Journal o! Studies on Alcohol, Vol. 3t•, No. I, I975
Probabilityof ArrestwhileDrivingunder the Influence
of AlcohoP
GeorgeA. Beitel,2 MichaelC. Sharpand William D. Glauz SVMMAaY.The •robabilit•to• arrestwhile drivingat a bloodalcohollevel over 0.10f$was .0058 (about I in 200).
HEREiS considerable interest in defining therelationship
between the probability ofbeing arrested fordriving under the influence of intoxicants (Dye) and blood alcohol concentration (Bac).a Such information,if accuratelyknown, could be put to a varietyof uses,includingpublic information,policepatrol managementinformation,Dty•patrol evaluation,and estimation of the number of drunken drivers on the road.
in surveysassociated with the AlcoholSafetyAction Projects (asa•,), thousandsof personshave been interviewedand asked, amongother questions,what they thoughttheir chanceswere of being stoppedby the policeafter havinghad too much to drink. The objectof sucha questionis to measurethe level of public awarenessof enforcementof the •tyx laws. Even those who pose the questiondo not know the answer,however;and sucha question has no singleanswerunlessthe level of intoxication,or Bac, is specified.There have been no detailedstudiesto establishsuch xFrom the Midwest ResearchInstitute, KansasCity, MO 64110. The experimental portion of this study was conductedby membersof the KansasCity Alcohol Safety Action Project in conjunction with contract No. DOT-HS-077-1-100 with the Na-
tional Highway Traffic Safety Administration.The opinions,findings and conclusionsexpressed in this publicationare thoseof the authorsand not necessarily those of the City of KansasCity or the National Highway Traffic Safety Administration. a Ariantic Richfield Hanford Co., Richland, Washington. 8Ba½ is defined as the percentageof ethyl alcoholby weight in the blood, and is the single best measureof the level of alcohol intoxication. ACKNOW•.•;DGM•;N;s.--We thank SergeantJohn Weddie and his unit for their cooperation in this experiment. Receivedfor publication: 15 February 1974. Revision:27 August 1974. 109
110
G.A. BEITEL,M. C. SHARPAND W. D. GLAUZ
probabilities.Previousestimatessuggestthat the probabilityof beingarrestedwhile makinga 10-mi!etrip with a BACabove0.105 is about .0015 (1). 4 Accurateknowledgeof the probabilitiesof beingarrestedfor Dv• is necessary if a public-education campaign againstdrunkendriving is to retain the trust and confidenceof the public. Thiskind of knowledgecouldalsoproveto be a valuablepolicepatrolmanagement tool.The officerin chargeof Dw patrolswould have a standardagainstwhich to measurethe performanceof his unit.
In addition,if the probabilityof arrestfor ota under specific patrolconditions can be established with confidence, it shouldbe possible-bypatrollinga particularareaand obtainingtrafficcount data-to infer the percentageof driverswho will have a given range.Sucha meansof estimatingthe numberof drunkendrivers would be more readily adaptableto communitieswithout AsAPs than a costlyvoluntaryroadsidesurvey. This reportdescribesa methodof determiningthe probability of being arrestedfor ov•, and appliesit to a driver with a given sACwho comesunder the surveillanceof a police officer skilled in the detectionof drunkendrivers.To computethe probability of arrestas a functionof sac, it is necessary to know the unconditionalprobabilityof beingarrested.A police-patrol experiment was designed and conducted whichprovidedthe requiredinformation The BACdistributionof the populationof driverswho are not arrestedwas takenfrom the resultsof a randomsurvey(2) of volunteermotoristsconductedwithin the patrol area 2 monthsbefore the initiation of the patrol experiment.The B•c distributiono! driversarrestedwas obtainedfrom policerecords. METHOD
Let P(Bj) be the unconditionalprobabilitythat a driver has a in range Bj where, for example,B• ----0.00•, B,•-- 0.01-0.04•, B3 ----0.050.09•, etc. The conditionalprobabilitythat a driver, who has not bee•
arrestedfor r•w, hasa •AC in rangeB• is P(B•IAo ). Theseprobabilities obtainedby a roadsidesurveyof volunteers,are presentedin Table 1
Theprobability thatan arrested driverhasa •ACin rangeB/, P(B•IA• can be obta/nedwith high precisionfrom previous•)w arrest records • The subjectsof this report were 836 alcoholicswho statedthat they had mad, an averageof 120 10-mile trips each per year after drinking,resultingin an averag of 0.18 ou• arrestsper person.We can also reasonablyassumethat their ,½ afte drinking was higher than 0.105.
