
15 Cal.App.3d 775 (1971)
93 Cal. Rptr. 471
BURTON F. BODENSCHATZ, Plaintiff and Appellant,
v.
STATE PERSONNEL BOARD et al., Defendants and Respondents.
Docket No. 9808.
Court of Appeals of California, Fourth District, Division Two.
February 19, 1971.
*777 COUNSEL
Kurilich, Slack, Ballard, Batchelor, Maher & McBride, Kurilich, Slack, Ballard, Batchelor, Maher & Ricks and Cecil E. Ricks, Jr., for Plaintiff and Appellant.
Thomas C. Lynch, Attorney General, and Alvin J. Korobkin, Deputy Attorney General, for Defendants and Respondents.
OPINION
TAMURA, J.
This is an appeal from a judgment of the superior court denying a peremptory writ of mandate to compel respondent State Personnel Board (Board) to set aside its decision sustaining appellant's dismissal from his employment as a traffic officer with the California Highway Patrol (CHP).
Appellant was served with a written notice of dismissal alleging, among other grounds, inefficiency in failing to meet departmental standards of enforcement activity. Appellant answered and hearings were held before a hearing officer of respondent Board. The hearing officer found that the level of appellant's enforcement activity "was so far below that which respondent could reasonably require of a State Traffic Officer as to clearly constitute inefficiency within the meaning of Government Code Section 19572, subd. (c)," and rendered a proposed decision sustaining appellant's dismissal on the sole ground of inefficiency.[1] The proposed findings and decision were adopted by respondent Board.
The trial court reviewed the record of the proceedings before the Board, found that the Board's decision was supported by substantial evidence in the light of the whole record and entered judgment denying a peremptory writ of mandate.
At the Board hearing, the CHP introduced statistical evidence compiled by it comparing appellant's level of enforcement activity while unsupervised to that of various groups of fellow officers and also to his own while working under the supervision of a superior officer. The Board considered such evidence in rendering its decision.
*778 Appellant urges that there was no substantial evidence to support the finding that his level of enforcement activity constituted inefficiency. The thrust of his attack is directed against the use of the statistical data compiled by the CHP to support the charge of inefficiency. He urges (1) the use of such evidence to prove a fact  in the present case the fact that appellant failed to take appropriate enforcement action against violations he observed or should have observed  is proscribed by People v. Collins, 68 Cal.2d 319 [66 Cal. Rptr. 497, 438 P.2d 33], and (2) assuming such evidence was admissible, it did not support a finding that appellant's level of enforcement activity constituted inefficiency.
Preliminarily, we define our function in reviewing the Board's decision. (1, 2) Respondent Board is a state-wide administrative agency deriving its adjudicating power from section 3 of article XXIV of the Constitution. Consequently, its factual determinations must be upheld by a reviewing court if they are supported by substantial evidence (Shepherd v. State Personnel Board, 48 Cal.2d 41, 46-47 [307 P.2d 4]) and all legitimate and reasonable inferences must be drawn in support of such findings (Orlandi v. State Personnel Bd., 263 Cal. App.2d 32, 38 [69 Cal. Rptr. 177]; Sweeney v. State Personnel Board, 245 Cal. App.2d 246, 251 [53 Cal. Rptr. 766]). It is not our function to reweigh the evidence. (Shepherd v. State Personnel Board, supra, p. 46.)
The record of the administrative hearing reveals the following:
Appellant commenced employment with the CHP in 1952. During most of his tenure and on the effective date of his dismissal (December 31, 1967), he served as a motorcycle traffic officer in the Orange County area.
The CHP introduced into evidence its Commissioner's General Policy Order 100.68, issued in 1960. It outlined the various functions to be performed by the CHP, including rendering of information and assistance to the public, prevention of traffic law violations, and the investigation (in conjunction with local law enforcement agencies) of crimes unrelated to traffic laws. But the order stated that the CHP's primary function is the enforcement of state traffic laws and declared it to be the departmental policy that members of the CHP take appropriate enforcement measures in regard to each observed violation. It directed that enforcement measures be accomplished "in a business-like, firm, fair, impartial, courteous, and uniform manner" using one of the following methods: (1) arrest, (2) issuance of a citation, (3) issuance of a written warning, and (4) issuance of an oral warning.
The CHP then introduced three groups of statistical compilations by *779 which appellant's level of enforcement activity was compared to that of his fellow patrolmen in the Anaheim area of Orange County.
Group 1: The following chart was introduced comparing appellant's level of enforcement activity with that of all CHP officers in the Anaheim area during the last half of 1965 and the first quarter of 1966.


