that may deter him from sexually reoffending in the future. REFERENCE: Lussier, P., Bouchard, M. & Beauregard, E. (2011). Patterns of criminal achievement in sexual offending: Unravelling the "successful" sex offender. Journal of Criminal Justice, 39,[433][434][435][436][437][438][439][440][441][442][443][444] Correspondence concerning this article should be addressed to P. Lussier, Pavillon Charles-De Koninck, 1030, ave. des Sciences-Humaines, Quebec, Quebec G1V 0A6, Canada. Tel.: +1 418 656 2131x5978. E-mail address: patrick.lussier@svs.ulaval.ca. Patterns of criminal achievement in sexual offending: Unravelling the "successful" sex offender After more than 50 years of research on sexual recidivism, researchers have been unable to provide a formal evidence-based explanation of the criminal activity of sexual offenders. The risk factor approach taken and pursued over the years have restrained possibilities of understanding the criminal career dynamics of individuals committing sex offences and recent empirical studies have emphasized the need to correct this (e.g., Amirault & Lussier, 2011; Lussier & Davies, in press; Lussier, Tzoumakis, Cale, & Amirault, 2010) . In that regard, this study is a departure from past research on this issue. The aim is not to identify a predictive model of sexual recidivism but rather to understand what is being predicted and who is being identified in the process. Sexual recidivism or in more technical terms, sexual rearrest and sexual reconviction, have become the gold standard measures to determine risk. While researchers have acknowledged that "official recidivism" carries an important limitation (i.e., it measures official reoffending or the likelihood or being caught, again), it has served to establish the risk of recidivism, the prevalence of dangerous offenders, who the dangerous offenders are and how to identify them using actuarial tools. In the process, these studies have helped condition the criminal justice's responses to sex crimes through strategies assumed to increase community protection (such as civil commitment, public notification, house residency restrictions, and electronic monitoring). Often relying on actuarial tools that identify the medium-and high-risk sex offenders (e.g., Lieb, Kemshall, & Thomas, 2011; Lussier, Deslauriers-Varin, & Ratel, 2010; Lussier & Healey, 2009 ), these post-release strategies bring significant costs, impact the workload for probation/parole officers, and yet, their ability to reduce the risk of sexual recidivism remains unclear (e.g., Armstrong & Freeman, 2011; Mancini, Shields, Mears, & Beaver, 2010; Payne & DeMichele, 2010) . By targeting offenders who are more likely to be rearrested or reconvicted as suggested by empirical studies, research may have systematically overlooked an important subgroup of sex offenders that do not fit the usual patterns. The predictors (i.e., risk factors) and the criterion (i.e., sexual recidivism) used by risk assessors to identify medium-risk and high-risk offenders are all based on official measures of PATTERNS OF CRIMINAL ACHIEVEMENT IN SEXUAL OFFENDING 3 offending (e.g., prior conviction for a sex crime). By relying on "official" indicators, the criminal justice system has focused on offenders more likely to have come to the attention of the police and the courts. Is it possible that the criminal justice system is not targeting the most prolific and dangerous sex offenders? To identify the "high-risk" offenders, the criminal justice system has relied on a-theoretical actuarial tools that do not take into account the criminal achievements of these offenders. Is it possible that the criminal achievement of adult sex offenders is telling a different story than the one told by actuarial tools? Drawing from the scientific literature on the criminal achievement, the current study revisits the "sexual recidivist" by examining its criminal career, both in terms of offending productivity and cost avoidance, to determine whether the most successful offenders are what the criminal justice system considers the "high-risk" sex offenders. To do so, an empirical study based on a large sample of convicted sex offenders is conducted to examine the variations in productivity and impunity in sex offenders. While it could be argued that studying inmates for criminal achievement is paradoxical given that they have already been caught, an analysis of both the criminal earnings (Morselli & Tremblay, 2004) , and the study of sanction avoidance (Bouchard & Ouellet, 2011; Kazemian & LeBlanc, 2007) of inmates show much variations prior to incarceration. We believe that the same may apply to individuals committing sex crimes. In the next section, we first review the scientific literature on criminal achievement and relevant findings to approach the issue of offending productivity and cost avoidance in sex offenders. Criminologists typically understand the criminal career to represent the