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ONE-OR TWO-OFFICER CARS? A PERSPECTIVE FROM KANSAS CITY

DAVID A. KESSLER

Planning and Research Division Houston Police Department

Houston, Texas 77002

ABSTRACT

The relationship of police patrol-car staf?ng to response time is examined. The first systematic study of police patrol-car staffing, conducted in San Diego in 1977. found that two one-offker car.y re- sponded to the scene of an incident faster than one two-ojficer car. Given the study design, this finding was puzzling. When two one-officer car.y are dispatched, at least one of the cars has farther to go. and the extra travel distance should require extra travel time. The present study replicated the previous empirical analysis with data from the Kansas City Response Time Analysis Study. Although it was expected that additional control variables would provide an explanation for the ,findings. the results were the same. Two one-officer cars are faster than one two-officer car. One explanation for this finding is that peer pressure among oJficer.5 provides different incentives for rapid response in one- and two-ojjicer cars. The policy implication is that the deployment of two-ofjicer cars cannot be justified by minimized response time.

A continuing controversy in police admin- istration is whether or not to put one or two officers in patrol cars. The outcomes that are attributed to this decision vary from the most mundane, such as flexibility in report writing, to the most fundamental, such as patrol efficiency, police response time, and officer injury. At a time when smaller police departments were relying on one-officer patrol cars, the first experiment in a major metropolitan area was implemented by Chief Bernard Brannon in Kansas City in 1953 (Chapman, 1970). Since that time, other large departments have adopted de- ployment schemes using various combina- tions of one- and two-officer cars. In 1977,

the first systematic study of the subject was completed in San Diego (Boydstun, Sherry, and Moelter, 1977). Among the more sa- lient of these experimental findings were that one-officer cars were safer, had fewer citizen complaints, and were more efficient than two-officer cars.

A puzzling finding of the San Diego study was that two one-officer cars traveled to an incident faster than one two-officer cars (Boydstun, Sherry, and Moelter, 1977: 6). There are circumstances under which this result might be expected to occur. One explanation that has been offered derives from the assumption that one-officer cars permit the distribution of more officers over

49

50 DAVID A. KESSLER

the same area. Each officer has a smaller beat to patrol; therefore, each officer has a shorter distance to travel when responding to a call. In addition, with more cars in the area, the probability is higher that a car close to the location of the request for service will be available to respond (Kaplan, 1979). This argument assumes that only one officer is necessary to handle the call.

However, in San Diego, both the design of the experiment and police department policies made this explanation inapplicable. In San Diego, beats that previously had been assigned one two-officer car were reassigned one one-officer car, and vice versa. Although the number of one-officer cars was never doubled within a beat, two officers were still dispatched to some calls in beats patrolled by one one-officer car. Thus, a cover car from an outside beat was required. Response time for two one-officer cars was measured from the longest of the two times, and the extra distance and dispatching time could be expected to delay response. The San Diego study did find a back-up car required an additional 7.2 minutes to respond. Two-officer cars that do not require cover should have response times equal to the minimum response time of two one-officer cars. Nevertheless, the empirical results found the maximum re- sponse time for two one-officer cars to be significantly less than the response time of one two-officer car. As Kaplan (1979) ac- knowledged, “It is indeed puzzling (as admitted by the San Diego researchers) why this reported maximum value is so low” (1979:335).

This anomaly suggests the need for fur- ther analysis of the issue. Any study which generates a large number of statistical tests is likely to contain statistical errors. It is possible that a type I error occurred. result- ing in the acceptance of a test hypothesis when the null hypothesis is true. This could only be determined through replication of the study. One source of data for replicating the San Diego experiment is the Kansas City Response Time Analysis Study. The policies of the Kansas City, Missouri Police Depart- ment are consistent with the design of the

San Diego experiment for several variables. As in San Diego, Kansas City uses a mixture of one- and two-officer cars without altering deployment. Two officers are assigned to a car for mundane reasons, such as overlap- ping schedules, or the need for extra officers to make up missed work days. Although more officers may be deployed, more cars are not. As in San Diego, Kansas City requires some calls to be serviced by more than one officer and has a policy requiring officers to rendezvous with their cover car for calls in which two one-officer cars are dispatched. Response time is measured by the car that takes the longest to respond. The argument to be examined in the Kansas City data set, as it was in the San Diego data set, is the effect of waiting for the cover car.

This article examines the issue of one- vs. two-ofticcr cars with respect to response time. First. it reviews some formal models, to clarify the assumptions from which the competing arguments are derived. Second. it tests these arguments with the Kansas City data. Third, it speculates about some possible explanations for the persistent discrepancy between the predictions of the analytical models and the empirical results. Finally, it discusses some policy implica- tions of the findings.

FORMAL MODEL

Models of response time have been devel- oped by Larson (lY72), and Kaplan (1979) has extended this analysis to the number of patrol cars deployed. The assumptions of these models do not conform with condi- tions in San Diego’or Kansas City at the time data were collected for the studies mentioned previously. but these models provide a point of departure for formal analysis of the assumptions underlying the empirical analyses. The basic structure of the models will be recapitulated, and the effects of different policy decisions on re- sponse time will then be examined.

For the sake of simplicity, imagine a hypothetical four-beat city as illustrated in figure 1. Each beat is of dimension u by U.

