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Journal of Quantitative Criminology
https://doi.org/10.1007/s10940-025-09609-7
ORIGINAL PAPER
Did More Stop andSearch byPolice Cause Less Knife Injury
inLondon? Evidence from2008–2023
AlexR.Piquero1· LawrenceW.Sherman2
Accepted: 27 March 2025
© The Author(s) 2025
Abstract
Objectives This study investigates the impact of police stop and search encounters (SSEs)
on knife injuries and homicides in public places in London. While prior research has stud-
ied SSE impact on crime in general, we focus specifically on SSE relations to weapon-
related injuries and deaths: whether conducting more SSEs over time has reduced such
crimes.
Methods The study analyzes 15years of data (183months) from the Metropolitan Police
Service (MPS) in London, including 58,503 recorded knife injuries and 4.3 million police
SSEs. Two quasi-experiments and Autoregressive (AR) models were employed to examine
correlations between changes in SSE volumes and trends in knife injuries and homicides
over time.
Results AR models revealed statistically significant reductions in knife murders and inju-
ries in response to increased SSEs. Specifically, if SSEs were conducted at the 2008–2011
rate of 45,000 per month, there would be an estimated 30 fewer knife murders per year.
Additionally, changes in SSE frequency were associated with notable crime rate shifts. A
66% reduction in SSEs from May 2014 led to 44 more knife murders and 1276 more inju-
ries than expected. Conversely, a 55% increase in SSEs in January 2018 resulted in 27
fewer knife injuries per month.
Conclusions The results suggest that increased SSEs can significantly reduce knife-related
injuries and homicides in public places. This reduction translates into preventable health-
care costs of approximately £216,000 per month. These findings highlight the potential
effectiveness of formerly higher levels of SSEs in preventing knife crime, with one fewer
injury occurring every day in London.
Keywords Stop· Search· Knife injuries· Homicide· Residual deterrence· Deterrence
decay· Weapons
* Lawrence W. Sherman
LS434@cam.ac.uk
Alex R. Piquero
apiquero@miami.edu
1 University ofMiami, CoralGables, USA
2 University ofCambridge andBenchmark Cambridge Ltd., Cambridge, UK
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Journal of Quantitative Criminology
Introduction
With a homicide rate of 1.3 per 100,000 people per year, London is one of the safest cit-
ies in the Western world. A recent report comparing crime rates with other global cities
(Ashby etal. 2024: 5) shows London’s homicide rate far below American cities includ-
ing New York and Toronto, and below European cities including Berlin, Paris, Barcelona
and Madrid. Yet London’s debate over policing tactics and strategies is as old as its police
service (founded 1829), with many questions still unanswered in the absence of careful
research. Its use of stop and search is a prime example (Casey 2023).
Research to date on the effects of police stop and search encounters (SSE) on crime in
London arguably suffers a lack of precision. Rather than identifying a precise causal path-
way between the nature of certain crimes and the potential effects of stop and search on
each of those crime types, these studies generally hypothesize that SSEs can be expected
to reduce many different types of crime. Carefully executed analyses of SSE correlations
with a broad range of crime types find mostly null effects (Brakmann 2022; Tiratelli etal.
2018). Yet there is little theoretical reason to expect that SSEs should reduce most crime
types. Nor have the tests addressed the crime type that is, theoretically, most likely to be
prevented by SSEs.
The target problem that prior British research has ignored is the one that drives the pol-
icy debate: crimes in which serious injuries and death are caused by weapons. Only one
study, a Home Office evaluation of SSE impact at the level of London’s 32 boroughs in
2008–9 (McCandless etal 2016), has apparently examined changes in SSE in relation to
several specific categories of knife-enabled crimes combined. Yet even that study did not
focus specifically on injuries or homicides caused by weapons.
In contrast, eight out of nine quasi-experimental research designs in North and South
America have shown intensive stopping of potential gun-carrying persons to reduce weap-
ons injuries, firearms discharges or homicides. The first test in Kansas City (Sherman and
Rogan 1995) found a 49% reduction in firearms discharges during a substantial increase in
occupied vehicle SSEs, while a comparison area with no change in police actions showed
no change in reported shootings. A test in Pittsburgh, which involved substantial use of
pedestrian and other stop-and-search encounters (SSEs) with erratic deployment patterns
on some nights but not others, found significant reductions in hospital treatments for gun-
shot wounds on high-search nights in both test zones (Cohen and Ludwig 2003). A replica-
tion of the Kansas City experiment in two areas of Indianapolis observed similar effects in
one target area but not the other, although homicide rates decreased substantially in both
target areas (McGarrell et al. 2001). A randomized controlled experiment in St. Louis
(Rosenfeld etal. 2014) found that substantial increases in vehicle SSEs in 8 test areas out
of 32 high-crime areas produced substantial reductions in nondomestic gun assaults com-
pared to no change in the other 24 areas—8 of which received increased patrol presence
but no increase in SSEs. Most recently, a 15-year analysis of substantial fluctuations of
city-wide SSE frequency in relation to homicides in Chicago estimated that the increases
had prevented 703 murders over 180months (Skogan 2022), or 4 murders a month, in a
city population of 2.7 million. Similar city-wide benefits had also been reported in two cit-
ies in Colombia (Villaveces etal. 2000).
Among the U.S. studies, the Pittsburgh analysis (Cohen and Ludwig 2003) provides
the most direct evidence of a causal link between SSEs and fewer weapons-related inju-
ries. The day-by-day analysis revealed a 34% reduction in 911 calls for shots fired and a
71% reduction in hospital-treated gunshot assault injuries on nights when high-volume
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Journal of Quantitative Criminology
SSE patrols focused on seizing firearms. The authors suggested that the local gun-carry-
ing population, aware of the patrols, were less likely to carry guns in public, leading to
fewer shots fired and, consequently, fewer injuries from gunfire.
That specific pathway–from SSE to deterrence of weapons-carrying–describes a the-
ory first specified by Moore (1980). This theory fits all six of the successful US tests of
SSEs focused on illegal gun-carrying. The theory is not one of reducing the weapons
supply by seizure of those weapons. Rather, the theory is that deterrence of weapons-
carrying in public places can reduce weapon use in those places. This deterrent effect
can arguably be achieved by highly visible SSEs demonstrating the threat of immediate
and certain (if brief) loss of liberty when police find a weapon and transport the sus-
pect to a police custody suite for at least several hours. This theory limits the scope of
intended effects in a way that breaks a chain of causation from owning a weapon, to car-
rying a weapon, to using it—often on the spur of the moment, in an unplanned encoun-
ter. A weapon not carried is a weapon not used.
The theory of weapons injury prevention (Moore 1980) is not limited to guns or the
United States. In pursuit of greater precision in understanding and using SSEs, we apply
this theory to focus on a single purpose of SSEs: the prevention of injury caused by
concealed weapons carried in public places in London. This objective not only offers
the clearest Utilitarian calculus for justifying the trauma imposed by SSEs (Bentham
1780; Weisburd etal 2023). It also offers the clearest theoretical model for a causal link
between SSEs and the reduction of harm to the public. That four-step chronological
model is best presented in reverse sequence:
1. A concealable weapon (knife, gun, or other) is how one person causes the death or injury
to another person in a public place.
2. The “cause of the cause’’ of that crime (Wikström and Kroneberg 2022: 184) is the
carrying of, or having immediate access to, the potentially lethal weapon; Braga (2023)
describes this as a ‘’precursor activity’’ which makes “makes personal disputes, rob-
beries, and other violent events more lethal.’’
3. The cause of the weapon’s availability is a decision to carry or maintain access to the
weapon (which might be hidden in a public place), based in part on some calculation of
estimated risk of detection and loss of liberty because of that decision.
4. The information that is used in the calculation by each person who decides to carry
or arrange access to a weapon is circulated by word-of-mouth communications about
(or direct observation of) police stopping or arresting someone for illegally carrying a
weapon in an area where those other persons were planning to carry (or hide) a weapon.
For police to prevent injuries or deaths caused by people carrying weapons illegally,
this theoretical model points to a general deterrent effect of public police actions that
shape the information in step 4 (Sherman 2023). That information can be intensified by
targeting more SSEs within the specific locations with the highest frequency of crimes
committed with weapons. The more SSEs in a particular area, the greater the likelihood
that they will be observed by weapons carriers (or potential carriers), who may then
leave the area. While a displacement hypothesis suggests that such a strategy merely
moves crime around to other locations rather than preventing it, a substantial body of
research has falsified that claim (Bowers etal. 2011) with micro-local analyses or city-
wide tracking of individual suspects (Mazeika 2014).
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Journal of Quantitative Criminology
Despite the generality of this theory, there are many limitations to using US evidence to
choose weapons policing policies that are effective in Britain. There are clear differences
between gun crime and knife crime, between homicide rates in US and UK cities, and
between US and UK police cultures and community institutions. The primary value of the
US studies is that they use the most theory-specific outcome measures of criminal injury
caused by weapons. Thus, a conclusion from the available UK studies that SSEs cannot
reduce knife crime injury is at least premature, and potentially incorrect. In the absence of
any strong evidence of the success of other UK police strategies in reducing knife injuries,
there is a great need to examine the largest data set on the subject available in Britain and
seek insights that London data may offer.
Deterrence inLarge Versus Small Areas
The theory of weapons crime prevention (cf. Moore 1980) outlined above is silent with
respect to the size of geographic areas to which it is applied. The information that poten-
tial weapons-carriers use to estimate the risk of detection may well be place-specific, as
the extensive evidence on hot spots policing suggests (Braga etal. 2019). Most of the US
research on this theory is focused on relatively small areas, such as the St. Louis experi-
ment (Rosenfeld etal 2014: 433) with 8 targeted street segments (corner to corner) in each
unit of analysis, or the Kansas City Gun Experiment (Sherman and Rogan 1995: 679) in an
8 X 10 street blocks area. Yet in his 15-year analysis of gun murders and SSEs in Chicago,
Skogan (2022) found clear and substantial effects at a city-wide level of analysis. Those
numbers were also at the core of political discourse about SSE numbers, which was framed
at the city level.