longitudinal sequence of crimes committed by an individual offender. Since the publication of the "Criminal Careers and Career Criminals" (Blumstein, Cohen, Roth, & Visher, 1986) , research on this issue has evolved around three main themes: (a) the modeling of offending, the longitudinal sequence of crimes, crime PATTERNS OF CRIMINAL ACHIEVEMENT IN SEXUAL OFFENDING 4 specialization, and the study of the "chronic offender" (e.g., Farrington & Loeber, 1998) ; (b) the understanding of criminal persistence by examining the role of formative years, early life stages and the study of the "early onset" offender (e.g., Moffitt, 1993) , and; (c) the life events, life transitions, informal controls, and the study of the "desistor" (e.g., Sampson & Laub, 2005) . A fourth theme emerged more recently, as research on the sociology of crime and criminal achievement, the role of mentorship, criminal networks, and professionalization has helped garnered information about the "successful criminal" (e.g., Bouchard & Nguyen, 2010; McCarthy & Hagan, 2001; Nguyen & Bouchard, 2011; Tremblay & Morselli, 2000; Morselli & Tremblay, 2004; Tremblay, 2010) . The focus of criminal achievement studies is not so much the volume of criminal activity or the individual frequency rate of offending, or lambda (λ), but the examination of whether crime pays, what the payoffs are, and for whom. The study of criminal achievement has its roots mostly in the study of economic and market crimes. Underlying the concept of criminal achievement is productivity or performance and efficiency in securing something valuable to the perpetrator (i.e., money, goods, status, etc.). Performance and efficiency therefore represent the maximization of gains relative to the number of crime(s) perpetrated which is distinct from λ. Highrate offenders may settle for low payoffs and low rewards opportunities, while others may restrict their volume of offending while seizing more profitable and rewarding ones (Tremblay & Morselli, 2000) . Illegal income has often been used as a performance measure of criminal achievement (e.g., McCarthy & Hagan, 2001; Nguyen & Bouchard, 2011; Tremblay & Morselli, 2000; Wilson & Abrahamse, 1992) . Illegal success varies across offenders and a few hypotheses have been raised to explain such variations, such as criminal capital (i.e., criminal experience, or skills) (Bouchard & Nguyen, 2010; McCarthy & Hagan, 2001; Nguyen & Bouchard, 2011) , especially those learned through offenders' social capital (i.e., resources found in offenders' relationships to others) (Bouchard & Ouellet, 2011; Bouchard & Nguyen, 2010; Morselli & Tremblay, 2004; Morselli, Tremblay, & McCarthy, 2006; McCarthy & Hagan, 2001) , and even low self-control PATTERNS OF CRIMINAL ACHIEVEMENT IN SEXUAL OFFENDING 5 (Morselli & Tremblay, 2004). McCarthy and Hagan (2001) , for example, showed that crime specialization, a desire for wealth, and willingness to collaborate with others have all been associated with higher criminal earnings. More specifically, the presence of a criminal network and a mentor can help increase criminal opportunities as well as recognizing the most profitable ones (Nguyen & Bouchard, 2011; Morselli Tremblay & McCarthy, 2006) . Mixed evidence has been found regarding the impact of conventional capital (such as educational attainment and involvement in the legitimate labour market) on criminal earnings (e.g., Charest & Tremblay, 2009; McCarthy & Hagan, 2001; Tremblay & Morselli, 2000) . At first glance, the idea of an offender contemplating the idea of pursuing his criminal career for monetary gains, goods, status, and prestige could not be more remote than the one involving an offender contemplating the idea of committing a sex crime. While the concepts of career and achievement are perhaps more intuitively suited for the study for economic and market-type offences, their application to sexual offending is certainly worth consideration 1 . The criminal sexual behavior, just like consenting sexual behaviors, carry something valuable to the offender, that is, sexual gratification. The inspection of sex offender's criminal behavior has lead researchers to conclude that they make a series of rational decisions to obtain sexual gratifications through illicit means, such as victim selection, determining crime location, planning victim transport to the crime site, and choosing a method of attack (e.g., Beauregard, Proulx, Rossmo, Leclerc, & Allaire, 2007; Deslauriers-Varin & Beauregard, 2010) . The rational and strategic sex offender may use deception, manipulation, alcohol/drugs, coercion, threat and/or physical violence to obtain sexual gratifications (e.g., Koss, Gidycz,&Wisniewski, 1987; Leclerc, 1 Like market offences (e.g., Tremblay & Morselli, 2000) , sex crimes provide a variety of benefits to the offender, including psychological benefits such as intimacy, self-esteem, excitement (thrill), power, control, and retribution (Felson, 