One-or Two-Officer Cars? A Perspective from Kansas City 51

2u

U

0

i I I Bert 2

I Beat 4

I I I

I .I ~~ I j ,xTeJ2; l (x’jd:) i Beat 3 I I

dx I I I U 2u

Figure 1. Hypothetical four-beat city

Following Larson’s assumption, streets run through each beat in a grid pattern, so that patrol cars travel at a right angle metric within a given beat. An incident may occur at any point (for example, coordinates x1 and y,). The occurrence of incidents is a uniformally distributed random variable (X,,Y,) throughout the beat, so that any incident may occur at any location within the beat with an equal probability. Like- wise, a police patrol car can be located anywhere within the beat. Since a patrol officer has no knowledge of where the next incident will occur, the location of the patrol officer is independent of the location of the incident. The location of the officer is also a uniformly distributed random variable (X,,Y,). When an incident occurs, the of- ficer travels along the right angle grid from the X2,Yz coordinate to the X,, Y, coordi- nate. The distance dx along the X axis is:

(1) dx=IXz-X,1. For the Y axis:

(2) dy=IY,- Y,I. The total distance is defined as:

(3) d=dx+dy. It is further assumed. for the sake of simplicity, that the patrol car travels at a constant velocity (v). Distance is also a function of time (t) and velocity (v), by equation:

(4) d-vt. Therefore,

(5) t=d/v=(dx+dy)lv. When police administrators make policies

regarding the staffing of patrol cars they must alter several decision variables simul- taneously. They must decide how many officers to put in each patrol car, and they must also determine how many patrol cars to put in a beat. If the status quo policy is two officers in a car and one car per beat, a change to one-officer cars requires either keeping the same number of officers in a beat and doubling the number of cars per beat, or keeping the same number of cars per beat and decreasing the number of officers in an area. If administrators decide to staff patrol cars with one officer, they must then decide whether all calls will be serviced by only one officer, or if some calls will still be serviced by two officers, requir- ing the dispatch of two patrol cars.’ If more than one officer is dispatched to a call, administrators must decide whether the first officer to arrive can begin servicing the call alone, or whether officers should be advised to wait for the assisting car. Four basic decision variables are thus involved in patrol car staffing: (1) the number of officers in a car; (2) the number of cars and officers covering an area; (3) the number of calls

52 DAVID A. KESSLER

requiring more than one officer to respond; and (4) whether both officers must arrive before the call is serviced or whether one is allowed to begin service alone.

Kaplan (lY7Y) analyzed the effects of changing from a policy of two officers per car to a policy of one officer per car where the same number of officers is maintained in an area and where additional cars are deployed. In Kaplan’s model, all calls are assumed to be serviceable by one officer. so there is no delay while waiting for an assisting officer. Under the two-officer car policy in the hypothetical four-beat city, there are eight officers in four cars. The expected response time E(t) for a two- officer car responding to a call within its assigned beat is .!?(f)=2u/3v (Larson, lY72; Beltrami, lY77; Larson and Odoni, 1981). Kaplan then assumes two cars are deployed to each beat. with one officer in each car. Within a given beat, the response time of each car to the call would be t, and t?. Assuming that only one car was required to respond to the call, and that the closest car was always assigned, the response time to the call would be min(t,,t?). Kaplan has shown that the expected travel time when such a policy is in effect is E(min(r,,r?)) = .48dv<E(r)= .67ulv (Kaplan, lY7Y: 333- 34). However, if police department policy stipulates that two officers must respond to the call, and the first officer to arrive must wait to service the call until the second officer arrives, then response time to the call would be max(r,,r,) and E(max(r,,r,))3E(r).

Kaplan extends his analysis with a spa- tially distributed queuing model to consider the contingency that cars are out of service, and that cars from outside the beat where an incident occurs must be dispatched. Given this complication, Kaplan produces results to show that one-officer cars reduce re- sponse time, primarily because time spent waiting for a car to become available is decreased substantially.

The results Kaplan provides are impor- tant because they are derived from an alternative that police administrators may want to consider. Since it is cheaper to add cars than to add patrol officers. the

indication that increased efficiencies can be obtained by adding more cars and shifting to one-officer cars has significant policy implications.

However. the assumptions of Kaplan’s model deviate from the experimental condi- tions in San Diego. To determine the implications of the model for the San Diego experiment. the following assumption must be altered, and new implications derived. In San Diego, some of the beats that had been one-officer car beats before the experiment became two-officer car beats. and vice versa. Some other beats were left un- changed in order to maintain experimental control. Therefore, the number of cars and the number of officers remained unchanged, although this deployment of one- and two- officer cars was altered. Some calls were assumed to require more than one officer, and officers were supposed to wait for the assisting car. Given the deployment of one car per beat. those beats with one-officer cars had to wait for another officer from out of beat to arrive before servicing the calls. The expected response times for the cars from adjacent and diagonal beats were derived by Kaplan and Larson and are all higher than the expected response times for a single car dispatched to an incident in its own beat. If police department policy stipu- lates that two officers must respond to the call, and the first officer must wait to service the call until the second officer arrives, then then the response time to the call will be max(r,,r>) and E(max(r,,rZ))sE(r).

To make the model more consistent with police department policies in San Diego and Kansas City, imagine that the hypothetical four-beat city receives calls for police ser- vice at a rate of A. These calls are equally distributed among the four beats. All re- quests are serviced. However. some of the calls require two officers, while others re- quire only one. Calls requiring one officer arrive at rate A,, and calls requiring two officers arrive at rate A?. The service times for one- and two-officer calls arc I/, and U2, respectively.