In addition to Skogan’s work, two city-wide tests in Bogota and Cali (Colombia) showed
substantial city-wide homicide reductions on designated days when SSEs were widely con-
ducted at police roadblocks and elsewhere across the cities (Villaveces etal. 2000). These
significant effects of 13–14% homicide reductions were clear in day-by-day tabulations,
comparing days in which all gun carrying was banned to days in which no proactive polic-
ing enforcement was delivered.
The present study, like Skogan’s, is conducted at the city-wide level of analysis. This
decision was not only a choice, but also a necessity, since reliable data as to locations of
stops and knife crimes were not available for the full time period. Even if they had been
correct at the level of the 32 boroughs, the mean number of knife injuries per month per
borough was under 10, with many borough-months having zeros and two-thirds of London
with no weapons crimes at all for a recent 24-month period (Agar etal. 2026).
As a choice for the first test of SSEs on knife crime, there is good reason to conduct a
city-wide analysis just as in Chicago. The substantial variability of SSEs (in both London
and Chicago) at the city-wide level–from over 50,000 per month to under 10,000—pro-
vides an important scientific opportunity to compare levels of weapons violence in short-
term periods with vastly different risks of SSEs per day city-wide. And as discussed below,
the presence of a highly used rapid transit system fosters many offences committed far
from the offenders’ residences.
The findings from the (mostly US) previous studies of SSEs and weapons crime harm
are consistent with the following conclusions. One is that in every Western Hemisphere
test—city-wide and local– increases of SSEs have been followed by reductions in homi-
cides or woundings (Sherman 2003). A second conclusion, as one anonymous reviewer
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Journal of Quantitative Criminology
of this paper suggested, is that the use of a city-wide unit of analysis may simply under-
estimate the effect of SSEs on weapons harm. Given the absence of weapons crime across
most of London’s territory, it is unlikely that a city-wide design would over-estimate the
effects of more SSEs on weapons crime. Since the study does find reductions in weapons
harm following increases in SSEs, the prospect of the true effects being even larger in
high-knife crime hot spots does not undermine a conclusion based on city-wide data.
Measurement Problems in Micro-locations of SSEs and Crimes. Further context for
our decision to focus on city-wide analysis comes from describing the data. The present
study does not have the benefit of precise recording of the locations in which SSEs were
conducted in London over the 15-year period examined, let alone the precise locations of
knife crimes with injury or death. The second author’s 2015 attempt to identify both SSEs
and knife injuries at local levels encountered longstanding imprecision in police reporting
systems, dating back to the 1990s. Despite the mandate from the Police Commissioner in
2015 to undertake a randomized trial of SSE effects, the data challenges to a micro-level
test posed a fatal barrier to that plan. A decade later, the most reliable and feasible research
design is to examine what can be learned from city-wide changes over 183months.
Future Potential for RCTs. While recent changes in Metropolitan Police data systems
now allow officers to drop a digital ‘’pin’’ on a digital map to locate each SSE, many other
barriers will prevent the conduct of a randomized trial in London for some time to come.1
Thus, the contribution of this study’s retrospective city-wide study at this point in time is
to fill a major gap in evidence of any kind on the question of whether more SSEs, or how
many of them per month, can be effective in preventing murders and knife injuries. Even if
benefits at a city-wide level understate a deterrent effect at micro-levels, evidence of harm
prevention from the current study could lead to stronger designs with smaller areas of anal-
ysis. The city-wide analysis may thus enhance the likelihood of conducting RCTs within,
perhaps, only the top 100 of the 15,772 hexagons (of 200m per side) into which the Metro-
politan Police have now divided the landscape they serve. That landscape is highly skewed
in a Pareto concentration of most weapons harm found in the top 700 areas, with 62% of
London having no criminal weapons harm in public places for all 24months of 2022–2024
(Agar etal. 2026). But to build a stronger future for more precision in stop & search, it is
essential to start with a macro-level view of what can be learned from substantial varia-
tions over time.
Costs & Benets ofSSEs: Police Discretion, Race, andTrust
The present study design also provides opportunities to assess costs and benefits of SSEs.
This assessment, however, must be seen from the standpoint of street-level decisions,
rather than top-level strategic choices made by New Scotland Yard. To understand how
costs and benefits are perceived, and how decisions to raise or lower SSEs are made, we
must begin with a review of how some 48,000 employees collectively produce a rise or fall
in frequency of SSEs.
1 The obstacles can explain why no police force to our knowledge has ever conducted an RCT in stop
& search volume. Such obstacles include the legal difficulty of directing officers where and when they
should–or should not– invest time in seeking legally acceptable evidence for undertaking stop & searches.
They also include policing-by-consent sensitivities about communities being treated as ‘’guinea pigs,’’ in
both directions: depriving them of a service that is given to other high-harm areas, or targeting them for
increased challenges to freedom of movement in public spaces.
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Journal of Quantitative Criminology
Police Discretion
Under English law, the office of Constable is an appointment by the King to keep the
King’s Peace. (Under tax law, constables are not even considered employees, but are
Crown officers). Since 1361, a statute has required Constables, like judges, to use their
discretion in when—and when not—to enforce the law (Judge 2011). The main criterion
is whether enforcement will help to keep the peace. No superior officer, in principle, can
order a Constable to make an arrest that the Constable does not think will keep the peace.
Each Constable, in deciding whether to conduct a stop & search, must decide whether they
think the SSE is legally justified and will help to keep the peace. This ‘’operational inde-
pendence’’ of the police means that numbers of stops and searches per month are beyond
the direct control of the Police Commissioner, the Mayor, the King or even their sergeant.
In England, the Constable decides.
Since the end of the present study period in 2023, the number of SSEs in London has
continued to drop substantially. This fact illustrates a major foundation of the current anal-
ysis: each and every SSE decision must be made by a Constable based on both the facts
of each situation and the relevant law. All officers can be encouraged or discouraged from
undertaking SSEs by their immediate, intermediate and senior supervisors, but not ordered
to do so.2
Testing Trends inPolice Discretion
This study is thereforenot a test of changes in law or police orders, but a test of the effects
of trends in police discretion. These trends can be shaped by a variety of ‘’influencers,’’
from the Prime Minister to police sergeants. They can certainly be shaped by Police Com-
missioners ordering police to work overtime in evening hours, looking for people who may
be carrying knives; the second author observed police do just that in July of 2008 after a
surge of knife murders of young men (under 18) in the first half of the year. But within two
years a new Home Secretary took office, and in three years a major riot occurred for which
police were blamed. In this swirl of events, police constables heard many people saying
they should do more SSEs, fewer SSEs, or racially even SSEs. At each point in history,
they collectively reacted in different ways.
This study examines two major changes in volumes of SSEs in London. One is the col-
lective behavior of constables to reduce their monthly SSEs (of up to 50,000) after major
cuts in police budgets and the 2011 riot. The data presented below shows the magnitude
of those changes, followed by a sharp drop in 2014 to 10,000 stops per month. That is the
first clear cutback we examine below, in relation to changes in rates of knife injuries. The
second is a collective surge in SSEs in 2018, when monthly SSEs tripled. Neither of these
“quasi-experiments’’ in numbers of SSEs was planned by any official, or by any police
leader. Public discussions abounded, but what happened was in the collective gift of the
tens of thousands of Constables exercising their lawful discretion in London.
Central to those shifts in police actions was the persisting issue of race.
2 Lord Chief Justice Igor Judge, SUMMARY JUSTICE IN AND OUT OF COURT . Police Foundation Har-
ris Lecture, London 7 JULY 2011.
https:// www. police- found ation. org. uk/ past- event/ 2011- rt- hon- the- lord- judge/
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Journal of Quantitative Criminology
Racial Discrimination andDisparity
The relationship between racial issues in SSEs and the King’s Peace became very evident
in the early years of the analysis presented here. Fully six days of riots in London and
beyond in August 2011 were sparked by an MPS officer lawfully3 killing Mark Duggan,
an armed Black man, during an intelligence-led vehicle stop. Yet the overall social con-
text was weighted by the disparate city-wide use of pedestrian SSEs with Black subjects
relative to White subjects. It is difficult to factor the cost of the riots into a model of pro-
portionality for the use of SSEs, especially given the parallel facts and issues of disparate
murder victimization by race.
A 2012 paper by the UK Human Rights Commission found that relative to their pro-
portions as residents in the 2011 Census, Black persons were 3.1 times more likely than
White persons to become an SSE subject.4 At the same time (2011), Blacks were 4.6 times
more likely to be murdered in London than Whites (Kumar etal. 2022: 212). The rela-
tionship between those two facts is immensely complicated, as well as controversial, in
both the geographic distribution of murders as well as demographic population groups. It is
even more challenging to assess when the comparison is limited to young men aged 16–24
years: Black men that age were almost 15 times more likely to be murdered than their
White peers (Kumar etal 2022: 215).5
Whether or not the racial disparity in stop and search can be considered as proportion-
ate to the racial disparity in homicide is, at least in part, an empirical question. If SSEs at
any level of analysis were found to be correlated with fewer homicides, then the increased
costs of SSEs for those who are searched could be seen as proportionate to a reduction in
their risks of being killed or injured. A conclusion as to proportionality, however, must not
only assess the number of lives saved and injuries prevented; it must also address the num-
ber of innocent persons stopped, as well as the psychological damage suffered from those
stops and the potential loss of police legitimacy.
Costs ofSearches fortheSearched
The costs to subjects of SSEs may include elevated risks of subsequent mental and physical
health problems. A recent systematic review of studies of these risks found significantly
worse health among past subjects of SSEs in 9 out of the 12 studies (Weisburd etal. 2023).