                            Miles          Patrol Hrs.    Enforcement Hrs.
                      ----------------    -----------    ----------------
                        Per       Per          Per         Per      Per
                       Arrest   Contact       Arrest      Arrest   Contact
3d Qtr.    Area Avg.     41        30           1.8          3.0      2.2
1965       App.'s Avg.   70        58           5.3          6.3      5.1
4th Qtr.   Area Avg.     46        32           2.0          3.1      2.2
1965       App.'s Avg.   90        58           5.6          6.3      4.1
1st Qtr.   Area Avg.     40        28           1.8          2.7      1.9
1966       App.'s Avg.   57        34           3.4          3.8      2.3

During the period covered by the study appellant was assigned to freeway patrol. There was testimony that freeway patrol duty presented a maximum potential for high level enforcement activity. The other traffic officers in the Anaheim area whose records were used for comparison were assigned to either freeway duty or patrols presenting fewer prospects for law enforcement activity than those covered by appellant. The chart reveals that appellant's performance level as compared to that of the other officers was markedly below the average in each of the various criteria used for comparisons. During the nine-month period covered by these figures appellant spent six months working day shift, two months working evenings and one month working the graveyard shift. There was testimony that opportunity for enforcement activity was greatest on the evening shift, followed closely by the day shift; graveyard duty presented markedly less potential for enforcement activity than the other two assignments. The distinction of shifts worked by the other officers in the Anaheim area during the period covered by the study is not known.
Group 2: The following statistics were presented comparing appellant's level of enforcement activity with that of a group composed of 10 motorcycle traffic officers working in the Anaheim area for the entirety of 1966 and the first three quarters of 1967.


*780
                              1966         First 1/2 1967    3rd Qtr. 1967
                         ---------------  ----------------  ---------------
                         Appellant  Avg.  Appellant  Avg.   Appellant  Avg.
Total Arrests              415      685     192      346       89      135
Rules of road arrest       193      367     105      189       52       81
Miles per arrest            64       45      99       60       76       57
Miles per contact           39       31      60       37       37       34
Patrol hours per arrest    3.6      2.1     5.3      2.6      3.8      2.7
Enforcement hours
per arrest                 4.2      2.8     6.2      3.1      4.5      3.3
Patrol hours per
hazardous arrest           4.1      2.5     5.8      3.1      4.6      3.1
Enforcement hours
per contact                2.6      1.9     3.8      1.9      2.2      1.9

The 10 officers in the control group were immediately junior to appellant in length of service and had less experience as motorcycle officers. They were working the same type of high activity freeway patrols in the Anaheim area as those assigned to petitioner. During the 21 months covered by the study, appellant spent 10 months on day shift, 9 months working evenings, and 2 months on the graveyard detail. The 10 officers in the control group averaged 6.9 months on the day shift, 11.4 months on evenings, and 2.2 months on the graveyard shift. Again the study shows a marked differential between appellant's performance and that of the group average in each of the criteria used for comparison.
Group 3: Statistics were also presented at the hearing summarizing appellant's level of enforcement activity while under the immediate supervision of a superior officer. Because of appellant's consistently below average rating in the level of his enforcement activity during 1965, he was placed on formal training status in January 1966, and underwent a series of training sessions averaging 2 hours each. During the sessions he was accompanied on routine patrol in a car (as opposed to a motorcycle) by a sergeant who monitored appellant's performance. Appellant and his monitor would patrol the beat regularly assigned to appellant on that day. The sessions were held at various hours, the earliest being from 8 to 11 a.m. and the latest from 7:30 to 10:30 p.m. They covered the period from January to July 1966, and totalled 84 1/2 hours. Approximately 40 reports prepared by the monitors and containing data reflecting appellant's performance while under observation were introduced at the hearing. They revealed that appellant's level of activity during the training sessions averaged *781 2.1 patrol hours per arrest as compared to his unsupervised average of 3.4 during 1966, 5.3 for the first half of 1967 and 3.8 for the 2d quarter of 1967. The 2.1 figure was precisely that of the control group of 10 during 1966. The study further showed that while under training supervision, appellant averaged 1.2 enforcement hours per contact as compared to his unsupervised average of 2.6 during 1966, 3.8 for the first half of 1967 and 2.2 for the 3d quarter of 1967. The average for the group of 10 for 1966 and the first three quarters of 1967 was 1.9.