If one one-officer car is assigned to each beat, then when a call requiring one officer

One-or Two-Officer Cars? A Perspective from Kansas City 53

to respond occurs in a specified beat, four mutually exclusive events can occur:

Ct-The officer in the beat is available and responds.

Cz-The officer in the beat is unavailable and an officer in one of the two adjacent beats responds.

(Z--The officers in the beat of the call and adjacent beats are unavailable, so an officer in the diagonal beat responds.

C-No officers are available, so the call is placed in a queue to wait for the first available officer.

Let t, represent the time required for the

inbeat officer (case C,) to respond. Let tz,

represent the time an adjacent beat officer

(case C) takes to respond, let tZh represent the time of an office from the other adjacent beat (tZa=f2h=t2), and let f,represent the time required for an officer from a diagonal beat to respond (case C,). Kaplan has computed the respective expected travel times as follows: E(t/C,)=E(tl)=2u/3v; E(t/C,) =E(t,)=4u/3v; and E(t/C3)=E(r3)=2u/v. When no officers are available, response time will consist of a waiting time (IV) and either t,, tZ, or tj, depending on which officer becomes available first.

If a call requires that two officers respond, and if each car has two officers, the possible events and times are identical to those for calls which require only one officer to respond. However, if each car has only one officer and two are required, two cars must be dispatched. In this situation, there are five mutually exclusive categories:

CS-The officer in the beat and an officer from an adjacent beat are available and respond.

C&The officers in the two adjacent beats are available and respond.

CrAn officer in one of the adjacent beats and in the diagonal beat are available and respond.

CrThe officers in the beat of the call and in the diagonal beat are available and respond.

C-Only one officer or no officer is avail- able for response, and the call is placed in queue until two officers become available and respond.

If officers are required to rendezvous with each other before servicing the call, then the response times for C5 through C, are the maximum times of the two officers respond- ing, and the expected travel times must be greater than or equal to the longest expected travel time of each of the two officers. For C,,

E(t/C5)=E(max(t,,r2))~E(tz). For C,, E(t/C6)=E(max(t,,,f2,,))~E(tz). For C,, E(t/C,)=E(max(t,,r3))>E(t3), and for Cx, E(t/C,)=E(max(t,,r,))>E(t,). Response time for C, will, again, be the

expected travel time for all of the officers to the beat of the incident, plus the waiting time. The calculation of the probabilities of C, through C, occurring is explained in the appendix.

Given that the strategy is to dispatch the car with the fastest expected response time, for a two-officer call that must wait for a back-up, the fastest expected response time is greater than 4u/3v, in contrast to 2ul3v for two-officer cars, or .48u/v for the minimum of two cars, as developed in Kaplan’s model. Clearly, a policy requiring two one-officer cars to rendezvous should increase response time. The expected response time for the hypothetical four-beat city can be calculated according to the following equation:

(6) EW,) = i E(tlC;) *P(C;), i= I

for one car responding.

-Qfl,) = i: NlC;) *P(ci), 1=5

for two cars responding.

E(R71 = i E(RT,)*P(l) i = I + E(RT*) * P(2),

for all calls.

where:

P(C,) = the probability of events 1 through 9 occurring.

P(1) = the probability that a call is a officer call.

P(2) = the probabililty that a call two-officer call.

one-

is a

54 DAVID A. KESSLER

There are two observations that should be highlighted from these equations. First, all of the travel times for two one-officer cars responding to two-officer calls are longer than the travel times for one-officer cars responding to one-officer calls. Second, because the number of servers is reduced by half when two one-officer cars are required to service a call, the probabilities of a car being unavailable is increased. These relationships can be observed by constructing an illustration from the Kansas City data.

Data from Kansas City were collected by nine observers (of which one was a substi- tute) for forty-two weeks. Eight observers accompanied patrol officers four days per week. Data were collected for 7,101 calls for service to which officers responded (although citizens were not always con- tacted). Each officer accompanied by an observer received 5.28 calls per day, or .66 calls per hour, on the average. For the hypothetical four-beat city, there would be a total of 2.64 calls per hour, so h=2.64. Data on total service time are not available from Kansas City, but data from San Diego indicate that one officer can service a call in 48.8 minutes (l/U), while two officers take 37.3 minutes. For one-officer calls, the number of servers (s) in the hypothetical city is four, while for two-officer calls, there are only two servers. Two officers were dispatched to approximately 35 per- cent of the calls. The utilization factor’ (p) for those calls requiring one officer (65 percent) is (.65*2.64*48.8)/60=1.39. For calls requiring two officers (35 percent), the utilization factor is (.35*2.64*37.3)/60 =.573. From the procedure describe in the appendix, the P(C,‘s) can be calculated. For one-officer calls, P( C,) = .3677, P(C?) =.2051, P(Ci)=.0369, and P(C,)=.3903. For two-officer calls, P(C,)= .3002, P(C,)=.O712, P(C,)=.O595, P(C,)=.O301, and P(C,)= .5378.

Note that the probability that the fastest expected travel time will occur is slightly less for two-officer calls and that the probability that a call will have to wait in

queue is increased substantially. Not only are the expected travel times longer for any combination of cars that may respond. but the probability that the fastest combination of servers is available is lower. This is true even though the number of two-officer calls is about half the number of one-officer calls. By comparison, if the four-beat city were staffed by four two-officer cars, P(C,)=.4829, P(C)=.2143, P(C,)=.O272, and P(C,)=.3027. Note that the probability that a call will have to wait for a car to become available drops substantially, and the probability that the car with the lowest expected travel time (C,) is available in- creases. Given the analytical results of the model, it can be hypothesized that one two-officer car should have a faster re- sponse time than two one-officer cars, and that there should be no difference in response time between one two-officer car and one one-officer car. Given these ana- lytical results, let us examine the empirical results from the Kansas City data.

