Bill Hillier Ozlem Sahbaz Bartlett School of Graduate Studies University College London

1. BEYOND HOT SPOTS: using space syntax to understand dispersed patterns of crime risk in the built environment. Bill Hillier Ozlem Sahbaz Bartlett School of Graduate Studies University College London b.hillier@ucl.ac.uk o.sahbaz@ucl.ac.uk

2. The spatial analysis of crime patterns has usually been conceived of in terms of the analysis of clusters of crime occurrence, or ‘hot spots’. However, as Newman observed (Newman 1972 p 109), occurrence is not the same as risk. For example, a busy street may have a higher number of street crimes that a quiet street, and so will appear as a hot spot, even though much higher movement rates may mean that the risk to individuals is lower than in locations with less crime (Alford 1999). We may say that the police need to know about occurrence, in order to deploy resources, but potential victims need to know about risk to work out strategies of avoidance. • The spatial pattern of risk will often take the form of a dispersed pattern of types of location, where local conditions facilitate one kind of crime or another,rather than a set of spatial clusters. Different kinds of crime are easier in different spatial conditions: residential burglary benefits from unsurveyed access, street robbery prefers a supply of victims one at a time and so on. Understanding the spatial pattern of risk often means understanding how and where such location types are distributed in the network of public space. • A possible tool for the analysis of such dispersed patterns is space syntax, a network approach to city spatial form which characterises spatial locations numerically, in ways which have been shown to reflect other kinds of patterns in the built environment such as movement flows (Hillier & Iida 2005) and land use types and mixes (Hillier 2000). So using this approach might also allow us to relate patterns of crime more precisely to these other aspects of city form and life (Hillier 2004. Hillier & Shu 2000, Hillier & Sahbaz 2005). • Here we show how the use of space syntax in the study of a large data base of residential burglary and street crime, against a background of demographic, socio-economic and physical data, can bring to light some unexpected relations between the physical, spatial and social characteristics of the built environment on the one hand, and the spatial patterns of these crime types on the other.

3. What then is space syntax ? It works by first reducing the street plan of the city to a least line map made up of the fewest lines that cover the system. (Turner et al 2004) recently showed that if this map is converted into a graph, treating lines as nodes and intersections and links (the inverse of the usual practice) there is probably a unique least line graph for any reasonable urban system. • We then convert the Ieast line map into a graph of the segments of lines between intersections, assigning three different weights to the relations between adjacent segments: the distance between the centres of segments, whether or not there is a directional change to another line, andthe degree of angular change. • We then calculate closeness and betweenness values for each segment with all three weightings separately.This allows us to describe the network in terms of shortest paths, fewest turns paths and least angle change paths from each segment to all others, or if you prefer in terms of its metric, topological and geometric structure. • We also vary the radius from each segment up to which the measures are calculated, up to the whole system, defining radius also in terms of metric distance, numbers of turns and degree of angular change.

4. We then colour the segments from red for strongest through to blue for weakest on whatever measure we are using, so as to make the pattern visible. Right above is a least angle betweenness analysis of part of central London at a radius of 2 kilometres. • The relevance of this is that these two measures reflect the two components of human movement: the selection of destinations, and the choice of routes. The closeness of a segment to all others indicates potential as a destination, since, assuming distance decay, human trips are less probable with increasing distance so a segment which is closer to others within a given radius offers more potential as a accessible destination – so you would locate your shop there if you could. The betweenness of a segment indicates the degree to which its lies on routes between all pairs of other segments in the system at a certain radius from that segment, so again this would guide you in locating your shop. In this way, space syntax assesses the movement potential of each segment both as destination and as route, using different definitions of distance though the weightings of shortest path, fewest turns, and least angle change, all of which have been canvassed by cognitive science as critical for human navigation in complex space patterns such as cities. With this matrix of measures we can test hypotheses about movement and land use patterns simply by correlating flows on segments with their spatial values.

5. Extensive studies have shown three things: • - that in most circumstances these spatially defined movement potentials account for around 60% of the differences in pedestrian movement flows on segments and about 70% of vehicular flows (most recently see Hillier & Iida 2005). • - that both pedestrian and vehicular movement patterns are best approximated by the least angle analysis, nearly as well by the fewest turns analysis, and least well by the shortest path analysis. • - that land use patterns are shaped by the way the urban grid affects movement flows, and this sets in motion a self-organising process through which the city evolves into its more or less universal form of a network of linked centres and sub-centres at all scales set into a background of mainly residential space. • Since movement and land use patterns are suspected of being critical variables in the spatial patterning of crime, either beneficially or negatively, depending on your paradigm, this analysis of the movement potentials created by the urban grid provides a powerful – and perhaps a necessary - tool for exploring spatial patterns of crime and their relation to other aspects of the life of the city.