TABLE1.--Distributionof Drivers as a Function of BAC between the Hours o• 2230 and 0130,• and the Probabilityo• Having a ParticularBAC i• Arrested •or DUI Surve!ted Drivers
Arrested Drivers
0 0.01-0.04 0.05-0.09
.68000
.20000 .06000
.0001 .0007 .0200
0.10-0.14 0.15-0.19 0.20-0.24 0.25-0.29 0.30-0.34 0.35-0.40
.04000 .01500 .00400 .00087 .00010 .00002
.2610 .4250 .2130 .0620 .0160 .0020
0.10-0.40 0.15-0.40
.06000 .02000
.9790 .7180
ß Distribution obtained from best fit negative exponential function describing actual data (2), The data were comprised of 1022 BACs obtained during the late evening and early morning hours, with the findings weighted to correspond to the hours of the police patrol experiment.
Figure I presentsthe distributionof BACsof drivers arrestedfor during the 1972 volunteersurveyby the same AsAPofficerswho con-
ductedthe patrolexperiment described in thispaper.Valuesof P(BjlA•) can easilybe obtainedfrom thesedata and are also given in Table 1. Alsoincludedin Figure I is the distributionof BACS from arrestsby the regular patrol. The similarity between the two distributionssuggests that the resultspresentedin this paperneednot be restrictedto a select group of police officers. Bayes' theorem allows us to compute the conditionalprobability
P(A, IBj) that a driverwill be arrested,if it is assumed that he has a •AC in range Bj, from the equation:
P(Ao)ßP(Bj]Ao)• P(A•) ß P(B•IA•)' where P(A•) is the unconditionalprobabilityof being arrestedfor if observedby a skilledofficer,and P(Ao)= 1- P(A•). Althoughwe
donotknow, P(A•) a priori,we canestimate it in thefollowing manner. From previousperformancerecordsof the KansasCity xsxP unit in
normalpatrol,we know that an officermakesapproximately one arrest each 5 hr of scheduledpatrol (this time includesarrest processing, lunch, coffeebreaks,and other nonpatrolactivities).The officersare usuallyon duty at times and placeswhere the traffic flow is in the' range of 100 to 1000 vehiclesper hr in 2 directions.Thus, we can place reasonableestimateson P(A•), i.e., .0002
Probabilityof ArrestwhileDrivingunder the Influence
of AlcohoP
GeorgeA. Beitel,2 MichaelC. Sharpand William D. Glauz SVMMAaY.The •robabilit•to• arrestwhile drivingat a bloodalcohollevel over 0.10f$was .0058 (about I in 200).
HEREiS considerable interest in defining therelationship
between the probability ofbeing arrested fordriving under the influence of intoxicants (Dye) and blood alcohol concentration (Bac).a Such information,if accuratelyknown, could be put to a varietyof uses,includingpublic information,policepatrol managementinformation,Dty•patrol evaluation,and estimation of the number of drunken drivers on the road.
in surveysassociated with the AlcoholSafetyAction Projects (asa•,), thousandsof personshave been interviewedand asked, amongother questions,what they thoughttheir chanceswere of being stoppedby the policeafter havinghad too much to drink. The objectof sucha questionis to measurethe level of public awarenessof enforcementof the •tyx laws. Even those who pose the questiondo not know the answer,however;and sucha question has no singleanswerunlessthe level of intoxication,or Bac, is specified.There have been no detailedstudiesto establishsuch xFrom the Midwest ResearchInstitute, KansasCity, MO 64110. The experimental portion of this study was conductedby membersof the KansasCity Alcohol Safety Action Project in conjunction with contract No. DOT-HS-077-1-100 with the Na-
tional Highway Traffic Safety Administration.The opinions,findings and conclusionsexpressed in this publicationare thoseof the authorsand not necessarily those of the City of KansasCity or the National Highway Traffic Safety Administration. a Ariantic Richfield Hanford Co., Richland, Washington. 8Ba½ is defined as the percentageof ethyl alcoholby weight in the blood, and is the single best measureof the level of alcohol intoxication. ACKNOW•.•;DGM•;N;s.--We thank SergeantJohn Weddie and his unit for their cooperation in this experiment. Receivedfor publication: 15 February 1974. Revision:27 August 1974. 109
110
G.A. BEITEL,M. C. SHARPAND W. D. GLAUZ
probabilities.Previousestimatessuggestthat the probabilityof beingarrestedwhile makinga 10-mi!etrip with a BACabove0.105 is about .0015 (1). 4 Accurateknowledgeof the probabilitiesof beingarrestedfor Dv• is necessary if a public-education campaign againstdrunkendriving is to retain the trust and confidenceof the public. Thiskind of knowledgecouldalsoproveto be a valuablepolicepatrolmanagement tool.The officerin chargeof Dw patrolswould have a standardagainstwhich to measurethe performanceof his unit.