EMPIRICAL ANALYSIS

Data from the Kansas City Resporzse Time Analysis Study provide a source from which the San Diego finding can be replicated, and with which competing explanations can be tested. There are several possible reasons for the findings of the San Diego study. A number of variables may have been interact- ing or confounding the real relationship between the number of officers per car and the rate of response time. If these variables can be controlled or their relationships specified, the puzzle may disappear. One explanation suggested by the San Diego findings is that dispatchers often fail to optimize response time, by assigning two- officer cars to mundane calls and two one- officer cars to emergency calls. Controlling for the type of call may reveal that when response time is important. two-officer cars are faster.

Second, it is well-known that patrol of- ficers do not stay in their assigned beats.

One-or Two-Officer Cars? A Perspective from Kansas City 55

Beats are artifacts of rules, and rules are made to be broken. Therefore, even if dispatchers consider an officer’s beat loca- tion in an effort to minimize response time, the dispatched officer may be out of the beat of the incident at the time the call is made. If this practice is random between one- and two-officer cars, then the advantages of using two-officer cars are lost. However, it may be that two-officer cars are more often in their beats, or at least that, when they are in their beats, their response time is faster than the response time of one-officer cars that must wait for a cover car from out of beat. Again, if this relationship can be properly specified, the puzzle may disappear.

Third, officers in one-officer cars fre- quently do not wait for cover cars. In Kansas City vernacular, this behavior is known as “busting” a call. For those inci- dents in which officers of one-officer cars wait for the cover car, two-officer cars should be faster.

Finally, police officers do not stay in their cars all of the time, and officers who are out of their cars at the time of dispatch have significantly longer response times than officers who are in their cars. If there is any tendency for two officers to leave the car more often than single officers, this would account for the delay in response. Con- trolling for this variable should reveal two- officer cars to be faster when the officers are in their car.

METHODOLOGY

In order to test the relationships between police patrol-car staffing and response time, data from 949 Part 1 crime calls observed during the Kansas City Response Time Analysis Study were used. Operationaliza- tion of the variables came from the field crime survey, which was filled out by ob- servers who were assigned to accompany police officers patrolling the study beats. The beats studied ranked in the upper twenty-seventh percentile in the city in the frequency of robberies and assaults.

The analysis required the operationaliza- tion of seven variables. The dependent variable was travel time. Travel time was operationalized as the interval from when dispatch ended, or when the officer began responding to the call, whichever came first, to the beginning of the investigation. The investigation began when the officer arrived at the scene of the incident, or contacted a citizen directly involved in the incident, whichever came first.”

The major independent variable to be operationalized was whether the response to the call was by one one-officer unit, one two-officer unit, or two one-officer units. Observers were asked, “How many officers were assigned to the car?” They were also asked, “Was more than one car officially dispatched?” From the responses to these two questions, three dummy variables were developed: one for one one-officer car, one for one two-officer car, and one for two one-officer cars.

The type of call and whether or not the call was an emergency were operationalized by two sets of dummy variables. The types of calls consisted of: rape, robbery, assault, burglary, larceny, and auto theft. Robbery was the reference group. The type of call was further classified as either involvement or discovery. Discovery incidents were those in which a citizen discovered the crime after the perpetrator had left the scene. Involvement cases were those in which a victim or witness saw, heard, or was some- how involved in the crime during its occur- rence. For example, there were involvement larcenies, in which storeowners appre- hended shoplifters, and discovery larcenies, such as the car owner who found his C.B. radio missing. The information needed to classify calls was obtained from the officers’ offense reports and from a survey of citizens who either reported the crime or were victims of it. Whether the call was an emergency or not was determined from a question on the observers’ questionnaire, “What was the response of the officer to the assignment?” Possible answers were:

(1) Code 1, utilized overhead lights and

56 DAVID A. KESSLER

(2)

(3)

(4)

(5)

(6)

siren, proceeded directly to dis- patched location. Code 1, utilized overhead light and siren, detoured en route to dispatched location. Seen as urgent, drove fast andlor utilized emergency equipment, pro- ceeded directly to dispatched loca- tion. Seen as urgent, drove fast and/or utilized emergency equipment, de- toured en route to dispatched loca- tion. Seen as routine, proceeded directly to dispatched location. Seen as routine, detoured en route to dispatched location.

A dummy variable was constructed, with responses 1 and 2 classified as one, and responses 3 through 6 classified as zero.

Measurement of whether the officer was responding from within the beat of the incident was straightforward. Observers re- corded the beat they were in at the time of dispatch and the beat to which they were dispatched. A dummy variable was con- structed which was equal to one if the beats were the same and zero if they were different.

Busted calls were those calls in which an officer began dealing with the incident prior to the arrival of the cover car. Observers

were asked to indicate if the call was busted or not. A dummy variable was coded one if the call was busted and zero otherwise.

Finally, whether the officer was in or out of the car at the time of dispatch was considered. The observers were also relied upon for this information. They responded to the question. “Was the officer(s) in his/her car at the time of official dispatch?” Possible answers were:

(1) No, officer(s) out of car. (2) Yes, car stationary. (3) Yes. car mobile. Multiple regression analysis was used to

test the relationships specified. Since most of the variables were dummy variables, this analysis is equivalent to analysis of variance. The regression analysis provides more infor- mation about the form and strength of the relationships.