6. Five years of street robbery (left) and residential burglary (right) in a London borough. While the robbery pattern is highly linear and follows the network of linked centres, burglary seems to have no pattern. • The numerical values that this analysis generates can then become the basis of a street segment based data table, to which any number of other numerical variables can be added for each street segment: in this case crime counts of various kinds, but also demographic, socio-economic and physical data such as house types, numbers of storeys, existence of back alleys or basements and so on. In effect we integrate all the variables on the basis of a spatial descriptions of all the street segments and so arrive as a description of the system of interest as a system of spatial location types plus their functional characteristics. • This will allow us to bring greater precision into the relation between crime and where it occurs. The figure above lefta shows the distribution of street crime over a five year period in a London borough. The pattern is strongly linear – hot lines ? – and closely follows the analysis which reflected the network of linked centres and sub-centres which can be seen behind it. Right shows the same for residential burglary, which seems to follow no obvious pattern. These spatial distributions form our research question. To see them more clearly I will magnify them.

10. We now present some results from an EPSRC funded study at UCL of urban design factors in the spatial distribution of crime, part of the inter-university Vivacity project under the Sustainable Urban Environments programme, We use this most recently developed form of space syntax analysis in conjunction with GIS to explore the crime-design relation at the micro as well as macro level. We call this technique high resolution analysis of crime patterns in urban street networks • Through the study, we seek to address key questions in the current debate between two opposed paradigms for ‘designing out crime’ in urban areas, one stressing open and permeable environments, mixing uses, and higher densities using the traditional city as its model, the other advocating more closed, relatively impermeable, smaller scale, mono-use low density environments, using Oscar Newman’s notion of ‘defensible space’ as its model. In the US this paradigm was goes under the rubric: Safescape against Defensible Space • The first is in effect saying having more people around makes you safer, so use spatial design to maximize co-presence and natural surveillance, and in this way make life more difficult for the criminal. The other is saying that people include criminals, and increasing numbers increase their anonymity, so reduce numbers to improve control by the resident community. • We suggest that each of these views is in a way true, but they are referring to different things. Part of our aim today is to clarify how apparently contradictory propositions drawn from past research go together – though others on both sides will turn out to be just plain wrong The key will be bringing much great precision in describing the relationship between urban design variables and crime risk. This greater precision is the prime concern of this paper.

11. So the specific paradigm questions we aim to address are: • - Are some kinds of dwelling inherently safer than others ? • - Does density affect crime rates ? • - Does mixed use reduce or induce crime ? • - Do people passing by make you safer or more vulnerable ? • - Should residential areas be permeable or impermeable ? • - Do physical and spatial factors interact with social and economic factors in crime risk ? • Here we show that in no case is there a simple ‘yes-no’ answer to these questions, but only if-then answers – given this and this and this design factor, then that may be safe, but otherwise unsafe. The key mesage is that spatial factors interact, and interact with social factors, to alter the vulnerability of locations to different kinds of crime, but do so in predictable ways.

12. The study reported here is of 5 years of all the police crime data in a London borough made up of: • A population of 263000 • 101849 dwellings in 65459 residential buildings • 536 kilometres of road, made up of 7102 street segments • Many centres and sub-centres at different scales • Over 13000 burglaries • Over 6000 street robberies • We are focusing our study on residential burglary and street robbery as these are the two crimes that people most fear today.

13. Residential burglary and street robbery data tables have been created at several levels: • the 21 Wards (around 12000 people) that make up the borough for average residential burglary and street robbery rates. At this level, spatial data is numerically accurate, but reflects only broad spatial characteristics of areas. Social data from the 2001 Census is available, including ‘deprivation index’, but at this level patterns are broad and scene-setting at best. • the 800 Output Areas (around 125 dwellings) from the 2001 Census, so social data is rich and includes full demographic, occupation, social deprivation, unemployment, population and housing densities, and ethnic mix, as well as houses types and forms of tenure. Unfortunately spatial data is fairly meaningless at this level due to the arbitrary shape of Output Areas. • the 7102 street segments (between intersections) that make up the borough. Here we have optimal spatial data, good physical data and ‘council tax band’ data indicating property values which can act as a surrogate for social data • Finally, the 65459 individual residential buildings, comprising 101849 dwellings. Here spatial values are taken from the associated segment, and again we have good physical data with Council Tax band as social surrogate. Street robbery cannot of course be assigned here. • So the richest demographic and socio-economic data doesn’t quite overlap with the richest spatial data, but the usefulness of creating data tables at different levels with different contents will become clear below as we switch between levels to seek answers to questions.