In addition,if the probabilityof arrestfor ota under specific patrolconditions can be established with confidence, it shouldbe possible-bypatrollinga particularareaand obtainingtrafficcount data-to infer the percentageof driverswho will have a given range.Sucha meansof estimatingthe numberof drunkendrivers would be more readily adaptableto communitieswithout AsAPs than a costlyvoluntaryroadsidesurvey. This reportdescribesa methodof determiningthe probability of being arrestedfor ov•, and appliesit to a driver with a given sACwho comesunder the surveillanceof a police officer skilled in the detectionof drunkendrivers.To computethe probability of arrestas a functionof sac, it is necessary to know the unconditionalprobabilityof beingarrested.A police-patrol experiment was designed and conducted whichprovidedthe requiredinformation The BACdistributionof the populationof driverswho are not arrestedwas takenfrom the resultsof a randomsurvey(2) of volunteermotoristsconductedwithin the patrol area 2 monthsbefore the initiation of the patrol experiment.The B•c distributiono! driversarrestedwas obtainedfrom policerecords. METHOD
Let P(Bj) be the unconditionalprobabilitythat a driver has a in range Bj where, for example,B• ----0.00•, B,•-- 0.01-0.04•, B3 ----0.050.09•, etc. The conditionalprobabilitythat a driver, who has not bee•
arrestedfor r•w, hasa •AC in rangeB• is P(B•IAo ). Theseprobabilities obtainedby a roadsidesurveyof volunteers,are presentedin Table 1
Theprobability thatan arrested driverhasa •ACin rangeB/, P(B•IA• can be obta/nedwith high precisionfrom previous•)w arrest records • The subjectsof this report were 836 alcoholicswho statedthat they had mad, an averageof 120 10-mile trips each per year after drinking,resultingin an averag of 0.18 ou• arrestsper person.We can also reasonablyassumethat their ,½ afte drinking was higher than 0.105.
TABLE1.--Distributionof Drivers as a Function of BAC between the Hours o• 2230 and 0130,• and the Probabilityo• Having a ParticularBAC i• Arrested •or DUI Surve!ted Drivers
Arrested Drivers
0 0.01-0.04 0.05-0.09
.68000
.20000 .06000
.0001 .0007 .0200
0.10-0.14 0.15-0.19 0.20-0.24 0.25-0.29 0.30-0.34 0.35-0.40
.04000 .01500 .00400 .00087 .00010 .00002
.2610 .4250 .2130 .0620 .0160 .0020
0.10-0.40 0.15-0.40
.06000 .02000
.9790 .7180
ß Distribution obtained from best fit negative exponential function describing actual data (2), The data were comprised of 1022 BACs obtained during the late evening and early morning hours, with the findings weighted to correspond to the hours of the police patrol experiment.
Figure I presentsthe distributionof BACsof drivers arrestedfor during the 1972 volunteersurveyby the same AsAPofficerswho con-
ductedthe patrolexperiment described in thispaper.Valuesof P(BjlA•) can easilybe obtainedfrom thesedata and are also given in Table 1. Alsoincludedin Figure I is the distributionof BACS from arrestsby the regular patrol. The similarity between the two distributionssuggests that the resultspresentedin this paperneednot be restrictedto a select group of police officers. Bayes' theorem allows us to compute the conditionalprobability
P(A, IBj) that a driverwill be arrested,if it is assumed that he has a •AC in range Bj, from the equation:
P(Ao)ßP(Bj]Ao)• P(A•) ß P(B•IA•)' where P(A•) is the unconditionalprobabilityof being arrestedfor if observedby a skilledofficer,and P(Ao)= 1- P(A•). Althoughwe
donotknow, P(A•) a priori,we canestimate it in thefollowing manner. From previousperformancerecordsof the KansasCity xsxP unit in
normalpatrol,we know that an officermakesapproximately one arrest each 5 hr of scheduledpatrol (this time includesarrest processing, lunch, coffeebreaks,and other nonpatrolactivities).The officersare usuallyon duty at times and placeswhere the traffic flow is in the' range of 100 to 1000 vehiclesper hr in 2 directions.Thus, we can place reasonableestimateson P(A•), i.e., .0002