FINDINGS

The results of the statistical analysis sup- port the findings of the San Diego study. The average travel time for 936 Part 1 crime is six minutes and fourteen seconds, with a standard deviation of three minutes and fifty-three seconds. A single one-officer car is slightly slower. with an average travel time of seven minutes varying within a

TABLE 1A

TRAVEL TIME BY TYPE OF CAR RESPONDING TO THE CALL

Dependent Variable: Travel Time (Logarithm)

Beta B Standard

Error F Simple r

Independent Variables One two-officer car Two one-officer cars

Constant

-0.03204 -0.029894 0.02808 1.133 0.05343 -0.43702 -0.29821 0.02055 210.671 -0.43075

0.99372 0.01062 8748.949

Multiple R: 0.43190 Sample: all Part I crime R square: 0.18653 N: 936 F: 106.97256 Reference group: one one-officer car

One-or Two-Officer Cars? A Perspective from Kansas City 57

TABLE 1B

TRAVEL TIME BY TYPE OF CAR RESPONDING TO THE CALL

Dependent Variable: Travel Time (Logarithm)

Beta Standard

B Error F Simple r

Independent Variables One one-officer car One two-officer car

Constant

0.48839 0.29821 0.02055 210.671 0.35048 0.28761 0.26831 0.03139 73.062 0.05343

- 1.29192 0.01785 5397.195

Multiple R: 0.43190 R square: 0.18653 F: 106.97256

Sample: all Part I crime N: 936 Reference group: two one-officer cars

standard deviation of three minutes and forty-four seconds. The travel time of one two-officer car is not significantly faster than that of a single one-officer car. The average travel time of one two-officer car is six minutes and forty-six seconds, with a stan- dard deviation of four minutes and twenty- one seconds. However, for two one-officer cars. travel time is significantly shorter. The mean is only three minutes and fifty-two seconds, with a standard deviation of three

minutes and one second. This result is similar to that of the San Diego study.

The results of the regression analysis are contained in several tables. Tables 1A and 1B indicate that there is no significant difference in the travel time of single cars with one or two officers, but when two cars with single officers are dispatched, they travel faster than single cars.

Table 2 illustrates this finding from a different perspective. The number of cars

TABLE 2

TRAVEL TIME BY NUMBER OF CARS DISPATCHED AND NUMBER OF OFFICERS IN A CAR

Dependent Variable: Travel Time (Logarithm)

Standard Beta B Error F Simple r

Independent Variables Two cars officially

dispatched -0.43702 -0.29821 0.02055 210.671 -0.43075 Two officers assigned

to a car -0.03205 -0.02989 0.02809 1.133 0.05343 Constant -0.66561 0.04473 221.394

Multiple R: 0.43190 R square: 0.18653 F: 106.97256

Sample: all Part I crime N: 936 Reference groups: one car dispatched, one officer assigned to a car

58 DAVID A. KESSLER

TABLE 3

TRAVEL TIME BY WHETHER OR NOT CALL WAS BUSTED FOR CALLS IN WHICH Two CARS WERE DISPATCHED

Dependent Variable: Travel Time (Logarithm)

Beta Standard

B Error F Simple r

Independent Variable Call was busted

Constant

-0.14970 -0.09761 0.04337 5.066 -0.14970

- 1.22889 0.03485 1,243.540

Multiple R: 0.14970 R square: 0.02241 F: 5.06635

Sample: calls in which two cars were dispatched N: 223 Reference group: call was not busted

officially dispatched makes a significant difference in travel time, but the number of officers in a car creates no significant differ- ence in travel time. Clearly, it is the number of cars, rather than the number of officers, that affects the speed of response.

The main argument for two-officer cars being faster is that one-officer cars must wait for back-up cars. However, it is well- known that officers do not always wait for the cover car. The time gained by moving in without assistance may account for one- officer cars being faster than two-officer cars. Tables 3 and 4 examine this relation-

ship. Busting a call does decrease response time. but for those calls that were not busted. two one-officer cars still arrived significantly faster than one two-officer car. This analysis substantially strengthens the San Diego finding, and suggests that delay in waiting for a cover car does not slow down response-time enough to offset the faster response time of two one-officer cars.

Table 5 combines all of the above anal- yses, and controls for the type of crime. If the urgency of the call is the reason some types of cars travel faster than others, the

TABLE 4

TRAVEL TIME BY TYPE OF CAR FOR CALLS WHICH WERE NOT BUSTED

Dependent Variable: Travel Time (Logarithm)

Beta B Standard

Error F Simple r

Independent Variable Two one-officer cars

Constant

-0.37243 -0.21151 0.04019 27.698 - 0.37243

- 1.01738 0.02708 1.411.475

Multiple R: 0.37243

R square: 0.13870 F. 27.69832

Sample: calls with two officers responding which were not busted N: 174 Reference group: one two-officer car

One-or Two-Officer Cars? A Perspective from Kansas City

TABLE 5

59

TRAVEL TIME BY TYPE OF CAR CONTROLLING FOR OTHER DETERMINANTS OF TRAVEL TIME

Dependent Variable: Travel Time (Logarithm)