14. First a health warning. Although the database is very large, it is confined to one region of London, and the findings must be reproduced in other studies for us to be sure that they have any generality, even in one country. • Having said that, the area is highly differentiated in terms of social composition and urban type, from inner city to suburban. This will allow spatial propositions to be tested by subdividing the data, for example into the 21 wards – which are each made up of a number of people comparable to one British Crime Survey – to see it they hold for each area taken separately. We can do the same with house type or council tax band, to see if propositions hold for each subdivision separately.

15. We can begin with some broad brush scene-setting at the highest level of aggregation: the 21 wards. Left above, burglary per household for the 21 wards (each with about 12000 people) is plotted against Deprivation Index (a multi factor index of social disadvantage widely used in the UK) falling from left to right, and right above the same for street robbery in the ward. • Using the data on the 21 wards we can first see that the concept of a high crime area may need to be qualified, as the patterns of residential burglary and street crime do not have the same peaks and troughs, although there is a broad decrease in both with lower social deprivation.

16. The weak areal relation between burglary and robbery can be clarified by plotting residential burglary in rank order from low to high as black dots, and the corresponding rank order for street robbery as circles (left above). • Right above we do the same for the 800 Output areas, showing an even greater pattern of discrepancy between the two crimes. This suggests that, analytically, we should not talk about high and low crime areas. Different crimes select different areas.

17. In fact what we find statistically is that robbery responds to social deprivation far more linearly than burglary. There is more robbery in socially disadvantaged areas. • But burglary, in terms of socio-economic grouping, is U-shaped. If we plot burglary rates against Council Tax Band – a local tax based on the value of property, and so a reasonable guide to socio-economic status - , the lowest tax households have high rates (even of reported burglary) but so do the small number of the highest tax households.

18. What we find at the ward level is that six of the wards have markedly higher burglary rates than all the others, and that they are all contiguous to each other in the south east corner of the borough. We can see from this image of all the 7102 segments coloured up for average tax band, from red for high through to green for low (the blues are segments with non-residential uses only), that this part of the borough has a mixed population with strong zones of relative affluence.

19. High burglary wards • Multi-variate analysis shows that the 6 wards with markedly high residential burglary rates have a distinct social, demographic and spatial profile. They have significantly: • smaller households • lower rates of owner occupation • the highest rates of converted flats • the lowest rates of residence at ground level (largely due to conversion) • the greatest incidence of basements • are in more spatially accessible locations – that means in the more urban south and east rather than the more suburban north and west • 3 of the 6 are centred on a strong ‘town centres’, and the other 3 are more up-market residential areas adjacent to these areas. • They are far from socially homogenous. They cover most of the range on mean tax band. On the ratio of high to low level of employment types, they include the 3 highest as well as the third lowest. They are not particularly high on unemployment or lone parent households. This suggest a complex process involving social and demographic processes with space featuring as where different groups choose to live. Can we learn more from the next level down, Output Area level ?

20. At the Output Area level, the pattern of burglary rates – red for high through to blue for low – is puzzling. High and low rate areas seem to be arbitrarily juxtaposed, barely reflecting even the shift from19th century terraced housing south-east through to inter-war suburbia north-west.

21. In fact at the Output area level (about 125 dwellings), we can look at demographic, ethnic, socio-economic, occupational and household composition data from the 2001 Census, deprivation index data, and data on dwelling and tenure types, in a much more disaggregated way. But stepwise regression of the whole database (taking all due precautions on distributions and inter-correlations) with respect to residential burglary tells a rather unexpected story. Apart from the Deprivation Index, the analysis seems to background social, economic and demographic factors, and highlight simple physical factors of dwelling types and densities. In fact we find • an increase in burglary with social deprivation • a strong effect from housing type, with purpose built flats and terrace houses beneficial and converted flats and flats in commercial buildings vulnerable • but a decrease with increased housing density (and people density, but housing is stronger, through the two correlate closely ) • These variables are pervasive and consistent. The first and second are known, for example from the British Crime Survey (BCS 2001), though in this case it is notable that the housing type effect is found independent of social factors. Let us look first at dwelling type. In what follows the data are aggregated from the single building database of 65450 residential buildings which we have constructed, and so are grounded in the most disaggregated data available.