2002; Groth, 1979; Knight & Prentky, 1990; Marshall, 1989; Baumeister, Catanese, & Wallace, 2002 , 1999). This conception of the "distressed" offenders, therefore, is difficult to reconcile with the vision of a rational individual trying to maximize crime payoffs. Several clinical researchers took a stance against such a generalization, arguing instead that different pathways best described sex offending and re-offending, including one characterizing a group of individuals seeking sexual gratifications through illicit means and feeling no remorse or cognitive dissonance with their offences (e.g., Hudson, Ward, & McCormack, 1999; Ward & Hudson, 1998) . This group is of particular interest here. Further, we argue that criminal achievement may be measured just as well with PATTERNS OF CRIMINAL ACHIEVEMENT IN SEXUAL OFFENDING 7 sex offenders as it is with money oriented offenders. The challenge, however, lies in translating the concept into theoretically meaningful indicators. We draw from past research and define sexual crime achievement as (1) the ability to maximize pay-offs from sexual crimes, and (2) the ability to avoid detection and sanctions. Sexual Offending and the Maximization of Pay-Offs The measure of criminal earnings has been at the forefront of past research on criminal achievement. One needs to go no further than Morselli and Royer (2008: 7) who defined the criminal achievement framework as built on three premises: (1) crime is a means to an end; (2) financial outcomes are fitting indicators of such ends; and (3) once we identify the factors that account for variations in financial outcomes from crime we can distinguish the significant minority of serious offenders (in that they take crime seriously) from the majority of opportunistic, sporadic, and lower earning offenders. This framework is limiting for our purposes in that it reduces achievement to earnings indicators, thereby excluding other potential indicators of success such as the ability to avoid detection, or any other non financial benefits from crime. The criminal achievement framework may be extended to accommodate sexual offending by replacing the concern for financial outcomes with the more general notion of "payoff", or "rewards" from crime. Whether such rewards are financial or sexual is a matter of (offending) context. In other words, while the successful thieves will seek opportunities that can generate maximum payoffs (i.e. larger amounts of money per crime committed), we make the argument that sexual offenders, at least some of them, may be looking for vulnerable victims with the maximum payoffs -i.e., a high number of sexual contacts and, by extension, of sexual gratifications. Notice that using money earned as an indicator of achievement is one step beyond a measure of offending frequency. In fact, it explicitly recognizes that large sums of money may be earned in at least three ways: (a) through the commission of a large volume of crimes at smaller payoffs per crime, or (b) through the commission of a more limited number of high pay-off crimes, or less frequently (c) through the commission of a large number of high pay-off crimes. As such, the PATTERNS OF CRIMINAL ACHIEVEMENT IN SEXUAL OFFENDING 8 frequency of crime commission becomes a predictor of money earned from crime to the same extent that skills, or social capital may be. Whether the money is earned efficiently or not becomes almost secondary. We believe that the translation of pay-off issues to sexual offending requires that the frequency of crime commission becomes in itself, part of the indicator of success. For sexual offending, an effectively completed crime contributes literally to make an offender "successful". The more of those effectively completed crimes per unit of time, the more productive and successful the offender is. This form of measurement assumes that each sexual crime brings an equal amount of gratification, an assumption which may be violated in many instances. This is why the number of victims should also be taken into account. For some offenders, success will be measured by the number of different victims they successfully approached/attacked (i.e., "the successful rapist"). For others, success will be measured by their capacity to find an opportunity they can exploit repeatedly (i.e., "the successful child molester"). The current study considers both types of measures as indicators of sexual crime achievement. Criminal achievement as offending productivity would be incomplete without the concept of impunity and cost avoidance. Despite ongoing research on the risk of apprehension (q) in various crime types (e.g. Bouchard, 2007; Collins & Wilson, 1990) , it has been a neglected area in sexual offending research (Bouchard & Lussier, 2011) , and consequently, the ability to escape detection and avoid sanction has been overlooked. Generally speaking, research in economic and market offences has shown that offenders