Beta B Standard

Error F Simple r

Independent Variables Two one-officer cars Officer in car at

time of dispatch Car in beat of

incident Emergency equipment

used Call is busted

Type of Call Rape Assault Involvement burglary Discovery burglary Involvement larceny Discovery Larceny Involvement auto

theft Discovery auto theft

Constant

-0.22742 -0.15773 0.04270 13.643 -0.38617

-0.12356 -0.05447 0.02105 6.694 -0.14846

-0.23395 -0.17264 0.03561 23.506 -0.22178

-0.13344 -0.17086 0.06482 6.948 -0.23586 -0.09300 -0.06005 0.03741 2.576 -0.31688

0.04355 0.12705 0.14056 0.817 -0.00137 0.07946 0.06818 0.04800 2.018 -0.09901

-0.00256 -0.00289 0.05891 0.002 -0.10801 0.23265 0.18116 0.04463 16.477 0.21892 0.11296 0.13394 0.06176 4.703 0.08856 0.12561 0.13756 0.06066 5.142 0.14071

-

0.11937 0.20360 -0.96728

- -

0.08981 5.141 0.06735 206.240

-

0.11747

Multiple R: 0.55135 R square: 0.30399 F: 11.31929

Sample: calls with two officers responding N: 324 Reference groups: one two-officer car, officer out of car at time of dispatch, car out of beat of incident, emergency equipment not used, call is not busted, robbery

differences should become insignificant when type of crime is controlled. While all of the variables, except busted calls, affect the rate of travel time, two one-officer cars remained significantly faster than one two- officer car, for those calls in which two officers were dispatched. In other words, controlling for the use of emergency equip- ment, the type of calls, whether the car is in or out of the beat of the incident, and whether the call is busted or not, two one-officer cars are still faster than one

two-officer car. A saturated interaction model was tested, but none of the interac- tions were found to be significant and multicollinearity did not appear to be a serious problem. Response time remains faster for calls in which two one-officer cars are dispatched than for calls in which a single car is dispatched.

The findings of the Kansas City study support the findings of the San Diego study. The empirical results are contrary to the deduced hypotheses from the analytical

60 DAVlD A. KESSLER

models. Two one-officer cars respond more rapidly to calls for service than do one two-officer car or single one-officer cars. For both studies, the probability of a type 1 error is substantially less than p= ,001. Since both samples are independent, the probabil- ity of this relationship occurring by chance in both studies is less than p=.OOOOOl. To discover a possible explanation. the assump- tions of the analytical model need to be reexamined. Throughout the derivations, it was assumed that the speed of travel is constant. However, if a cover car must travel further to an incident and still arrives faster. the officer must be traveling substan- tially faster. The question is, why do officers in two one-officer cars travel faster than others? A number of variables that could affect these calculations have already been controlled, i.e., the type of incident. the perception of the seriousness of the inci- dent, whether or not it was an emergency. These variables do affect the speed of travel, but the arrangement of officers and cars dispatched still has a significant effect. The question which must be addressed is how this arrangement changes the incen- tives of officers to travel either faster or more slowly.

One explanation for the difference in performance of officers in two one-officer cars may lie in the structure of accountabil- ity of patrol officers to their peers. As one patrol sergeant explained, officers in one- officer cars do not know where their col- league is or if there is any risk of injury. and they do not want to be blamed for not being there when they were needed.” Police of- ficers are a tight fraternity of colleagues who depend on each other.

While theories about relationships among supervisors and colleagues are more difficult to quantify and to develop into formal mathematical models than are time and distance equations, these relationships may be no less important in understanding the performance of patrol officers. Harvey Lie- benstein develops, in Beyond Economic Mm (1976), a systematic argument concern- ing the effect of peer and supervisor rela- tionships on production, and participant

observer studies provide some support for Leibenstein’s analysis.

Leibenstein argues that the incentives a firm provides determine the effort a worker expends in productive activity. Two impor- tant sources of incentives are approval by a supervisor and approval by peers. The ap- proval of supervisors and peers is based on their perceptions of employees’ efforts; per- ceptions which are obtained through moni- toring. Alchian and Demsctz (1972) point out that the cost of monitoring team produc- tion is an important factor in designing social organizations that control shirking.

The capacity of supervisors and peers to monitor and provide approval are important variables determining production output. Supervisors cannot monitor as closely as peers who work with each other. Whether peer pressure improves production depends on whether workers view their relationship to the firm as one of conflict or cooperation, and their relationship with each other as conflict or cooperation. Production is high- est if peers view both their relationships with the firm and with each other as cooperative. Peers can monitor each other easily and accurately, and if they perceive their interests as similar to those of the tirm, they will support productive behavior cfti- ciently. Production is lowest when peers view their relationships both with the firm and with each other as relationships of conflict.

In this context, travel time may be thought of as a production output. The dispatching of one- or two-ofticer cars and the number of cars dispatched structures the incentives and monitoring of officers with regard to their supervisors and peers. When a single officer is dispatched, the approval of peers is not affected by the officer’s perfor- mance. Peers are not affected if the officer performs poorly. and they are not present to monitor the officer’s behavior. Therefore. peer pressure is irrelevant. Pressure from a supervisor is also not important. One of the games in police administration is “finding your man” (Rubinstein. 197.1). Since the supervisor must monitor several officers, he cannot monitor every call an officer makes.

One-or Two-Officer Cars? A Perspective from Kansas City 61

Therefore, an officer will not be rewarded or punished for his/her response on a large number of calls. Officers responding to a call must provide reasonably satisfactory service, but citizen satisfaction with re- sponse time is not directly dependent on response time (Kansas City, Missouri Board of Police Commissioners, 1977). Therefore, the officer’s effort depends primarily on his/her own motivation. There is no real accountability in this situation.