22. Burglary rates for dwelling types • Type sample burglary single multiple rate (5yrs) occupancy occupancy • Flats > 15st 676 .084 • Flats 6-15st 228 .066 • Flats 5-6st 4249 .092 • Flats 3-4st 11745 .079 • Low terraces T 13993 .121 .129 .117 • Low terraces t 2469 .109 .115 .096 • Linked2-3st 3570 .093 .073 .100 • Tall terraces 1489 .144 .352 .128 • Linked semis 14350 .117 .117 .116 • Standard semis 22312 .135 .141 .112 • Large semis 5465 .193 .223 .175 • Small detached 3535. .166 .173 .139 • Large detached 2190 .200 .294 .161 Whole sample 65459 .130 .135 .112 • The samples for the high flats are hundreds rather than thousands and are uniformly social housing. So lets assume that the lower rates may be helped by non-reporting. But the lower flats represent the whole range of social classes, as do all the categories of housing and cannot be so explained. In general risk increases with the number of side on which you are exposed – a simple physical factors. But why are multiple occupancy risks systematically lower ? Perhaps because a multiple burglary is reported as one ? Or because the ground floor protects the upper floor by offering the first target ? This could be a case of difference between occurrence and risk.

23. Type 1 – very tall blocks, point block slabs .084 • B 590 .084 • Type 2 – tall flats 6-15 storeys .046 • B 228 .046 • We can use the variable of Council Tax Band, a local tax based on an assessment of the value of the property, running from A for the lowest value through to H for the highest, to see how this pattern interacts with socio-economic factors. It is a far from perfect indicators of social advantage, but it is a pretty good approximation given sufficiently large samples. For the two samples of taller flats, all dwelling are B rated, the second lowest, and are social housing left over from the times when we built high rise housing for socially disadvantaged people. So let’s momentarily discount these apparently lower rates as being likely to be contaminated by non-reporting.

24. Type 3 – medium height flats 5-6 storeys - .109 • A 732 .086 • B 588 .193 • C 1098 .118 • D 1031 .111 • E 431 .105 • F 87 .093 • G 23 .087 • But if we take medium rise flats, the data cover the range of house values, so the low mean risk of .109 over five years compared to the overall average of .130, is very unlikely to be an artefact of non-reporting. Let us also worry that the samples for the higher tax bands are increasingly small. But we do seem to see a progressive reduction in risk with increasing social advantage.

25. Type 4 – lower 3-4 storey and smaller flats - .084 • A 1018 .096 • B 2198 .081 • C 5673 .080 • D 1136 .065 • E 256 .142 • The overall mean for low rise flats is lower still, and again falls with increasing social advantage, though there is a marked rise to above average risk for rather small sample in the E-band, hinting again at the U-shape.

26. Type 7 – low terraces with small T - .111 • B 133 .132 • C 594 .098 • D 1296 .093 • E 358 .159 • F 24 .391 • Low terraces with small back additions again have a lower than average risk, but now the relation to social advantage really does begin to look U-shaped, though again with a caveat on small sample size at the low and high tax band ends of the data.

27. Type 6 – low terraces with large T – 120 • A 66 .180 • B 1176 .111 • C 5013 .116 • D 4201 .107 • E 2070 .117 • F 847 .165 • G 175 .231 • Low terraces with large back additions are also well below average risk, but the data has better coverage of the range of tax bands, and now really does look U-shaped. It really does begin to look as though in this dwelling type, the poor and the rich are at higher risk compared with the middle classes.

28. Type 8 – linked and step-linked 2-3 storeys and mixed - .078 • A 175 .137 • B 444 .136 • C 1070 .129 • D 1403 .059 • E 296 .062 • F 53 .019 • G 41 .073 • Linked and step-linked low rise housing (whose precise form we have not so far been able to ascertain) shows one of the lowest overall rates, and again the lowest rates are in the middle of the sample and the higher rates at the ends.