differ in terms of their ability to avoid detection (e.g., Bouchard & Nguyen, 2010; Bouchard & Ouellet, 2011; Kazemian & LeBlanc, 2007; McCarthy & Hagan, 2001) . There is much heterogeneity in cost-avoidance reported for victimless crimes (e.g., drug selling), and there are no a priori reasons to believe that it is not the same for victim-type offences. Some offenders are better than others at avoiding detection, and the same applies to sex offenders (Beauregard & Bouchard, PATTERNS OF CRIMINAL ACHIEVEMENT IN SEXUAL OFFENDING 9 2010). Yet, it is commonly believed that, most of the time, sex offenders get away with their crime. While it is understood that official data on offending is only capturing a proportion of the total criminal activity of sex offenders, Gene Abel's oft-cited self-report study on men referred to his clinic (Abel et al., 1987; see also Weinrott & Saylor, 1991) suggested that this proportion may be minuscule 2 .Two decades earlier, however, Gebhard et al. (1965) conducted a large survey of sex offenders in a prison setting and reported that about 15% of sex crimes committed by sexual aggressors of women were unknown by the authorities. The proportions were 20% for incest offenders and 29% for exhibitionists. Those numbers were less spectacular and might explain the fact that they went almost unnoticed by the scientific community. Yet, these numbers were informative in suggesting that q (the risk of apprehension) may increase when the offender is not a relative of the victim and when violence is used. Gebhard et al. 's (1965) results are in line with those reported with general samples of offenders which showed that violent offenders, as well as frequent drug users with a history of unemployment and job instability are not as successful at avoiding detection (e.g., Kazemian & LeBlanc, 2007) . Gebhard et al.'s study was also informative in suggesting that different criminal opportunities could condition the risk of apprehension. Indeed, their findings highlighted the fact that when a child victim was targeted, an adult friend or relative was usually reporting the event to the police. The child tended not to maintain secrecy in situations where physical violence was used. When a female adult was targeted, it is typically the victim herself who reported, which may also explain why these offenders were more likely to be arrested. 2 For example, the 224 heterosexual child molesters interviewed revealed a total of 4,435 victims, the 153 homosexual child molesters were responsible for 22,981 victims while the 126 rapists interviewed reported 882 victims. These numbers not only suggested that all sex offenders were extremely active, but also that q (risk of apprehension) was extremely low. Such numbers, however, have never been replicated and their validity has been questioned (e.g., Marshall, Barbaree, & Eccles, 1991) . Furthermore, individual rates of offending (and variation of) were not presented, creating the impression that all sex offenders were chronic sexual deviates, an impression that was well suited to the idea that all sex offenders were in need of a specialized assessment/treatment in a clinical setting. offended against both intra and extra familial victims. PATTERNS OF CRIMINAL ACHIEVEMENT IN SEXUAL OFFENDING All study participants met individually with a research assistant in the weeks after their admission to the penitentiary. The offenders included in this sample had received their classification 3 The study was based on the first 373 of the 553 consecutive admissions at the penitentiary, or between 1994 and 1998. We conducted a series of comparative analyses to determine whether the 373 offenders selected were comparable or different to the 160 excluded cases using a series of descriptive indicators. We did not find any differences between the two groups in terms of education, ethnic origin, length of the prison sentence, victim type, and nature of conviction for index offence. However, the selected sample was younger at prison admission. This difference suggests a temporal effect in the offender's age at admission during the study period (1994)(1995)(1996)(1997)(1998)(1999)(2000), where relatively older offenders were incarcerated towards the end of the study period. It is unclear how these differences can be explained. Age at prison admission was added as a covariate for this study. 