The same review found that 7 out of 9 studies of attitudes towards police—including trust,
legitimacy and respect for police—were lower among people who had been the subjects
of SSEs compared to similarly situated people who had not been. These findings were not
limited to experimental or systematic assignment of SSEs to some and not other people
who served as controls, and hence may reflect correlations with the kinds of people police
3 According to a Coroner’s Jury verdict of 8–2 on January 8, 2014; see Matt Prodger (8 January 2014).
"Mark Duggan Inquest: Why killing was deemed lawful.’’ BBC News, 8 January 2014. Downloaded
15/09/2024 at https:// www. bbc. co. uk/ news/ uk- engla nd- london- 25321 711
4 Karen Hur rell, Race Disproportionality in Stops and Searches, 2011–12. London: UK Human Rights
Commission.
https:// www. equal ityhu manri ghts. com/ sites/ defau lt/ files/ briefi ng- paper-7- race- dispr oport ional ity- in- stops-
and- searc hes- 2011- 12. pdf
5 A recent analysis of data from the US Centers for Disease Control similarly reports demographic varia-
tion in homicide victimization. In that study, Piquero and Roman (2024) found that, among those persons
aged 15–19years in 2021, the rate for Blacks was 27 times the rate for Whites.
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Journal of Quantitative Criminology
selected for SSEs rather than an independently causal effect of the stops. Nonetheless, the
findings suggest a broader understanding of the possible costs of the SSE tactic.
Public Attitudes onSSEs
General public opinion of SSEs, in contrast, has changed very little over the period of time
covered by this study, with little difference evident in relation to the volume of SSEs. The
London Mayor’s Office for Police and Crime (MOPAC) publishes a Public Attitude Survey
(PAS) of 19,200 London residents per year capturing a wide range of perception data.6
With response rates in the range of 40–50%, public approval of SSEs dropped substan-
tially (from 81 to 76% approval) after the murder of George Floyd in the US, then declined
from 76% in second quarter of 2020 over the next eight quarters to 71%. Meanwhile, the
numbers of SSEs in our own data dropped from 40,000 to 10,000 per month. A similar
pattern in that time period showed somewhat declining confidence (from 65 to 61%) that
police were using SSEs fairly. Thus, on both measures, public approval of SSEs declined as
numbers of them declined—not as they increased. This evidence is therefore not consistent
with linking greater use of SSEs to a ‘’cost’’ of overall loss of public confidence in police,
especially, as the data presented below demonstrate, when knife crime injuries and murders
were rising as SSEs were falling.
London Data 2008–2023
With some important limitations, this article can track the monthly volume of two vari-
ables over 183months in London: SSEs and knife crime injuries. Most of the data have
been extracted from current police data files, primarily since 2012. Prior to that time the
counts come from public data archives, as well as from the copies of those files created
by an expert on London crime and policing data.7 We have little reason to believe that the
earlier public archive data differed from the later sources in MPS systems in any way that
affected the conclusions. Our comparison of findings with and without the public archive
data produced the similar results, with even stronger effects for the later period.8
As a separate issue from data sources, we cannot be entirely certain that at any point in
time the data follow consistent definitions, such as knife crime injuries in public places or
non-domestic crimes that exclude violence between family members or intimates. Many
people worked to create these records, with substantial turnover across the lengthy time
period. Yet a single crime recording system (CRIS, the MPS criminal records information
system in use until early 2024) remained in place over entire the time period, with minimal
6 https:// data. london. gov. uk/ datas et/ mopac- surve ys
7 We gratefully acknowledge the assistance of Gavin Hales of the Police Foundation by his sharing of some
of these data with us, as well as his postings of moving averages of both SSEs and knife injuries in London
@gmhales.
8 To address this issue further, we performed all of the city-wide analyses for both knife injuries and knife
homicides using data from April 2012 forward through September 2023 (thereby removing the 45months
of our data). These results provided substantively similar results regarding the relationship between SSEs
and both knife injuries and knife homicides. In fact, the point estimates were even stronger than those
contained in the main body of the manuscript. Specifically, the estimates for SSEs on knife injuries was
− 2.374, while the estimate for knife homicides was − 0.148, both statistically significant at p < .05. Given
the similarity of findings using both the full time series as well as the limited time series, we believe that
the use of the full time series is the most appropriate strategy.
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Journal of Quantitative Criminology
changes in data entry systems or screen structure. Our best information is that the defini-
tions of the events measured have remained fairly constant, and that it is unlikely that any
sharp changes in measurement occurred simultaneous with sharp changes in either SSEs or
knife injuries.
Counting Only Injuries toVictims
A major source of confusion in public discourse about ‘’knife crime’’ is that it is often
defined as including police arrests for carrying knives or other weapons illegally. Our data
systematically exclude such crimes that are proactively discovered by police and limit the
analysis to victim-named reports of suffering a criminal knife injury. Some of the prior UK
studies may not have separated the proactively detected crimes of knife carrying (in which
the victim is the Crown, i.e., the state) from the reactively recorded accounts of victims
who were injured by knives, or witnesses who reported such events to police (Reiss 1971:
88–97). A recent article, for example, apparently treated possession of weapons offences as
part of a dependent variable called “weapons offences,” as well as counting the SSEs that
detected the crimes as part of the independent variable (Braakman 2022: 1375). In order
to prevent the confusion created by current crime recording methods, a recent consensus
statement endorsed by statisticians and police chiefs called for complete removal of proac-
tive detections from a weighted crime harm index (Sherman etal. 2020). That is the proto-
col we applied to the data used in the present analysis.
The Metropolitan Police data we analyze covers 183 consecutive months from July
2008 through September 2023, with records including dates of all 58,503 recorded knife
injuries and 4,286,096 recorded SSEs in the time period. While the mean ratio of these two
variables is 74 SSEs for every knife injury, that ratio varies widely from month to month.
It is that variation in ratio, and co-variation of the two variables, that we use to examine the
question of the force-wide effects of SSE volume on knife injuries.
Methods: Time Series Model & 2 Quasi‑Experiments
Given the time-oriented nature of our data, the current study uses a combination of
time series analyses to follow conventional approaches in this area of research in gen-
eral (Chatfield 2013; McDowall etal. 1980) and in criminology in particular (McDowall
etal. 2024; Wolff etal. 2022). In order to situate our analyses over the long time period,
we use time series analysis to investigate the long-term relationship between SSEs and
knife injuries as well as knife homicides (from July 2008 through September 2023).
More specifically, we use time series models which take into consideration the temporal
dependencies of time series data. Before we considered the substantive results of our
work, we engaged in a series of pre-analysis data checks with respect to the distribution
of the knife injury and knife homicide data to assess stationarity and the presence of
autocorrelation. The estimation equation for the time series analysis can be expressed as
follows:
(1)
Yt=β
0+β
1SSEt+β
2Yt−1+𝜖t
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Journal of Quantitative Criminology
In Eq.(1),
Yt
represents the outcome variable (either knife injuries or knife homicides)
at month of year t, and
SSEt
denotes the police stop and search encounters (SSEs) at time t.
The term
Yt−1
is the lagged value of the outcome variable, accounting for temporal depend-
ency. The coefficient
β1
represents the effect of SSEs on the outcome variable, while
β0
is
the constant term. The error term
ϵt
accounts for any unobserved factors affecting the out-
come. This model captures the long-term relationship between SSEs and knife injuries or
homicides, considering the temporal dependencies and autocorrelation in the data.
First, we assessed stationarity and the presence of autocorrelation. To test for stationar-
ity, we used the Dickey–Fuller Test. For the knife injury data, the test statistic was − 5.231
(p < 0.01), which is below the critical values at the 1% (− 4.013), 5% (− 3.439), and 10%
(− 3.139) levels. This suggests that the time series is stationary and does not follow a ran-
dom walk.
Next, we calculated both the autocorrelation function (ACF) and the partial autocorrela-
tion function (PACF). A slow decay in the ACF would indicate non-stationarity; however,
in our case, it dropped quickly, further supporting the conclusion that the trend is station-
ary. The PACF also showed evidence of stationarity, although there was some indication of
autocorrelation. Specifically, the first PACF estimate was well outside the 95% confidence
interval, and the second estimate was just outside the same interval, suggesting autocor-
relation. The Cumby-Huizinga test confirmed autocorrelation beyond the AR(1) model,
which we address in the time series model section.
We then tested for heteroskedasticity, which occurs when the variance of the errors is
not constant across observations. This involved two steps: first, running a naïve regression
equation predicting knife injuries from stops, followed by the Breusch-Pagan/Cook-Weis-
berg test for heteroskedasticity. The results produced a χ2(1) of 15.15 (p < 0.05), indicating
evidence of heteroskedasticity. To correct for this, we logged the number of knife injuries.
After this transformation, the Breusch-Pagan/Cook-Weisberg test returned a χ2(1) of 0.775
(p > 0.05), suggesting that heteroskedasticity is no longer a concern in the analysis.9
Next, we perform a Durbin-Watson test, where the null hypothesis is that there is no
first-order autocorrelation. The test produces a DW-d statistic, which takes on values
between 0 and 4 and a value near 2 indicates non-autocorrelation. Values of d less than 2
suggest positive autocorrelation, whereas values of d greater than 2 suggest negative auto-
correlation. The DW-d statistic was 0.514, indicating that there is autocorrelation present
in the time series and that it needs to be taken into consideration.
We examined an Autoregressive Integrated Moving Average (ARIMA) model contain-
ing three parameters (p, d, q), where p is the order of autoregressive terms (AR1, AR2,
etc.), d is differencing (earlier results show that there is no need for differencing the series),
and q is the order of the moving average process. Although there are many ways of select-
ing a final ARIMA model, we follow a procedure that starts with three models, based on
the results of the preliminary tests above. First, (1,0,0) AR(1) process. Second, (2,0,0)
AR(2) process. And third, (2,0,1) AR(2) and MA (1) processes. We examine the AR and
MA coefficients as well as goodness of fit measures (AIC and BIC scores) to assess overall
model fit across the various estimations to arrive at a best fitting model and then we will
proceed to adding the main covariate of interest, stop search, to the best-fitting model. Spe-
cifically, we fit the following models:
9 It is important to note that we estimated AR models using both the logged and unlogged number of knife
injuries. Both sets of analyses returned similar substantive results with respect to the effect of the number
of stops on knife injuries. Because the unlogged estimates are more interpretable, they are presented in the
main results section. The logged estimates are available upon request.