With two officers in the car, the incentive structure is similar. The officers can monitor each other, but neither has any incentive to infuence the other’s performance. If they delay very long, they are “in it together.” Peer support is important to officers, and they are not likely to jeopardize relation- ships over a slow response time to a call.

However, if two one-officer cars are dispatched, the effect of peer pressure is substantially altered. Officers depend on each other for support, especially in risky situations. When two officers in separate cars are assigned to a call, they each have a responsibility to arrive as quickly as possible for their mutual protection. For reasons of his/her own protection, each officer has an incentive to observe who is reliable and who is not, and sanctions may be disbursed accordingly.

Policemen take careful notice of who comes in on emergency calls, which men tend to be first most often, who does not show up at all, and which men seem to arrive just a little bit late. There are few district policemen who can stand being labeled a “traffic cop,” an insult which implies a man has no stomach for risk-tak- ing. The recognition that colleagues con- sider someone a coward is usually sufficient to drive a man out of the district, and any man who wishes to stay must learn to accept the risk of fast driving and dark alleys. (Rubinstein. 1973: 100)

Peer disapproval could be severe if an officer puts another officer in a dangerous situation. The more dangerous the situation is, the worse the disapproval. On the other hand, an officer may appear heroic and receive peer approval if he arrives at a

dangerous situation before another officer. In this case, the more dangerous the situa- tion is, the greater the reward. Peer moni-

toring is much more accurate than supervi- sor monitoring when an officer is sitting and waiting for support and wondering why the cover car is taking so long to respond. Given uncertainty about how long it will take the officer in another car to arrive, or about how dangerous the situation is, the rational strategy for an officer is to try to arrive first. Since police officers can vary their rate of response somewhat according to their moti- vation (by the speed they drive, the route they take, and the interruptions they allow), it can be hypothesized that because of the need to sustain their colleagues’ approval, two officers in single cars will be more highly motivated to respond quickly than will an officer or officers in a single unit, and travel time will, accordingly, be faster.

CONCLUSIONS

This research has analyzed a puzzling finding from the San Diego study and reproduced this finding with data from the Kansas City Response Time Analysis Study data set. The findings indicate that two one-officer cars respond more rapidly to calls than one two-officer car. The implica- tions are that the technological explanation for response time may be less important than human motivation. The constraints on achieving rapid response time are behav- ioral rather than physical. Technological innovations will have little effect on re- sponse time because they do not address the binding constraint of officer behavior.

This conclusion may have important im- plications for policy beyond the question of whether to use one or two officers in a car. While peer pressure is frequently viewed by administrators as an uncontrollable obstacle to programs they wish to implement, the findings provide an example where peer pressure can be structured to improve of- ficer performance. Given the theoretical bases provided by Leibenstein, the findings

62 DAVID A. KESSLER

suggest that improved performance in other areas of police activity may come less from the addition of technological gadgetry than from the careful structuring of institutional incentives to motivate individuals. Police administrators who adopt this latter strategy in innovative ways may find the perfor- mance of their departments substantially improved.

Regardless of the theoretical explanation for the findings, the implication is that the deployment of two-officer cars cannot be justified by improved response time. Both studies tested the condition where two- officer cars should have the fastest response time, and both studies found that the most rapid response time can be achieved by sending two one-officer cars when a cover car is needed. Since redeployment is re- quired in a major policy change from two-officer to one-officer cars, an additional decrease in response time can also be expected to accrue, as predicted by the mathematical models. The decision to use two-officer cars can, therefore, only be justified by objectives other than response time.

ACKNOWLEDGMENTS

Data used in this analysis were collected fcr the Department of Justice. Law Enforcement Assistance Administration, National Institute of Justice, Grant Number 73.NI-99-00476. Points of view or opinions stated herein are those of the author, and do not necessarily represent the official position or policies of the U.S. Department of Justice. The author would like to thank the National Institute of Justice and the Kansas City, Missouri Police Department for making these data available. The Workshop in Political Theory and Policy Analysis, Indiana Uni- versity. provided support for computer analysis. Patty Smith and Teresa Therrien prepared the final manuscript. Stephen L. Percy. John P. McIver. Roger B. Parks, and Elinor Ostrom reviewed and commented on earlier drafts of this paper. Bob Decker and Wayne Winston assisted with the mathe- matical modeling.

NOTES

’ Although increased officer safety is a dubious outcome of two-officer calls, some mediation tech- niques can only be used by two officers. Therefore, it is likely that police departments will always be

required to send two oflicers to some proportion ol calls for service.

’ Defined as p = h/x(/ (Larson and Odoni. 1981: 190).

’ After the interval was computed. it was logarithmi- cally transformed because of the distribution of the data. The transformed variable and the untrans- formed variable were both analyzed. The differences in the results were slight. The statistical significance of the variables did not change. and the substantive interpretation of the results was not affected. The results on the transformed variables were reported for regression analysis. so that the findings would be consistent with those of the original response time study.

’ Interview with Sergeant Ron Robbinette, Kansas City, Missouri Police Department.

APPENDIX

The calculation of I+(C) follows the procedure described by Kaplan (1979: 352). There are macrostates that refer to the number of cars that are busy at any given time and microstates that refer to the probability that a car in a specific beat is available for a specified macrostate. For the hypothetical four-beat city, it is assumed that there is one car assigned to each beat. At any given time that a call may arrive, there may be no cars busy (S,,). one car busy (S,), two cars busy (S,), three cars busy (S,), or four cars busy (S,). For each macrostate, there are several possible microstates. For example, if two cars are busy (Sz), there are six microstates, consisting of the following cases:

(1) beats 1 and 2 are busy; (2) beats 1 and 3 are busy: (3) beats 2 and 3 are busy; (4) beats 2 and 4 are busy; (5) beats 3 and 4 are busy; and (6) beats 1 and 4 are busy.