11 risk (i.e., low, medium, high) and were awaiting their transfer into another institution when they met with the research assistant. All research assistants were graduate students in criminology or psychology and trained by a licensed psychologist. Participation in this study was strictly voluntary, and all subjects signed a consent form indicating that the information collected would be used for research purposes only. All subjects were explained that their participation would have no consequences on their classification risk (already received) and their prison sentence. Furthermore, subjects did not receive any compensation (e.g., money) for their participation in this study. The for this sample was 2.69 (SD=1.92; range: 0-9) with 30.1% being low risk, 38.7% being medium-low, 23.4% being medium-high and 7.8% being high risk. Because of the small number of high-risk offenders, this group was collapsed with the medium-high risk group for analyses. The Static-99 was scored based on information available at prison admission. Measures of sexual crime achievement Table 1 presents the indicators used and the coding for each of them. The key variables for this study were the number of sexual crime events and the number of victims as they allow the computation of offending productivity. This information was available for 369 of the 373 subjects included in the study. The number of events refers to the total number of separate occasions in which the offenders had sexual interactions with a victim. Productivity was simply computed by dividing the number of crime events by the number of victims. Both the number of crime events and victims refer to the events that lead to the current conviction. Hence, these indicators do not include events or victims of past convictions. To control for this aspect, we included a measure of prior conviction for a sex crime. This indicator also allows examining the link between past conviction and criminal achievement and answer questions such as whether those with a prior sex crime conviction are detected or convicted sooner than others. In total, 33.3% of this sample had a prior sex crime conviction. Two λ measures were created simply by dividing both the number of crime events (λ events) and the number of victims (λ victims) by the time at risk. Time at risk refers to the non incarcerated time spent in the community since turning eighteen years old. For cost avoidance, we included a measure indicating the time (months) that elapsed between the onset of offending (i.e., date of first crime event) and the beginning of sentencing (i.e., date at prison admission). The onset of offending refers to the date of the first crime event that led to the current conviction. Date at prison admission was used because there was no information available on the date of detection 4 . Hence, our 4 The time gap between detection and prison admission vary across sex offenders. One study conducted on child sexual abuse cases reported that the time between law enforcement report and disposition took less than one year in 12% of the cases analyzed but more than two years in 36% (Walsh, Lippert, Cross, Maurice, & Davison, 2008. Case characteristics were found to be weakly linked to the criminal justice processing time. We hypothesize that this gap may be influenced by whether the offender confessed to the police, whether there was plea bargaining, if there was a trial, and the length of the trial. 13 measure refers to the ability to delay sanctions (Mean=67.7; SD=95.7). The other measure included to tap into the dimension of cost avoidance is the sentence received for the index crime (years) (Mean=4.0; SD=2.8). --Insert Table 1  The analyses are divided in three sections. First, we looked at the offending productivity broken down into multiple categories to determine the prevalence of offenders along the continuum of productivity, but also to inspect how heterogeneity in offending productivity varies in terms of nature and rate of sexual offending, cost avoidance, and actuarial risk status. Second, we inspected the covariates of offending productivity to analyze the characteristics of the most successful sex offenders in terms of the nature of their sexual offending, socio-demographics, criminal and conventional capital. The models analyzed were conducted using negative binomial regression with a log link. Negative binominal regression was used over a Poisson regression to address the issue of over dispersion of the variance in offending productivity found in our data. Four measures of offending were necessary for the regression analysis -i.e., number of crime events, number of victims, λ (events), and λ (victims) . Although the four productivity indicators were analyzed, we only report here the covariates of the λ of crime events and the λ of victims due to space limitations. For the number of crime events, the log number of victim was used as an offset variable to determine the covariates of event-to victim ratio. For the λ (events), the number of events was used as the response and the log time-at-risk not incarcerated since turning 18 years old was used as the offset indicator. The same strategy was used for λ (victim). For all covariates examined the odds ratios are presented with a 95% confidence interval 5 Offending productivity as defined in the current study has a time-component embedded into it which explains our decision to include two λ indicators. It takes time in order to revictimize the same victim more than three hundred times. It also