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Journal of Quantitative Criminology
With respect to the three different models, the (1,0,0) model (2) returned a significant
AR1 parameter estimate while the (2,0,0) model (3) also returned significant AR1 and
AR2 parameter estimates, with the latter model (4) fitting slightly better than the former.
This suggests that the significant AR1 and AR2 effects indicate that the past two months of
knife injuries predict current counts in London. When a MA(1) parameter was added to the
(2,0,0) model, hence a (2,0,1) model, the MA(1) parameter (
𝜃
) was not significant indicat-
ing no need for incorporating a moving average did not improve prediction. This was the
case for both knife injuries and knife homicides.
Now, with our preferred AR10(2) model (3) in hand, we proceed to our substantive
analysis, examining the relationship between stop-and-search encounters and knife inju-
ries (and separately for knife homicides). Importantly, we account for seasonality and any
potential period-specific shocks in the data by including monthly and yearly dichotomous
variables within the independent variable space, in addition to the two autoregressive (AR)
parameters. We also use robust standard errors to address potential heteroskedasticity.
Granger Causality: Directional Tests
Readers may notice that our AR models specify a relationship running from stop-and-
search encounters (SSEs) to both knife injuries and knife homicides, which could raise
concerns about potential specification issues. This challenge is common in criminological
research, such as studies examining the relationship between police numbers and crime
rates (Marvell and Moody 1996; Kovandzic etal. 2016). To address this, we conducted a
Granger causality test (Granger 1969) to assess the causal direction between SSEs and both
knife injuries and knife homicides, using two lags for each outcome.
Specifically, the null hypothesis for the Granger causality test is twofold: (1) lagged
values of SSEs do not cause knife injuries (and knife homicides), and (2) lagged values
of knife injuries (and knife homicides) do not (Granger) cause SSEs. Regarding knife
injuries, the results indicated that lagged values of SSEs (Granger) caused knife injuries
(χ2 = 10.959, p < 0.05), but lagged values of knife injuries did not cause SSEs (χ2 = 2.201,
p > 0.05). Similarly, for knife homicides, the results were consistent: lagged values of SSEs
caused knife homicides (χ2 = 7.60, p < 0.05), while lagged values of knife homicides did
Model 1: AR(1) Process
(2)
Yt=β
0+β
1Yt−1+ϵ
twhere p =1, d =0, q =0
Model 2: AR(2) Process
(3)
Yt=β
0+β
1Yt−1+β
2Yt−2+ϵ
twhere p =2, d =0, q =0
Model 3: AR(2) and MA(1) Process
(4)
Yt=β
0+β
1Yt−1+β
2Yt−2+θ
1ϵt−1+ϵ
twhere p =2, d =0, q =1
10 Readers should note that while we started our preliminary analysis within the ARIMA context, the
results show that there is no need for differencing nor was there evidence of a moving average. Therefore,
we end up with an AR model.
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Journal of Quantitative Criminology
not (Granger) cause SSEs (χ2 = 1.175, p > 0.05). Although Granger causality, sometimes
referred to as “forecasting,” cannot establish "true causality" in a theoretical sense, the
results of these tests provide confidence that the direction of the relationship does indeed
run from SSEs to both knife injuries and knife homicides. The Granger causality tests are
specified by the following models:
The first model (5) examines the relationship between stop-and-search encounters
(SSEs) and knife injuries. It includes lagged values of SSEs up to two periods, along with
lagged values of knife injuries, to account for any temporal dependencies. The second
model (6) assesses the relationship between SSEs and knife homicides, following a similar
structure to the first model, with lagged values of both SSEs and knife homicides included.
In both models, the coefficients
αi
and
γi
capture the influence of the lagged terms, while
the error term
𝜖t
accounts for unobserved factors affecting the outcomes. These models are
used to investigate the Granger causal direction between SSEs and the two outcomes, knife
injuries and homicides.
Two Quasi‑Experiments
The second portion of our analysis assessed effects of two quasi-experimental interven-
tions, one by rapid reduction in SSEs and one by a sudden surge of more SSEs. These anal-
yses rely on Poisson regression, a generalized linear regression model designed to measure
count data, with controls for month, year, and appropriate lags.11
AR Model Results
CITY‑WIDE Knife Injuries
Between July 2008 and September 2023, there were a total 58,503 recorded knife injuries
and exactly 4,286,096 recorded SSEs. Figure 1 shows the time series relationship trend
between the monthly SSEs and knife injuries.
Table 1 presents the results examining the relationship between SSEs and knife inju-
ries. As can be seen, the parameter estimate for SSEs is negative and statistically signifi-
cant. With a parameter estimate of -1.509, this result indicates that for each additional 1000
SSEs there are 1.5 fewer knife injuries. This link was observed despite controls for month
and year, as well as autoregressive parameters.
(5)
Knife Injuries
t=β
0+
2
∑
i=1
αiSSEst−i+
2
∑
i=1
γiKnife Injuriest−i+𝜖
t
(6)
Knife Homicides
t=β
0+
2
∑
i=1
αiSSEst−i+
2
∑
i=1
γiKnife Homicidest−i+𝜖
t
11 It is sometimes the case with count data, that there is overdispersion in the variable of interest which
would necessitate an adjustment to the Poisson regression model, or the estimation of a negative binomial
regression model if the standard deviation is greater than the mean of the variable of interest. In our case,
there was no over-dispersion necessary as for both outcomes, knife injuries and knife homicides, the stand-
ard deviation was never greater than the mean.
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Journal of Quantitative Criminology
In order to provide a visual interpretation of our results, we graph the relationship
between SSEs and knife injuries by obtaining the predicted count of knife injuries result-
ing from our regression models at various levels of SSEs. Table2 presents the predicted
count of knife injuries citywide that are anticipated between 10,000 and 45,000 SSEs,12
while Fig.2 presents these results graphically. As can be seen in Fig.2, there is a nega-
tive, linear relationship between SSEs per 1000 and the predicted count of knife injuries
citywide. Specifically, at 10,000 SSEs per month—about the actual level in early 2024—
the predicted count would be 340 knife injuries; at 25,000 SSEs per month the predicted
count would be 317 knife injuries; and at 45,000 SSEs the predicted count would be 287
knife injuries per month. Thus, the predicted percent change in knife injuries between the
low (10,000 SSEs) and high (45,000) end would be about 16% fewer knife injuries, or 600
fewer per year with 45,000 SSEs per month (540,000 per year), which was about the level
delivered in 2008–2012 and again in 2021, but below that of the surge in 2017) (Table3).
City‑Wide Knife Homicides
Between 2008 and 2023, there were a total of 1038 knife homicides.13 Figure3 shows the
time series relationship trend between the monthly SSEs and knife homicides. We do not
display the relationship of SSE counts to all homicides since the AR model found no statis-
tically significant relationship between SSEs and all murders.14 What we do show is that if
the volume of SSEs increased from its 2023 level of around 10,000 per month to its 2011
level of some 45,000 per month, there would be an estimated reduction of about 30 knife
murders per year—about one-fourth fewer total homicides in London.15
Next, we estimated an AR (2,0,0) model, the results of which showed that SSEs were
negatively and significantly (p = 0.052) related to the number of knife homicides. The coef-
ficient estimate is not very large, yet the reduced death rate is clearly related to the increase
in SSEs.
In order to provide a visual interpretation of our results, we graph the relationship
between SSEs and knife homicides from the fitted models using a margins plot. Table4
presents the margin estimates between 10,000 and 45,000 SSEs and the predicted count of
knife homicides citywide; Fig.4 graphically presents these results. As shown in Table4,
there is a linear negative relationship between SSEs and predicted homicides such that at
10,000 SSEs per month, the predicted outcome count would be 6.671 knife homicides per
month; at 25,000 SSEs per month, the predicted count would be 5.585 knife homicides
per month; and at 45,000 SSEs per month, the predicted count would be 4.13 knife homi-
cides per month. In short, the predicted percent change in knife homicides between the low
(10,000 SSEs) and high (45,000 SSEs) end would be about 38% fewer knife homicides
with the larger number of SSEs (Table5).
12 These numbers were chosen as the bounds observed in the SSE data over time.
13 During this same time period, there were a total of 1883 homicides. The knife homicides accounted for
55.1% of the total number of homicides recorded by the London Metropolitan Police.
14 This is likely a power issue. It is worth noting that SSE effects have to be 1.6 × as large the size they are
for knife injuries to be able to forecast murders.
15 We obtained the 30 figure by taking the number of predicted homicides at 10,000 stops (6.67) less the
predicted number of homicides at 45,000 stops (4.13), which amounts to 2.5 homicides. Taking 2.5 homi-
cides per month at 12months per year, amounts to 30 fewer predicted fewer homicides (see estimates in
Table4).
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Journal of Quantitative Criminology
Two Quasi‑Experiments
This section presents an analysis of two rapid changes in the monthly volume of SSEs,
each of which is conceptualized as a Level 2 quasi-experiment with no simultaneous
control group (Sherman etal. 1998). Level 2 is located on the Maryland Scale of 1–5,
in which criminologists rate a randomized controlled trial with a large sample size and
strong statistical power as a 5, and a cross-sectional correlation as a 1. In the Level
2, no-control group research design, inference benefits from the temporal sequence
(Granger 1969), but conclusions of causal relationships suffer a threat to internal valid-
ity by possible correlations with other changes affecting knife injuries at exactly the
same time. A standard procedure in such cases is to scan the environment for any likely
candidates to make these Level 2 test conclusions spurious. Another practice is to exam-
ine the speed with which counts of the response variable (knife injuries, in this case)
change in response to changes in the independent variable (in this case, SSEs).