29. Type 5 – tall terraces, 3-4 storeys - .193 • B 237 .063 • C 599 .130 • D 446 .213 • E 37 .159 • F - - • G 75 .393 • With tall terraces, we find the first above average risk, but now a shift towards higher risk for higher social advantage is clear, even if we aggregate the top three bands for greater statistical security. Why are tall terraces so much more vulnerable. Almost certainly because most higher terraces have basements, and basements were shown by the Output area data to be a significant factor in increased risk.

30. Type 11 - semis in multiples of 4,6,8 - .117 • B 859 .177 • C 2349 .102 • D 8076 .113 • E 2570 .138 • F 153 .149 • Another form of grouped housing whose precise form we have again not been able to ascertain with any security, shows a below average rate again with the peaks at either end.

31. Type 10 - standard sized semis - .138 • B 493 .249 • C 3268 .097 • D 4268 .120 • E 10819 .145 • F 2529 .148 • G 507 .152 • Now we are in the realm of the famous English semi-detached house, here at standard size. We find a clear above average risk on the large sample, and a clear U-shape.

32. Type 12 - large property semis - .199 • B 307 .268 • C 1581 .169 • D 1322 .153 • E 969 .210 • F 606 .211 • G 489 .260 • With larger semis the risk increases markedly, and again with a marked U-shape. We may notes at this stage that our B tax band people which in high flats we might think were non-reporting, now seem to be reporting in what we might now think of as the predictable numbers. As we saw, the rates for smaller detached houses was .160 and for large .200, but with insufficient number to permit the breakdown into tax bands. • It is clear that two factors are involved in the shifting pattern of risk with dwelling type: the simple physical fact of degree of exposure: on how many sides is your dwelling not contiguous with others ? and social advantage, with the poor and the rich at higher risk. But houses are more at risk than flats, the more so as they become more detached, and the better off you are the more you are at risk in a house and safe in a flat.

33. These result suggest that density may be a factor, but in the opposite to the normally expected sense. However, we saw that the density component in the Output Area was also strongly in this direction. So what is going on ? Other studies have found density neutral, and few studies have shown such seemingly strong effects. But at the Output Area level, the findings may be unreliable, due to great differences is the amount of open or non-residential space included in output areas. However, we can switch levels and explore the issue further through the individual house data base. • We take the individual dwelling data on GIS, and for every dwelling in the borough, create a variable for how many other dwellings are, in part or wholly, within 30 metres of each dwelling, so measuring the density of dwellings in the neighbourhood of all dwellings in the sample. We then use logistic regression to see how far a lower or higher value of this variable affects the likelihood of the dwelling being burgled at least once (of course we lose information on repeats with this technique). • We find that for the dataset as a whole higher density at ground level substantially reduces the risk of being burglarised, while the opposite is the case for non-ground level density. Neither seems to be affected by the presence of other variables. More surprisingly, the presence of non-residential uses within the buffer is mildly beneficial. The pattern holds if we split the data – and remember this is over 65000 residential buildings – into single and multiple dwelling units, though with the multiple non-residential uses switch to a slight disbenefit.

34. To test this, we split the data three ways: first by the 21 wards (each with about 12000 people and 3-4000 dwellings) and ask if these relation holds in every region regardless of social, economic or layout and physical type and mix; second by dwelling type, regardless of the area in which they occur; third by Council Tax band • On the first we find that high density at ground level reduces vulnerabiilty substantially in 20 out of 21 wards, and that in 19 cases the relation is statistically highly significant, and in the other weakly. In the one case where the relation is not found, the result is statistically insignificant. So this effect seems to hold in spite of the great social, economic, demographic and morphoplogical variation in physical and area type across the borough. • Splitting the data by dwelling type, we find that the relation holds for all dwelling types taken separately except tall terraces, and is in each case highly significant. In the case of tall terraces, there is no significant relation. Splitting by tax band, we again find the relation holds in all cases, with high statistical significance in all cases bar the small sample of top tax band cases. • Higher ground level density does then seem to mean lower burglary. But a worrying pattern is beginning to appear. You are safer if you live in a flat, but you increase the risk to those locally living in houses. There could be a simple statistical effect here. If flats are harder targets, as they seem to be, then within an area that is being target, the higher the proportion of harder flat targets the greater the risk to the smaller proportions of easier target houses on the ground. By Ockham’s razor, we would suggest this is the case.