requires a combination of circumstantial and situational factors (e.g., offender's motivation, absence of capable guardian, presence of a vulnerable victim, etc.) that are conducive to a sex crime that may not present itself on a daily basis. PATTERNS OF CRIMINAL ACHIEVEMENT IN SEXUAL OFFENDING (C.I.). The regression models were conducted to inspect three set of factors: (a)Model 1 is a baseline model that included only offender's age, type of victim targeted, prior conviction for a sex crime; (b) Model 2 introduced measures of conventional and criminal capital specifically, and; (3) Model 3 combined all indicators into a single model. In the third section, the covariates of both detection and sanction avoidance were examined. Cox regression was used for detection avoidance due to the time dependent nature of the dependent variable. Trimmed models were inspected to analyze the contribution of different sets of indicators (i.e., productivity, conventional capital, etc.). Hazard ratios with 95% C.I. were reported. Regression models with a gamma distribution were used to inspect the covariates of sanction avoidance given the asymmetric distribution of the dependent variable. All models were run using PASW statistics 18.0. Due to missing data, the sample size of the multivariate models tested varied between 357 and 363 cases 6 . Descriptive Analyses of Criminal Achievement Table 2 presents descriptive information on the criminal achievement of the sample of adult sex offenders. More disparity was found between offenders in terms of the number of crime events than the number of victims (the same observation can be made for the two lambda measures). Indeed, a wide gap between the mean (180.7) and the median (5) number of crime events was found, with scores ranging from 1 to 5524 events. The mean number of crime events, therefore, was virtually meaningless. The same could not be said about the number of victims where the mean and median were more in line. In total, 50% of our sample had 5 crime events or less and only 1 victim before getting caught. Hence, it appears that offenders differ more in terms of the number of events they are responsible of than number of victims they offended against. Again, a wide gap between mean and 6 Hence, of the 373 cases included in this study, a maximum of 16 was lost in multivariate analyses due to missing data (4.3%). Logistic regression models were conducted to identify any pattern in the missing data. Keeping in mind that the missing data was very small, only one trend emerged -i.e., missing data for the number of crime events did not appear to be occurring randomly with respect to age (pb.05) and time-to-sentence (pb.10). The missing cases were older at prison admission (i.e., in their fifties) and delayed detection and sanction (i.e., for about a decade). We suspect that memory recall may have been a factor limiting the estimation of the number of crime events for these cases. 16 median was found for this indicator directly attributable to the great variance found for number of events. In total 50% or less of our sample had re-offended at least three times against their victim before getting caught. A small group of individuals were much better at delaying detection and sanction as shown by the large standard deviation and the gap between the mean (68 months) and median (24 months) time elapsed between onset of offending and prison admission. Hence, half of this sample survived two years before being sanctioned after committing their crimes. At the end of the spectrum, just over 11 percent of the distribution survived more than 16 years before being sanctioned for their sex crime(s). --Insert Table 2 --For descriptive purposes, the offending productivity indicator was broken down into multiple categories and crosstabulated with several indicators of productivity, cost-avoidance, sexual offending and actuarial risk (Table 3) . Several observations can be made here. First, when looking at the eventsto-victim ratio, clearly the norm is to offend only once against the same victim. In total, over 40 percent of this sample was characterized by an offending productivity ratio of 1 or less. In contrast, at the other end of the continuum, just over 11 percent of this sample had a productivity ratio over 300. Second, what appears to have facilitated a high event to victim ratio for the most productive offenders is the ability in delaying detection. Whereas for the less productive offenders the average time between the onset of offending and sanction was just below 16 months, it was close to 20 years for the most productive (>600 and over). Third, offending productivity is clearly unrelated to sentencing. Hence, offending once or 300 times against the same victim leads, more or less, to the same prison sentence. This also speaks about cost-avoidance -i.e., the most productive offenders received the same sentence (more or less) than the less productive offenders