0
100
200
300
400
500
0
10000
20000
30000
40000
50000
60000
2008/07
2009/03
2009/11
2010/07
2011/03
2011/11
2012/07
2013/03
2013/11
2014/07
2015/03
2015/11
2016/07
2017/03
2017/11
2018/07
2019/03
2019/11
2020/07
2021/03
2021/11
2022/07
2023/03
Monthly SSEs & Knife Injuries
(July 2008 -September 2023)
Left Axis = Stops, Right Axis = Injuries
Stop Search Knife Injuries
Fig. 1 Monthly SSEs & knife injuries (July 2008–September 2023)
Table 1 AR(2) Results
Predicting Number of Knife
Injuries
*p < 0.05. Model includes controls for month, year, and two autocor-
relation parameters (not shown) as well as robust standard errors to
account for heteroskedasticity
Variable Estimate Robust SE 95% CI
SSEs Per 1000 − 1.509 0.669* − 2.822 to − 0.196
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Journal of Quantitative Criminology
Our review of the recent 15-year history of London policing, during which the second
author worked closely with police leaders in the UK, produced no likely rival explanations
for the two rapid changes in monthly knife injuries. This includes the foremost question of
the varying numbers of Metropolitan Police officers from 33,260 in 2010 to under 31,000
260 280 300 320 340 360
Predicted Count of Knife Injury Incidents Citywide
10 15 20 25 30 35 40 45
Stops *1000
Data Source: London Metropolitan Police
Monthly Knife Injuries as a Function of 1,000 Stops
Fig. 2 Margins plot of predicted knife injuries at different levels of SSEs per 1000 per month
Table 3 AR(2) Results
Predicting Number of Knife
Homicides
† p < 0.052. Model includes controls for month, year, and two autocor-
relation parameters (not shown) as well as robust standard errors to
account for heteroskedasticity
Variable Coefficient Robust SE 95% CI
SSEs Per 1000 − 0.072 0.044†− 0.159 to 0.014
Table 2 Margins plot predicted
knife injuries at different levels
of SSEs per 1000 per month
Margin Std. Err z [95% conf.
interval]
10,000 SSEs 340.367 9.512 35.78* 321.722 359.011
15,000 SSEs 332.818 6.344 52.46* 320.383 345.253
20,000 SSEs 325.269 3.528 92.18* 318.353 332.185
25,000 SSEs 317.720 2.662 119.34* 312.502 322.938
30,000 SSEs 310.171 4.915 63.10* 300.536 319.806
35,000 SSEs 302.622 7.979 37.92* 286.982 318.263
40,000 SSEs 295.073 11.208 26.33* 273.105 317.042
45,000 SSEs 287.525 14.492 19.84* 259.120 315.929
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Journal of Quantitative Criminology
in several years thereafter and then a return to almost 33,000: was change in SSEs merely a
function of officer numbers? While ‘’total officers’’ is a crude measure that may not reflect
the potential for SSEs by officers on foot patrol or other duties in public places, the two
periods of greatest increase in total officers (2013–2016 and 2020–2022) were accompa-
nied not by a decrease in knife injuries, but by an increase in them. In those same time
periods, however, there was a decrease in SSEs.16
Other rival hypotheses might theoretically include economic changes, changing num-
bers of males aged 16–24, or the availability of knives in the population. Yet none of these
0
2
4
6
8
10
12
14
16
0
10000
20000
30000
40000
50000
60000
2008-07
2009-02
2009-09
2010-04
2010-11
2011-06
2012-01
2012-08
2013-03
2013-10
2014-05
2014-12
2015-07
2016-02
2016-09
2017-04
2017-11
2018-06
2019-01
2019-08
2020-03
2020-10
2021-05
2021-12
2022-07
2023-02
2023-09
Monthly SSEs & Knife Homicides (July 2008 -
September 2023)
Stop Search Knife Homicides
Fig. 3 Monthly SSEs & knife homicides (July 2008–September 2023)
Table 4 Predicted Knife
Homicides at Different Levels of
SSEs Per 1,000
Margin Std. error Z-value 95% confi-
dence Interval
10,000 SSEs 6.671 0.641 10.40* 5.414 7.929
15,000 SSEs 6.309 0.436 14.46* 5.454 7.164
20,000 SSEs 5.947 0.261 22.74* 5.435 6.460
25,000 SSEs 5.585 0.214 26.09* 5.165 6.005
30,000 SSEs 5.223 0.350 14.91* 4.536 5.909
35,000 SSEs 4.861 0.546 8.89* 3.789 5.932
40,000 SSEs 4.499 0.757 5.94* 3.013 -5.984
45,000 SSEs 4.136 0.974 4.25* 2.227 -6.046
16 See numbers of Metropolitan Police officers by year in results of Google Search on 23 March 2025 at
https:// www. google. com/ search? client= firef ox-b- d&q= how+ many+ police+ offic ers+ were+ there+ in+ Lon-
don+ in+ 2010- 2022 + :
2010: 33,260 (excluding special constables)
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Journal of Quantitative Criminology
possibilities could have changed so rapidly as to fit the sudden shifts in trends in knife
injury as summarized in Fig.1.
Moreover, both of the changes in SSE volume that we examine were made in the con-
text of substantial public debate about the appropriate level of SSE volume.
Table 5 Poisson Regression
Predicting Knife Injuries
*p < 0.05; Model includes controls for month, year, and two lags of
knife injuries (not shown)
Variable IRR Robust SE 95% CI
SSEs per 1000 0.994 0.002* 0.989–0.999
Cutback (= 1) 1.144 0.069* 1.016–1.289
2011: 32,380 (excluding special constables)
2013: 30,398 (excluding special constables)
2014: 30,932 (excluding special constables)
2015: 31,877
2016: 32,125
2017: 30,817
2019: 30,980 (excluding special constables)
2020: 32,766 (excluding special constables)
2022: 34,900 police officers
Footnote 16 (continued)
2 4 6 8
Predicted Count of Incidents Citywide
10 15 20 25 30 35 40 45
Stops *1000
Data Source: London Metropolitan Police
Monthly Knife Homicides as a function of 1K Stops
Fig. 4 Margins plot of knife homicides at different levels of SSEs per 1000 per month
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Journal of Quantitative Criminology
As to the speed of the changes, there is an evidence-based concept of residual deter-
rence (Sherman 2023; Koper 1995; Barnes etal. 2020) by which changes in crime may not
occur immediately after changes in policing, depending on the nature of police changes
and circulation of local information. Hence, there is no established fixed time period of
deterrence decay (Sherman 2023) to compare to the increases in knife injury in response
to reductions (or an increase) in SSE volume. In both quasi-experiments, however, the
length of the total time periods in both “before” and ‘’after” conditions was great enough
to observe substantial differences in both SSE volumes and knife injury outcomes.
Quasi‑Experiment 1: Cutback from2014–17
In May of 2014, records show that police officers collectively decided to substantially
‘’cut back’’ the volume of SSEs.17 This “cutback” transition came after they had already
been reducing SSEs in the aftermath of the 2011 London Riot, and the Home Secretary
exhorting them to limit SSEs. Yet the perfect storm in early 2014 pushed SSEs to the bot-
tom for the next several years, with no reason for residual deterrence to last very long.
Accordingly, for this portion of the analysis, we use the period beginning right after the
“Cutback” change in May 2014 through December 2017 as the post-Cutback “after”
period (n = 44months), while the period from July 2008 through April 2014 we defined
as the pre-Cutback period with SSEs generally well above the 10,000 per month level
(n = 70months). We focus our comparison on the changes in SSEs and knife injuries across
the pre- and post-Cutback periods.
As shown in Fig.5, the results are striking: knife injuries significantly increased after
the Cutback began as SSEs significantly decreased. The mean number of knife injuries
each month increased from 314 to 343, or a 9.34% increase (for an additional 1276 knife
injuries during the Cutback period), while the mean number of SSEs decreased by 66%,
from 35,811 in the 70-month pre-Cutback period to 12,302 per month in the 44-month
Cutback period. Effect size calculations revealed a moderate to large effect, with a Cohen’s
d of − 0.551 (r = − 0.266) for knife injuries and 3.789 (r = 0.884) for SSEs.
When we estimated a Poisson regression controlling for month, year, and two lags of
knife injuries, the results showed that SSEs were preventive of knife injuries while the Cut-
back was associated with an increase in knife injuries. Recall that Incident Rate Ratios
(IRRs) below 1.0 are indicative of a negative effect while IRRs above 1.0 are indicative
of a positive effect. While the effect of SSEs per 1000 on knife injuries was negative and
statistically significant, its effect on knife injuries was not very large; that is consistent with
the large drop in SSEs after the Cutback. On the other hand, the IRR of 1.144 associated
with the Cutback indicates that the risk of knife injuries is 14% higher during the period
after the Cutback compared to the period prior to it.
Next, we take the final Poisson-based estimates and calculate the predicted number of
knife injuries at different SSE increments under the Cutback. Again, while the Cutback was
designed to lessen the number of SSEs, it remains the case that the volume of SSEs that
was delivered could still have prevented knife injuries. The predictions shown in Fig.6 and
Table6 also indicate that with an increase in the number of SSEs, many more knife injuries
would be prevented. Specifically, at 10,000 SSEs, the predicted monthly number of knife
17 https:// www. thegu ardian. com/ law/ 2014/ apr/ 30/ there sa- may- reform- police- stop- and- search- powers
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Journal of Quantitative Criminology
injuries would be 350, while at 50,000 SSEs it would be 282 knife injuries per month, a
decrease of 19.27%.
Consistent with the results above showing that the Cutback was associated with an
increase in knife injuries, the results for knife homicides point to an even stronger adverse
trend during the Cutback period. In this case, as shown in Fig.7 during the period after
the Cutback, monthly knife homicides showed a statistically significant increase from an
average of 4.57–5.56, or about one per month on average, for a total of 44 knife homicide
deaths, with a Cohen’s d effect size of 0.4.18
In addition to these analyses, we also estimated a regression discontinuity (RD) design
for both knife injuries and stop searches. These types of designs are being used increas-
ingly in criminal justice that surround causal questions (Owens and Ludwig 2013). Spe-
cifically, we used robust RD with Sharp RD estimates using local polynomial regression.