35. What about the relation of burglary to movement then ? Is it perhaps, like density, a more complex relation than we thought ? It is. Most studies have concluded that proximity to movement increases risk, casting doubt on the Jane Jacobs belief that passing strangers are more ‘eyes on the street’. The key argument is that if you are located in an accessible location with strong movement, then you are more likely to lie on the burglars search path. I am sure this is often the case, but syntactic studies have also shown that within residential areas the more important roads for movement have less risk. Can we reconcile these different findings ? • We can do the simple things first and use the ‘burgled or not’ logistic regression on the movement variables. The pattern we find suggests that both arguments are right, but at different scales of the system. At the level of to-movement, or accessibility, at the city scale, we find a substantial increase in risk. But through-movement at this scale has much less effect. To my mind, this supports the search path hypothesis, because being accessible at this level does not imply though movement at this level which has a much lower effect. If we go down to the local scale, then the accessibility penalty becomes negligibly small, and through movement becomes beneficial. This does suggest that both parties are right, but that is local through movement that is beneficial, global not so. Note by the way that the simple spatial variable of segment connectivity is slightly beneficial in this analysis, but this may be to do with the relatively small number of cul de sacs in this largely nineteenth and early twentieth century area.

36. This suggests that we might examine the space structure more closely to see if we can find out more by looking at the data at the level of the street segment rather than the individual building. For this we must digress from results to methodology for a moment and talk about the problem of a rate. • The problem of establishing a rate for a small spatial element is this. Suppose there is a random process of assigning burglaries to houses, saying numbering the houses and selecting the ‘burgled’ ones by a random number selector. As the process proceed, we will find that whatever spatial unit we choose, then over time the number of burglaries on that spatial unit will be proportionate to the number of targets on that unit. So it will appear that there is ‘more’ burglary on units with more targets, and a random result might appear to be a pattern – a hot spot, say. • If we then try to get over this problem by establishing a rate, that is by dividing the number of burglaries into the number of targets, then we find the inverse problem: that for a significant part of the process the rate will appear to be lower on units with more targets since random events occurring on that unit will be dividing into a larger denominator. Of course, in the long run, as the process is iterated infinitely many times, then the number of burglaries will be perfectly proportionate to the number of targets – but we don’t know how close we are to getting there, and in any case when we get there the information about rates is useless since all we need to know is the number of targets.

37. We can illustrate this problem by showing the distribution of crimes against targets as simple numbers and as rates. Left top is the simple count of burglaries against dwellings for segments, and right top the rate of one against the other. Below left is the simple count of robberies against segment length, and below right the rate per unit of length. It is clear that neither pattern in meaningful. We find two kinds of illusory result: the simple figures, and the rate obtained by dividing robberies into length. Shorter segments would appear safer with simple numbers and more dangerous with a rate, and vice versa with longer segments.

38. We need to solve this problem, because the segment as a spatial unit is critical to all our measures, and there would be great gains from being able to link spatial descriptors to crime figures at the disaggregated level of the segment. How can we do it ? Our reasoning is this. From the point of view of the occurrence of burglary or robbery on segments, the number of targets is the primary risk factor for burglary, and the length of segment the primary risk factor for robbery. By primary risk factor, we mean a distribution that would arise from the random assignment process. No analysis of spatial units will be relevant unless it builds in a solution to the primary risk problem. • The problem can be solved by aggregation. For example, if we take all the segments with a given number of targets, count all the burglaries on those segments, and divide into the total number of targets, we no longer have the ‘denominator’ problem, and we have a true rate, though only at the aggregate level. The same applies to length of segment for robbery. We take all segments within a given length band and aggregate the total length and the total number of robberies, and we have a true rate.

39. So let us explore primary risk band analysis. There are 436 kilometres of street with at least one residence in the borough, made up of 4439 segments with an average length of 98 metres, and an average of 17.1 dwellings per segment, of which 15 are on the ground floor and 2 on upper floors. • Primary risk band analysis means taking all the segments with a given number of dwellings, counting the total number residences and the total number of burglaries, and dividing the latter into the former. The number of dwellings on the segment is now not involved in the calculation, so we escape the ‘denominator effect’. The number of dwellings on the segment is now a condition for that aggregate. • For example, if we take the 328 segments with exactly one dwelling, which have on average 3.15 nonresidential units, then we find a total of 197 residential burglaries have occurred over 5 years in the 328 dwellings, a rate over 60% or 12% a year, compared to an overall average in the data of 3.37 per year. • If we take the 34 segments with more than 90 dwellings per segment we find a total of 3708 dwellings and 419 burglaries over five years, a five year rate of 11.3% or 2.26 per year.