By assuming that the arrival of request calls for service is equally likely for all four beats, the number of microstates in which an officer is available provides the probability that a given car is available to respond.

For example, given the macrostate that two cars are busy (S,), there are six microstates. Now suppose a request for service which requires only one car arrives in beat 1. Then beat 1 is the in-beat car corresponding to C,. The

One-or Two-Officer Cars? A Perspective from Kansas City 63

TABLE A

STATE STRUCTURE FOR ONE- AND TWO-OFFICER CALLS

#EventslMicrostates

#Microstates1 One-O#icer Calls Two-Ofjicer Calls

Macrostate Macrostate C* C, C.3 Cd c-5 G c, c, c,

S,, (0 cars busy) 1 1 0 0 0 1 0 0 0 0 S, (1 car busy) 4 3 1 0 0 3 1 0 0 0 Sz (2 cars busy) 6 3 3 0 0 2 1 2 1 0 Sj (3 cars busy) 4 1 2 1 0 0 0 0 0 4 S4 (4 cars busy) 1 0 0 0 1 0 0 0 0 1

car in beat 1 will be available to respond in three of the six microstates (3, 4, and 5). Given the macrostate Sz, the probability that the in-beat car is available to respond to a one-officer call is X, or .5.

To compare the effect of sending two one-officer cars to a call, assume that the request for service was the type for which department police stipulated that two of- ficers must respond. There would still be six microstates, corresponding to those enu- merated above. However, two cars must be available to respond rather than one. Con- sider the probability that the in-beat car and an adjacent beat car are available to re- spond (C,). Three microstates are elimi- nated, because the beat 1 car is busy (1, 2, and 6). One microstate is eliminated, be- cause both adjacent beat cars are busy (3). Therefore, there are two microstates in which the in-beat car and an adjacent-beat car can respond to the call (4 and 5). The results for all of the macrostates, micro- states, and events are presented in Table A.

The mobabilities that the given macro-

(A3) P(S;) = P(S,) * ;

i=O,l,...,s-1

s - I

(A4) P(S,) = 1 - x P(S;) i=o

(A5) Wq = & * P(S,) (1 - pisy .

The probabilities must be calculated sepa- rately for calls requiring one officer to respond and calls requiring two officers to respond. For one-officer calls, the model is an MIMI41 process, while for two-officer calls, the model is an M/M/2/ process. The arrival of calls requiring one officer and of calls requiring two officers are independent events. For a city which has a mix of one- and two-officer calls, the probability of a given macrostate occurring is the joint probability that a macrostate occurs because of a one-officer call and a two-officer call (see Table B). For the four-beat city. let:

I ”

states will occur follow an M/M/s/ model. P l(0)

The equations are as follows: Pi(l)

(Al) p = A/u Pl(2)

s-l 642) W,) = c ; + -$P*$+ 1 -I i=o Pl(3)

represent the probability that no cars are busy from a one-officer call: represent the probability that one car is busy from a one-officer call; represent the probability that two cars are busy with two one-officer calls; represent the probability that three cars are busy with three one-officer calls;

64 DAVID A. KESSLER

TABLE B

JOINT MACROSTATE PROBABILITIES FOR BOTH ONE- AND TWO-OFFICER CALLS

One-Oficer Calls WO)

Two-OfJicer Calls

E(2) E(4)

p l(O) .1174 .0673 .0541 .2388 PI(l) .1641 .0941 .0756 .3338

Pl(2) .1147 .0657 .0528 .2333

Pl(3) .0535 .0306 .0246 .1087

Pl(4) .0421 .0241 .0194 .0855

.4918 .2818 .2264 1.0000

Pl(4)

PW)

E(2)

m(4)

represent the probability that four weighting the probabilities C, through C, by cars are busy with four one-officer the probability that a call is a one-officer call calls; (P(1)) or a two-officer call (P(2)). represent the probability that no cars are busy on a two-officer call; represent the probability that two cars are busy on a two-officer call; represent the probability that four cars are busy on two two-officer calls.

4

E(R7') = P(1) * c E(t C;)* P(C;) + i= I

P(2) * E E(t CJ * P(C;) i=S

Then the probability that s cars are busy is as follows:

P(&) (all cars are in service) = Pl(o)*p2(0);

P(SI) (one car out of service) = Pl(l)*P2(0);

P(S2) (two cars out of service) = P1(2)*P2(o)+Pl(o)*P2(2);

P(&) (three cars out of service) = P1(3)*p2(O)+Pl(l)*P2(2);

P(&) (four cars out of service) =

1 -P(&) + P(SI) + P(S2) + P(h). The probability of a given event, C,, can

now be calculated according to the following equations. For one-officer calls:

P(C1) = P(s,,)+%P(s,)+% P(&)+%P(s,) P(C2) = %P(.s,)+KP(&) +KP(Sj) P(C3) = %P(&) P(C4) = P(S,).

For two-officer calls: P(C5) = P(s,j)+%P(s,)+% P(S2) P(C6) = %P(S,)+%P(S) P(C7) = %P(S2) P(C8) = KP(S2) P(C9) = P(Sx)+P(&). Finally, the expected response time for

the city as a whole can be calculated by

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