These results provided strong evidence of a significant change in both variables, with knife
injuries increasing after the cutback (coeff = 58.343; std. err = 25.547, z-value = 2.2838,
p = 0.022) and stop searches decreasing (coeff = − 2.054; std. er r = 2.109; z-value = − 0.973;
p = 0.330). Figure 8 presents the RD plot for knife injuries while Fig.9 presents the RD
plot for stop searches. Full results may be found in Technical Appendix I.19 The general
form for the RD model was estimated by the following form:
In the RD model (7) estimates the effect of a cutback on the outcome variable
Yt
(KnifeInjuriesorSSE)
using a regression discontinuity (RD) design. The binary variable.
Post-Cutbackt
indicates whether the observation falls before or after the cutback, while the
function f
(
X
t)
represents a local polynomial regression of the running variable time to cut-
back (− X to + X) to account for smooth trends near the cutoff. The coefficient
β1
captures
the causal effect of the cutback on the outcome
Yt
, controlling potential non-linearities in
the relationship with the running variable.
Quasi‑Experiment 2: ‘’Surge’’ from2018–2020
In January 2018, the MPS collectively produced a reversal of the Çutback trend. We now
examine whether the police “Surge” increase in SSEs commencing from January 2018 was
associated with a decrease in knife injuries.20
Because the last few years of our city-wide time series runs up to and through the
COVID-19 epidemic, the analysis is complicated by lockdowns, soft openings, re-open-
ings, partial shutdowns, and other disruptions. We therefore decided to consider the period
of the Surge as inclusive from January 2018 through February 2020, a period of 26months
that culminates in March 2020 when London and the rest of the world virtually shut down
(7)
Yt
=β
0
+β
1
Post-Cutback
t
+f
(
X
t)+ϵ
t
18 While we caution readers that the absolute number of knife homicides is small each month, knife attacks
comprise the majority of all homicides in both London and England & Wales (https:// www. stati sta. com/
stati stics/ 862984/ murde rs- in- london/).
19 Some readers will observe from Fig.9 that stop searches were already decreasing prior to the May 2014
cutback announcement from political figures (as noted in Footnote #17). Yet, the decrease in stop searches
continued after the May 2014 directive to even lower stop search levels.
20 There was no significant effect of the surge on knife homicides, with the average increasing from 6.269
to 7.230.
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Journal of Quantitative Criminology
295
300
305
310
315
320
325
330
335
340
345
350
0
5000
10000
15000
20000
25000
30000
35000
40000
Before Cutback (July 2008 - April 2014;
n=70 months)
After Cutback (May 2014 - December
2017; n=44 months)
Cutback Test: Monthly SSEs & Knife Injuries
Left Axis = SSEs, Right Axis = Injuries
Fig. 5 Cutback test: monthly SSEs & knife injuries. Time period: 70months before, 44months after May
2014 CUTBACK. Blue = Homicides. Orange = SSEs
250 300 350 400
Predicted Count of Incidents Citywide
10 20 30 40 50
Stops *1000
Data Source: London Metropolitan Police
Monthly Knife Injuries as a function of 1K Stops: Cutback
Fig. 6 Cutback: margins plot of predicted knife injuries at different levels of SSEs per 1000 per month
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Journal of Quantitative Criminology
due to COVID-19 restrictions. Thus, in order to have a 26month comparison period prior
to the Surge, we use the period of time from November 2015 through December 2017.
During that entire 52-month period before (26 months) and after (26 months) the
change to the Surge significantly increased police SSEs, there were a total of 774,463 SSEs
and 18,549 knife injuries. These totals are distributed as follows: 303,611 pre-surge SSEs
and 470,852 post-surge SSEs; 9,626 (pre-surge) knife injuries and 8,923 (post-surge) knife
injuries. A means-difference test indicates that there were significantly fewer knife inju-
ries, on average, in the post-surge (Mean injuries = 343.192 per month) compared to the
pre-surge (Mean = 370.23) periods (p < 0.05), or about a seven percent drop. A means-
difference test indicated that police significantly increased their searches after the surge
(Mean = 18,109.69) compared to the 26 month period beforehand (Mean = 11,677.35)
(p < 0.05), amounting to an increase of 55%. For the surge intervention, effect size calcula-
tions revealed a moderate to large effect, with a Cohen’s d of 0.522 (r = 0.252) for knife
injuries and − 1.527 (r = − 607) for SSEs. Figure10 presents a graphical depiction of knife
injuries and SSEs before and after the surge increase.
A Poisson regression was estimated for the effect of SSE increase during the surge, with
controls for month and year and two lags of knife injuries. As shown in Table7, the number
Table 6 Estimated predicted
number of knife injuries at
different stop increments under
the cutback
Margin Std. Err. z [95% Conf.
Interval]
10,000 SSEs 350.498 15.858 22.10* 319.415 381.581
20,000 SSEs 332.226 6.405 51.87* 319.672 344.780
30,000 SSEs 314.906 3.691 85.30* 307.670 322.142
40,000 SSEs 298.489 10.944 27.27* 277.038 319.941
50,000 SSEs 282.928 17.878 15.83* 247.888 317.969
0
1
2
3
4
5
6
0
5000
10000
15000
20000
25000
30000
35000
40000
Before Cutback (July 2008 - April 2014;
n=70 months)
After Cutback (May 2014 - December
2017; n=44 months)
Cutback Test: SSEs & Knife Homicides
Left Axis = SSEs, Right Axis = Homicides
Fig. 7 Cutback test: SSEs & knife homicides. Blue = Homicides. Orange = SSEs
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Journal of Quantitative Criminology
250 300 350 400 450
0 50 100 150
Sample average within binPolynomial fit of order 4
Cutback Test: RD Plot Knife Injuries
Fig. 8 Cutback test: RD plot knife injuries
10 20 30 40 50
0 50 100 150
Sample average within binPolynomial fit of order 4
Cutback Test: RD Plot Stops Per 1k
Fig. 9 Cutback test: RD plot stops per 1k
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Journal of Quantitative Criminology
of SSEs per 1000 was negatively and significantly related to a reduction in knife injuries
but the surge coefficient did not emerge as a significant predictor. This is not entirely unex-
pected given that the change in knife injuries was not nearly as large as the increase in
police SSEs per 1000 after the surge was announced.
Finally, we again use the Poisson-based estimates to calculate the predicted number
of knife injuries at different stop increments under the Surge. The results are found in
Table8 and Fig.11 below. In short, these results show that at 10,000 SSEs per month, we
325
330
335
340
345
350
355
360
365
370
375
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
Before Surge (November 2015 -
December 2017; n=26 months)
After Surge (January 2018 - February
2020; n=26 months)
Surge Test: SSEs & Knife Injuries
Left Axis = SSEs, Right Axis = Knife Injuries
Fig. 10 Surge test: SSEs & knife injuries. Orange line = Monthly SSE counts. Blue line = monthly knife
injury counts
Table 7 Poisson Regression
Predicting Number of Knife
Injuries
*p < 0.05; Model includes controls for month, year, and two lags of
knife injuries (not shown)
Variable IRR Robust SE 95% CI
SSEs per 1000 0.986 0.004* 0.977–0.994
Surge Increase 1.073 0.075 0.935–1.232
Table 8 Estimated predicted
number of knife injuries at
different stop increments under
the surge
Asterisk indicates result falls outside the 95% confidence interval
Margin Std. Err z [95% Conf.
Interval]
10,000 SSEs 380.742 7.966 47.79* 365.128 396.356
20,000 SSEs 331.549 8.342 39.74* 315.199 347.899
30,000 SSEs 288.712 19.575 14.75* 250.345 327.078
40,000 SSEs 251.409 27.916 9.01* 196.695 306.124
50,000 SSEs 218.926 33.796 6.48* 152.687 285.166
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Journal of Quantitative Criminology
150 200 250 300 350 400
Predicted Count of Incidents Citywide
10 20 30 40 50
Stops *1000
Data Source: London Metropolitan Police
Monthly Knife Injuries as a function of 1K Stops: Surge
Fig. 11 Surge: margins plot of predicted knife injuries at different levels of SSEs per 1000 per month
200 250 300 350 400 450
0 10 20 30 40 50
Sample average within binPolynomial fit of order 4
Surge Test: RD Knife Injuries
Fig. 12 Surge test: RD knife injuries
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Journal of Quantitative Criminology
10 15 20 25 30
0 10 20 30 40 50
Sample average within binPolynomial fit of order 4
Surge Test: RD Stops Per 1k
Fig. 13 Surge test: RD stops per 1k
200250 300350 400450
Number of Knife Injuries
2008m12010m12012m12014m12016m12018m1 2020m1 2022m1 2024m1
Month
10,000 Stops 45,000 Stops
Marginal Effects of SSEs on Knife Injuries (July 2008 - September 2023)
Fig. 14 Marginal effects of SSEs on knife injuries (July 2008–September 2023). Note: Semi-robust standard
errors two lags.
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Journal of Quantitative Criminology
would predict 380 knife injuries, but at 45,000 SSEs we would predict 218 knife injuries,
a decrease of 42.5%. Compared to the other directives, this is by far the largest decrease
in knife injuries (with increasing SSEs) especially given the small duration of the surge
assessed with our data prior to the COVID-19 lockdowns. At 162 fewer injuries per month,
the annualized total (1944) is almost 2000 fewer knife injuries per year (Figs. 12, 13 and
14).
Finally, as was the case with the first quasi-experiment, we also performed a robust RD
test (Sharp RD estimates using local polynomial regression) for both knife injuries and stop
searches during the Surge. Once again, the RD Test confirmed the results noted above but
the effects were not as strong likely because of the small number of monthly observations
available for analysis before and after the surge. Specifically, knife injuries significantly
decreased after the surge (coeff = − 42.186; std. err = 22.39; z-value = − 1.884; p = 0.060),
while stop searches had both a decrease, large surge, and then plateau after the surge lead-
ing to an overall negative coefficient (coeff = − 0.864; std. err = 0.756; z-value = − 1.142;
p = 0.253).21 Full results may be found in Technical Appendix II.