even though they were involved in a much higher number of crime events. --Insert Table 3--PATTERNS OF CRIMINAL ACHIEVEMENT IN SEXUAL OFFENDING   17 Fourth, as the event-to-victim ratio increases so is the true lambda based on crime events. For example, the offenders having an event-to-victim ratio of 1 or less have a λ of .16 (or .16 event per year at-risk) as opposed to 44.5 for those with a ratio of more than 600. When λ is based on the number of victims, the picture is reversed suggesting that offenders with a low event-to-victim ratio have a victim-rate higher than those with a high event-to-victim ratio. In other words, a substantial group of offenders may choose to offend against multiple victims once as opposed to those who may offend repeatedly against a limited number of victims. The two main strategy scenario is reinforced by the fact that event-to-victim ratio is weakly related (r=.11, p>.05) to the total number of victims. Fifth, productivity increases when offenders target children (only), and, to a lesser extent, when they target their own. At the same time, the results show that the ability to maximize the number of events per victim is not limited to incestuous fathers. A majority of the most productive offenders were offending against extrafamilial victims. Finally, looking at actuarial scores, the findings show that the high-risk and medium-high risk offenders were mainly amongst the less productive offenders. In fact, 44% of the offenders with an event-to victim ratio of 1 were either medium-high or high risk sex offenders according to the Static-99. At the other end, between 6-7% percent of offenders with a events-tovictim ratio varying between 101 and 600 were medium-high or high-risk sex offenders, while just over 14% of those with a ratio over 600 had the same risk status. Hence, the items of the Static-99 seem to be targeting the less productive sex offenders, who are also the least efficient at avoiding detection. In that regard the correlation between event-to-victim ratio and the Static-99 score is revealing (r=−.39, p>.001). Covariates of offending productivity The λ of crime events. In this section, the λ of events and victims were both examined using negative binomial regression analyses 7 . The covariates of the λ of sex crime events were first analyzed (Table 4 ; Model 1-3). Several key findings were observed. The λ increased with the offender's age (OR=1.05) meaning that the older the offenders were, the higher their rate of offending was. Also, λ increased for those who offended strictly against children (OR=4.01), within the family setting --Insert Table 4 -- The λ of victims. The next set of regression models examined confirms that the covariates of the λ based on the number of victims were operating differently than with the ones based on the λ of the number of crime events. Whereas a positive relationship between age and number of events was found earlier, a negative relationship is now found between age and number of victims (Model 1). In other words, the younger the offender, the higher the lambda of victims (OR=.97). Note that none of the 7 The volume of offending (number of crime events and number of victims) were also analyzed using the same strategy. The findings were similar to those observed for the λ of crime events and the λ of victims. The findings are available upon request to the first author. victim characteristics are significant in model 1. These results suggest that, to some extent, both sexual aggressors of children and sexual aggressors of women may be as successful in offending against multiple victims. However, the association with intrafamilial victim became marginally significant (p>.10) in model 3, suggesting a separation between incestuous aggressors and others when it comes to offending against multiple victims. The negative OR shows a reverse the one found in the crime event model where non incestuous offenders have a higher likelihood of increasing their lambda of victims. In model 2, it can be observed that conventional and criminal capitals are not significantly associated with λ. In fact, the regression model is not significant. When adjusting for other covariates (model 3), crime specialization becomes significant (OR=1.98), with the most productive offenders being more specialized in sexual offending (Model 3). Taken together, not only sex crime specialists had a higher volume of events and victims, but offended at a higher rate irrespective of the strategy taken (event oriented, victim-oriented) 8 . Additional analyses were performed to determine whether our findings were attributable to extreme cases in the sample or describing a trend in the data. Both indicators of productivity were dichotomized 9 . For event-to-victim ratio, we found much similarity in the findings with respect to the offender's age at prison admission, victim characteristics (targeting children, intrafamilial), prior conviction and crime specialization. Note here that none of our measures of conventional capital were associated (all p values > .10) with the event-to-victim ratio contrary to what had been reported earlier. This suggested to us that a subgroup of offenders might have been responsible for this earlier finding. In other words, conventional capital might operate only for the most successful offenders, or it may be that conventional capital may help offenders beyond a certain threshold of offending productivity 10 . 