40. We then divide all segments into bands according to their number of dwellings, giving an average of 94 segments per band of average total length 9.3 kilometres with an average of 1600 dwellings per band. We then calculate the true rates for each band, and plot them on a line chart with dwellings per segment on the horizontal axis and the burglary rate on the vertical (in fact taking the log of each). • We see that the risk of burglary decreases steadily with with increasing numbers of neighbours on your street segment. We can also express this as a simple regression, and we find an r-square of .78. Remember we are dealing with over 100,000 dwellings here.

41. We can see the dwellings per segment pattern visually by colouring segments from red to blue for high to low numbers of dwellings on the segment. We see the high dwelling, safer segments are often in quite grid like areas.

42. Is this the density effect we saw before, or is it simply to do with the number of neighbours ? By adding the numbers of dwellings on the segment on which dwelling lies as a further variable in the logistic regression on density on the residential building data table (so again we switch levels), we show that both hold in the presence of the other, and so we can have no doubt that the two effects are to some extent independent, though this varies from one area to another and from one housing type to another. But in general the numbers of dwellings on the segment and the density of dwelling around the dwelling both act to reduce vulnerability to burglary. • There could be two reasons for this. One is of course surveillance. Another is perhaps more interesting. Recently Kate Bowers of JDI showed that a burglary in an area was likely to lead to others soon after. We suggest there may also be a ‘saturation’ effect. Once a certain number of hits have been made in a target area, then the target is deemed saturated and the burglars move elsewhere. Statistically this could lead to the effect we find if block faces were identified as target areas, and show why where seems to be safety in numbers living on a larger rather than smaller block.

43. This result is very much in accordance with the space syntax theory of cities, in which residential areas have larger block sizes, and so spread the lower levels of movement over fewer spaces. Small block sizes occur not in residential areas but in ‘live centre’ areas where small blocks facilitate ease of movement from all parts to all others, a vital feature of a retail or service providing areas. • This has important implication for current design practice. It is clear that ‘permeability’ is now often being provided for its own sake without regard to how well used permeabilities will be. It is known from previous studies that unused access to residential environments is likely to increase crime levels. • It is clear from these new results that permeability should be provided sufficient to structure real movement patterns in all directions, but should not be provided beyond this, especially when it will not be well used. This implies a larger block size than is often now the case.

44. So, with some complications, higher densities and good number of line neighbours seem beneficial. But what about the issue of layout ? The generator for layout is segment connectivity. A 1-connected segment can only be the end of a cul de sac, while 6-connected must approximate a grid like layout.

45. If we plot segment connectivity from red for 6 down to blue for 1, we see that 6 connected segments occur in two kinds of place: in the high street, and in the more grid like residential areas. There are 81 1-connected segments with at least one dwelling, 451 2-connected, 748 3-connected, 1868 4-connected, 1050 5-connected and 261 6-connected - though the 6-connected still account for nearly 4000 dwellings.

46. If we compare this to the plot for the number of dwellings per segment, we will see that there is some overlap in the residential areas, but in the high street areas we find the opposite: a very low residential rate is associated with 6-connectivity. In these areas of course we find the highest concentrations of non-residential activity.

47. This leads us to a basic morphological fact about city layout at the most elementary level of segment connectivity and segment length (and so number of targets). For pure residential segments, length increases with connectivity. But for segments with non-residential activity length decreases with connectivity. This has to do with grid intensification and the way centres and sub-centres are formed. We must take great care then in trying to link these layout primitives to crime.

48. For example, if we plot segment connectivity against the ‘primary risk’ dwellings per segment variable, we find high connectivity for both very low and very high numbers of dwellings, the former corresponding to high street areas and the latter to grid like residential areas.

49. If we plot out primary risk bands against spatial accessibility, one of the configurational variable that best models real movement rates, we find that like segment connectivity, integration has high values both with low number of dwellings per segment and the high numbers.

50. If we then plot burglary rates for the primary risk bands against accessibility, we find a bifurcation in the data, with one arm rising and the other seemingly falling with integration. If we then split the primary risk band about half way into those with less than 25 dwellings per segment on the left and those with more on the right, then it seems that the effect of integration – and therefore movement on crime depends on the amount of residence. If this is the case, then it would seem to go some way to explaining the divergent findings in earlier research.