Supplemental Sensitivity Analysis
We also performed two additional supplemental analyses. In the first, we estimated a vector
autoregression (VAR) where we predicted multiple time series (for stop searches and both
knife injuries and knife homicides) along with two lags of each. Those results were sub-
stantively similar to what was reported in the main portion of the AR time series analysis.
Namely, in the models predicting stop searches and knife injuries, lagged effects of stop
searches were negatively and significantly related to lagged effects of knife injuries but
the inverse was not the case. Similarly, lagged effects of knife homicides were not related
to lagged effects of stop searches but lagged effects of stop searches were negatively and
significantly related to lagged effects of knife homicides.
In the second supplemental analysis, we performed an additional vector autoregression
that also added the use of an exogenous variable, our measure of cutback and surge. To
simplify the model, the time series consists of pre-cutback, during cutback, post-cutback,
COVID-19 cutback (post-February 2020). Under this construction, the time series has an
indicator for 1, 0, 1, 0, which seems especially good because the time series has two surges
that are disrupted by a decision to cutback due to policy choice or COVID-19—which are
arguably exogenous.
The VAR “is a seemingly unrelated regression model with the same explanatory vari-
ables in each equation” (Stata, 2019, p.776). Following Lütkepohl (2005), the VAR(p) with
exogenous variables as (and with two lags of both stop searches and knife injuries (and
separately for knife homicides)):
where
Yt
is the K × 1 vector of endogenous variables, A is a K × Kp matrix of coefficients
(to include both stop searches and knife injuries (and separately for knife homicides), B₀ is
a K × M matrix of coefficients, xt is the M × 1 vector of exogenous variables, ut is the K × 1
vector of white noise innovations, and Yt is the Kp × 1 matrix given by.
(8)
Yt=AYt−1+B0xt+ut
21 Readers should take the RD tests regarding the Surge with caution, especially given the small number of
months before and after the Surge.
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Journal of Quantitative Criminology
Yt =
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
Yt
.
.
.
.
𝐘t−p+1
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
With respect to knife injuries, these results show that stop searches significantly
predict knife injuries but not the other way around. Also, importantly the surge time
interval significantly predicts a change in stops (positive) but is not predictive of knife
injuries in the simultaneous equation—which is what we would have anticipated. The
VAR model shows a slightly larger effect of stop searches on knife injuries (− 2.055)
compared to the one observed in the AR model shown earlier in the paper (− 1.509).
Finally, the Granger test shows that lagged stops predict knife injuries but lagged knife
injuries do not predict stop search levels. Turning to knife homicides, the results show
that stop searches significantly predict knife homicides but not the other way around. As
well, the surge time interval significantly predicts a change in stops (positive) but is not
predictive of knife homicides in the simultaneous equation. The VAR model shows a
very similar coefficient estimate of stops on knife homicides (− 0.069) compared to the
one observed in the AR model shown earlier in the paper (− 0.072). In sum, these find-
ings are all consistent with those from the AR models presented earlier for both knife
injuries and knife homicides.
Finally, we also provide an additional margins plot from these analyses that include the
entire time series. We made two choices regarding stop search levels, 10,000 and 45,000,
since those represent roughly the bottom 5% and top 95% of stop search ranges. Based on
these data, it can be seen that at 45,000 compared to 10,000 stop searches per month we
can expect 9671 fewer knife injuries or what is equivalent to 53 fewer knife injuries per
month over the 183-month time series.
Costs ofBenets
Our estimates of the benefits of higher levels of SSEs can be contrasted with two possible
costs. One is the potential loss of trust in the police: an undermining of policing by con-
sent. The other is the use of police time that could have been devoted to other activities
with more benefit than that produced by SSEs.
Loss ofTrust?
The key question for many police leaders is not whether stop and search prevents weapons
crime, but whether it undermines trust in policing too much to use proactively. Our data
on this question is limited but instructive. From 2016 through 2022 we can draw on an
independent quarterly survey conducted (“mostly’’ face-to-face) by the London Mayor’s
Office for Policing and Crime (MOPAC), with 600 respondents per year for each of the 32
boroughs (19,200 total) comprised of 4800 responding households per quarter. The survey
began well before 2016, but only included a specific question on trust in the Metropolitan
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Journal of Quantitative Criminology
Police from 2016 (MOPAC 2024). The exact wording of the question is as follows, with
the percent in agreement as the reported quarterly result:
“To what extent do you agree or disagree with the following statement: The Metropol-
itan Police Service is an organisation that I can trust’’ (Parliament, UK, Undated).
Over the seven-year period from the inclusion of that question to the end of our data
series, the volume of SSEs varied widely: from 10,000 per month to 30,000 and back to
10,000. While those numbers were related to reductions and increases in knife injuries,
they bear no apparent relationship to overall trust levels (see Figure15). While this general
household response cannot reveal differences among subsets of the population, including
people who have experienced an SSE compared to those who have not, it does at least
indicate a stable level of resilience of trust by the community in general to rising levels of
stop and search—indeed to tripling it (200% increase) and reducing it by 66% to its start-
ing point in the same 7-year period, with only a 19% relative decline in trust over these ups
and downs of SSEs. Moreover, the 19% decline is observed almost entirely after the shock
of the highly publicized March 2021 arrest, and later sentence to life in prison, of a Police
Constable for the murder and rape of Sarah Everard.
The issue of whether some subgroups of ethnic minorities in London had more loss
of trust when SSEs increased is one we can address indirectly, if not with measures of
trust for each group. Because London’s population in the 2021 Census was 46% Black and
minority ethnic (Trust for London 2024), it is unlikely that a substantial correlation of lost
minority group trust in police with increased city-wide SSEs can be concealed within the
flat trend of the entire population. For that to be possible, a surge in white trust in police
would have been required to compensate for the loss of minority trust, with a correspond-
ing decline as fewer SSEs increased minority trust. For these reasons, the data displayed
in Figure15 provide reasonable evidence that a general loss of public (or minority group)
trust is not a demonstrable cost of rising SSEs.
Other Police Tasks?
The amount of time police take to conduct an SSE is generally based on about 4 offic-
ers conducting a search for about 15min if nothing is found, and some 2 to 4 h if con-
traband is seized and the suspect placed under arrest—to be transported to a “Custody
Suite’’ for processing by at least two of the arresting officers. At the rate of some 25%
stops resulting in an arrest, the formula for a 10,000 SSE month would be 1 officer hour X
7500 SSEs = 7500h, plus ~ 3h X 3 officers = 9 officer hours X 2500 arrests = 22,500 officer
hours. The 2500 arrests and 7500 non-arrests sum to 30,000 officer hours per month at
10,000 SSEs.
For 50,000 SSEs, the sum would be five times as large (30,000 X 5) = 150,000 officer
hours. Given a rough estimate of 1500 h of operational time on the streets per officer,
150,000 officer hours is the annualized equivalent of 100 officers. While that is a large
number of officers by standards in the US, it is a tiny fraction (0.2%) of some 34,000 offic-
ers in the Met. Police.
While other tasks could clearly be done by officers engaged in SSEs, it would be hard
for them to equal the apparent benefits of SSEs as identified in this article. The cost savings
from prevention of each knife injury is substantial for society as well as for the possible
victim. Every knife injury prevented is a potential criminal case of Grievous Bodily Harm
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Journal of Quantitative Criminology
(GBH), for which English Sentencing Guidelines begin at 4years (1460days), at a £50,000
per year cost to the taxpayer if the sentence served (typically) is only two years. In prison
costs alone, then, each knife injury prevented could save up to £100,000. If only 10% of
them lead to imprisonment, however, the actual cost would be about £10,000.
Medical costs to the National Health Service may also be reduced by more London
SSEs. Recently, the Trauma Audit Research Network (TARN) at the University of Man-
chester calculated the cost of a treated stabbing per victim to the National Health Service
was £7,196.22 Recall that our analysis covered a period of time with 58,503 reported knife
injuries, which carried a current estimated cost to the NHS of £420,987,588 (£2.8 million
per year). When this is coupled with the increase in trauma-team workload at local hospi-
tals (Malik etal. 2020), it is one more reason for police efforts to reduce knife injuries to
remain high priority.
Conclusions
This study combined a 15-year longitudinal London-wide correlational analysis with two
quasi-experimental tests: one that reduced SSEs and one that increased them. All three
tests, as well as two supplemental sensitivity analyses, support the conclusion that more
SSEs helped to prevent knife injuries, while two tests showed SSEs prevented knife homi-
cides. The study is not able to completely rule out other possible explanations for the
“Granger causality’’ in which changes in SSE volume forecast changes in knife violence.
Yet in the absence of contrary evidence on the precise question addressed, it may be rea-
sonable to describe a London-wide use of SSEs as ‘’evidence-informed” policy to maintain
at least 10,000 SSEs per month, and possibly 45,000. Yet that may not be the best option
available, especially in light of other evidence.
Evidence onHarm fromSSE andRacial Disparity
There are certainly other kinds of evidence to consider. Foremost for a Hippocratic
approach to policing (Sherman 2018) is the evidence of high levels of post-traumatic stress
and depression associated with the experience of young men being stopped and searched
in various cities (Weisburd etal 2023). The subjects of SSEs can be severely traumatized
by the experience. That trauma may spread to others in their family and communities, with
a larger effect of undermining public trust in the police. It is for that reason that police use
of SSEs must be as proportionate as possible to the benefits that can balance the harm that
SSE subjects can suffer. The benefit that may be most proportionate as a justification is a
reduction in knife injury and murder. Yet there still must be every step taken to maximize
that benefit.