8 In a series of models (not shown), we analyzed the number of crime events per victim by adding the number of victim as a covariate to the models. Also, when analysing the number of victims, a model was conducted including the number of crime events as a covariate. In both cases, the addition did not change the model and the added covariate was not statistically significant (p>.10). This finding is in line with our hypothesis that maximizing the number of victims and maximizing the number of events are two distinct offending strategies. 9 The covariates of the number of victims [0=one victim (61.4%); 1=at least two victims (38.6%)] and the event-to-victim ratio [0=ratio equal or smaller than one (41.7%); 1=ratio superior to one (58.3%)] were analyzed using a series of logistic regression (not shown). 10 To further clarify the issue, negative binomial models were performed again, removing the 5%, 10%, 15%, 20%, and bottom 25% of cases (in terms of productivity) in a series of models. The coefficients for the measures of conventional capital become unstable and non significant after removing the bottom 20% of cases which corresponds to an event-to-victim ratio of 100. Logistic regression models were also performed on the dichotomized indicator representing the number of victim. As observed earlier, crime specialization emerged as a significant covariate of offending productivity. However, the models also showed that targeting intrafamilial victim was inversely (OR=.44, p > .05) related to the number of victims. Hence, these findings may suggest that incestuous fathers may be less likely to move on to other victims outside the family settings. Considering that few other covariates helped distinguish sex offenders who successfully offended against different victims, it seems reasonable to conclude that these productive offenders are of a different kind from those who maximized the number of times they offended against the same victim. Detection Avoidance Time-to-sentence. Cox proportional hazard models were conducted to examine the covariates of time-to-sentence or the ability to avoid and delay detection. Hazard ratios for each of the covariates tested in the four tested models are presented in Table 5 . Older offenders (HR=.94), targeting exclusively children (HR=.52), without a prior conviction for a sex crime (HR=2.08) survived detection and sanction significantly longer (Model 1). The (inverse) association between a prior record and time-to-sentence reinforces this idea that official data on offending captures, at least in part, cost avoidance. These three indicators remained significantly related to time-to-sentence after adjusting for other covariates (Model 4; Model 5). We did find some evidence suggesting that targeting victims within the familial environment delayed sanction longer (HR=.67; Model 2), but that effect disappeared after adjusting for other covariates. Offending productivity measures were both associated with time-to-sentence, indicating that the most productive offenders both in terms of a higher event-tovictim ratio (HR=.99) and number of victims (HR=.73) were able to delay sanction longer (Model 2). The effects were also observed after adjusting for the other covariates (Model 5). Similarly, the λ of sex offending, both in terms of events (HR=.98) and victim(HR=.27) was associated with the ability to delay detection (Model 2), and the effect remained after adjusting for all other covariates (Model 4). PATTERNS OF CRIMINAL ACHIEVEMENT IN SEXUAL OFFENDING --Insert Table 5 -- Length of prison sentence. The same modeling strategy was used to examine the covariates of sanction avoidance (Table 5) . Using the length prison sentence as a dependent variable here was pivotal to determine whether: (1) the most productive offenders were also those receiving the more stringent sentences, and; (2) only more productive but also more efficient at delaying detection and avoiding more stringent sanction.
Patrick Lussier REF proposed a concept of achievement in sexual offending defined as the ability to maximize the payoffs of a crime opportunity while minimizing the costs and showed a wide variation in criminal achievement, a variation that is not correlated with the severity of sentences meted out or the actuarial risk scores obtained by those offenders.
Patterns of criminal achievement in sexual offending: Unravelling the “successful” sex offender
Journal of Criminal Justice
Psychology