This point connects directly to issues of racial disparity, in London as in many other
cities of diverse populations. As is the case with gun crime in the United States (Piquero
2024; Piquero and Roman 2024), the racial disparity in relation to London’s knife crime
is most extreme on the dimensions of victimization. In the ten years to 2021, Londoners
22 https:// healt hcare- in- europe. com/ en/ news/ stabb ings- injure- public- healt hcare. html#: ~: text= At% 20an%
20ave rage% 20cost% 20of,exceed% 20% C2% A33.2% 20mil lion% 20ann ually (accessed April 20, 2024).
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Journal of Quantitative Criminology
aged 16–2024 were 13 times more likely to be murdered (mostly by knives) if they were
Black men than if they were White men (Kumar etal. 2022). In the most recent financial
year (2023–2024), the homicide victimization ratio has barely changed, at 11 times greater
probability of young Black men than young Whites being murdered (Sherman and Roner
2024). Viewed from the perspective of victimization, in London as in many other cities, the
state is unable to provide equal protection of the law from homicide.
A more frequently discussed racial disparity is the probability of being stopped and
searched. That dimension is linked to both locations of knife crime and to police practice.
Many debates on this issue have focused on the causes of this disparity, but the present
analysis may, alternatively, point to a solution. The direction of travel for that solution is to
locate the occurrence of knife crime in a city of almost ten million residents—where they
occur repeatedly, and where they never occur at all.
Evidence onLocations ofWeapons Harm
In a forthcoming paper (Agar etal. 2026), a Metropolitan Police analysis of weapons crime
across all 15,772 hexagons (of 200m per side) that comprise all the land in London will
report extreme concentration of most weapons harm in under 5% of these 103,000 square
metre (equal-sized) areas. That paper also shows that over a recent 24months, 61% of Lon-
don’s hexagons had not one weapons crime victimization recorded by police. Yet in the
top 500 hexagons rank-ordered by a Cambridge Crime Harm Index scaling of harm from
weapons-enabled crime, accumulated harm scores per square metre averaged 20 times
higher than the rest of London.
This extreme concentration of weapons crime in a small number of places is not cur-
rently matched by the distribution of SSEs. Absent the analysis needed to undertake such
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
5000
10000
15000
20000
25000
30000
35000
Mar-16
Jul-16
Nov-16
Mar-17
Jul-17
Nov-17
Mar-18
Jul-18
Nov-18
Mar-19
Jul-19
Nov-19
Mar-20
Jul-20
Nov-20
Mar-21
Jul-21
Nov-21
Mar-22
Jul-22
Nov-22
Mar-23
Jul-23
Trust in Met
SSE's
Month-Year
Relationship between SSE Trends and Percent Trust in the Met
SSETrust in the Met
Fig. 15 Volume of Stop & Search compared over time to Public Attitudes Survey for London on Trust in
Police Opinions
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Journal of Quantitative Criminology
a strategy, no police agency to our knowledge has ever focused SSEs tightly on weapons
harm peaks using Pareto-ranking methods. Now that the necessary analysis has been done
in London, it opens the door anywhere to considering a proposal offered by Gladwell
(2019). That proposal is to focus SSEs on places where they can have the most benefit,
while minimizing their use as a proactive, preventive strategy outside of such locations.
Recognizing long-standing issues between law enforcement and minority communities
around the world, especially with respect to stop, frisk, and search policies (Fagan etal.
2016; Meares 2016), much reduction in tension might achieved in two ways. One way is
for police to explain and justify proactive searches by the trustworthy motive of protecting
the person who is being searched. The other way is for every SSE to apply all four princi-
ples of procedural justice (Tyler 1990).
Hence our conclusion about the past effects of SSEs need not be extrapolated to a simi-
lar future. Our evidence is city-wide, but it could have yielded even greater benefits in
harm reduction had the proactive SSEs been focused on the 5% of London where weapons
harm is concentrated. While reactive SSEs in response to an allegation of crime is required
anywhere and everywhere when it is appropriate, those SSEs can be clearly distinguished
from SSEs delivered by proactive teams whose aim is to deter weapons-carrying in pub-
lic places. With precise enough directions for locating proactive SSEs, the total number
of such encounters city-wide could possibly be reduced even further, while still reducing
knife harm.
Costs ofKnife Injuries
For all our limitations, this paper does show the clearest UK evidence to date on a wide-
spread police practice that is widely approved and paid for by taxpayers. One other cost
implication is that SSEs can also be understood to reduce the very high medical and health
care costs associated with knife crime. This is no small matter. And just as SSEs them-
selves may correlate with mental health issues subsequent to the search, injuries and deaths
from knife crime are also very harmful, and very important to prevent.
Limitations
This analysis has limitations. First, we only have data on knife injuries and knife homicides
that come to the attention of the authorities; many may never be reported, especially the
injuries. Second, as with any quasi-experimental observation study, we must be mindful
that we have not been able to establish clear theoretical causality; alternative rival hypoth-
eses may still fit the facts. Third, our analysis only considers London as a case study, and
may have limited application outside of London. Yet given that SSEs are a common fixture
of policing activity around the globe, our analytic approach could also be extended to other
areas to assess replicability.
Implications
The key implication of this analysis is what it offers for building trust in police and legiti-
macy for their work. The policing of knife crime and the racially disparate use of SSEs
have been lightning rods of debate for decades in cities from Los Angeles to Sydney to
London. One critique of the Metropolitan Police (which employed the second author) is
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Journal of Quantitative Criminology
that it under-protects and over-polices young Black men. Exactly how those terms are
defined is important, but not as important as the need to address the claim. This study
offers the first clear evidence of a correlation between more SSEs and fewer knife injuries,
potentially for people of all ages and ethnicities. It may even lead to greater equality in pro-
tection against victimization.
Many community leaders in minority areas have asked for more SSEs but say they would
like police in every SSE to be “nicer” in how they conduct the encounter. As described by a
retired police commander (Sutherland 2017), these citizens are asking for more procedural
justice (Tyler 1990) in SSEs. The analysis in this paper supports one dimension of that
approach, which is to offer trustworthy motives for imposing police authority. The trust-
worthy motive demonstrated in this paper is that it supports a claim that police SSEs can
protect the subjects of the SSEs from suffering knife injuries themselves. Police may be
able to cite these findings in every SSE they conduct in high knife-harm areas—especially
if weapons harm levels are 20 times higher there than in the rest of London.
In addition to locating the precise places where knife crime does the most harm, citi-
zens and police can support more investment in the police training and quality assessments
needed to raise the standards for delivering procedural justice. The training can improve
not just where they conduct SSEs, but how they do them. As seen in the best experimental
evidence from the US (Weisburd etal 2022), such training can not only increase trust in
police; it can help reduce harm as well.
Technical Appendix1: Robust RD Results (Cutback; N = 114, 71
beforeCutback, 44 afterCutback)
Knife injuries
Cutoff c = 71 | Left of c Right of c Number of obs = 114
-------------------
+---------------------- BW type = mserd
Number of obs | 70 44 Kernel = Triangular
Eff. Number of obs | 9 10 VCE method = NN
Order est. (p) | 1 1
Order bias (q) | 2 2
BW est. (h) | 9.327 9.327
BW bias (b) | 17.324 17.324
rho (h/b) | 0.538 0.538
Outcome: knife. Running variable: time.
-------------------------------------------------------------------------------
-
Method | Coef. Std. Err. z P>|z| [95% Conf. Inter
val]
-------------------
+-----------------------------------------------------------
-
Conventional | 58.343 25.547 2.2838 0.022 8.27191 108.41
5
Robust |- - 2.3510 0.019 11.4475 126.197
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Journal of Quantitative Criminology
Stop searches
Cutoff c = 71 | Left of c Right of c Number of obs = 114
-------------------
+----------------------
BW type = mserd
Number of obs | 70 44 Kernel = Triangular
Eff. Number of obs | 8 9 VCE method = NN
Order est. (p) | 1 1
Order bias (q) | 2 2
BW est. (h) | 8.589 8.589
BW bias (b) | 15.125 15.125
rho (h/b) | 0.568 0.568
Outcome: stops2. Running variable: time.
-------------------------------------------------------------------------------
-
Method | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----------
--------+-----------------------------------------------------------
-
Conventional | -2.0541 2.1091 -0.9739 0.330 -6.1878
2.07969
Robust |- --0.5527 0.581
-6.79843 3.80779
-------------------------------------------------------------------------------
-
-
Technical Appendix2: Robust RD Results (Surge; N = 52, 26
beforeSurge, 26 afterSurge).
Knife injuries
Cutoff c = 27 | Left of c Right of c Number of obs = 52
-------------------
+----------------------
BW type = Manual
Number of obs | 26 26 Kernel = Triangular
Eff. Number of obs | 26 26 VCE method = NN
Order est. (p) | 1 1
Order bias (q) | 2 2
BW est. (h) | 27.000 27.000
BW bias (b) | 27.000 27.000
rho (h/b) | 1.000 1.000
Outcome:
knife. Running variable: time2.
------------------------------------------------------------------------------
-
-
Method | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------------
+-----------------------------------------------------------
-
Conventional | -42.186 22.39 -1.8841 0.060-86.0706 1.6983
2
Robust |- --0.2682 0.789-81.0785 61.55
8
-------------------------------------------------------------------------------
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Journal of Quantitative Criminology
Stop searches
Cutoff c = 27 | Left of c Right of c Number of obs = 52
-------------------
+----------------------
BW type = Manual
Number of obs|
26 26 Kernel = Triangular
Eff. Number of obs | 26 26 VCE method = NN
Order est. (p) | 1 1
Order bias (q) | 2 2
BW est. (h) | 27.000 27.000
BW bias (b) | 27.000 27.000
rho (h/b) | 1.000 1.000
Outcome: stops2. Running variable: time2.
------------------------------------------------------------------------------
-
-
Method | Coef. Std. Err. z P>|z| [95% Conf. Interval
]
-------------------
+-----------------------------------------------------------
-
Conventional | -.86451 .75675 -1.1424 0.253-2.34771 .61868
9
Robust |- --0.9373 0.349-3.08995 1.0906
3
------------------------------------------------------------------------------
-
-
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