I
Use of the statistical evidence for the purpose of evaluating appellant's efficiency was not, as urged by appellant, proscribed by People v. Collins, 68 Cal.2d 319 [66 Cal. Rptr. 497, 438 P.2d 33].
People v. Collins, supra, does not foreclose all use of statistical compilations as evidence to establish the existence of a fact. In Collins, the prosecution introduced evidence tending to establish that a robbery was committed by a couple in a yellow automobile, one, a blonde Caucasian woman wearing a pony tail, and the other, a Negro male with a beard and mustache. The prosecution assigned arbitrary numerical values to the probability of encountering those circumstances in a random population and, by applying a theory of mathematical probability known as the "product rule," purported to calculate with mathematical precision the probability of encountering the conjunction of those circumstances in a random population. In reversing defendant's conviction, the Supreme Court established restrictions on the assignment of numerical values to the probability of encountering a given set of circumstances in a random population, and the use to which such coefficients might be put. (See Finkelstein and Fairley, A Bayesian Approach to Identification Evidence (1970) 83 Harv. L.Rev. 489; Kaplan, Decision Theory and the Factfinding Process (1968) 20 Stan.L.Rev. 1065.)
In the instant case no attempt was made to assign a numerical figure to the probative value of the inferences which might be drawn from the statistical compilations. Moreover, the trier of fact was not asked to make a finding based on a mathematical theory of probability but merely to draw inferences from statistical facts derived from actual experience and observation. (3) The various statistical compilations by the CHP, when considered as a whole, were reasonably reliable as indicators of appellant's level of efficiency as compared to those of officers performing like duties under like circumstances. (1) The comparisons were made over a sufficiently extended period of time so as to eliminate the effect of any fluctuations due to transitory conditions; (2) the individual and members *782 of the group were performing comparable activities under comparable conditions; (3) the criteria used for comparison reflected the range of activities in which the individual and members of the group were engaged; and (4) the group with whom appellant was compared was sufficiently large and its members were selected on such a basis as would assure a fair representation of those performing like duties as appellant. The studies were competent and relevant on the issue of appellant's efficiency; their use was not subject to the strictures of People v. Collins, supra, 68 Cal.2d 319 [66 Cal. Rptr. 497, 438 P.2d 33].

II
Appellant argues that even assuming that the statistical compilations were properly received in evidence, they do not justify an inference that he failed to take enforcement action against violators he saw or should have seen. His argument is directed primarily at the data contained in Group II. He theorizes that the difference between his level of enforcement activity and that of the control group with whom he was compared is as explicable on the premise that officers in the control group were engaging in more enforcement activity than was warranted as on the assumption that appellant was lax.
At the hearing before respondent Board appellant urged that the differential between the level of appellant's enforcement activity and that of other officers was explainable on the theory that the other officers were overzealous in their enforcement activity. He charged that it was the policy of the CHP to encourage its personnel to engage in more enforcement activity than circumstances warranted. Had such policy or practice been shown to exist, it would have, of course, been clearly against the public interest and the use of statistical evidence derived from enforcement experience under such policy to support a disciplinary action for inefficiency could not be sanctioned. (4) But if such policy existed, the burden was on appellant to show it. In the absence of such a showing, we must presume it did not exist. There is a presumption that official duty has been regularly performed. (Evid. Code, § 664.) Appellant not only failed to produce evidence to support his charge as to the existence of such policy or practice, there was direct testimony that no such departmental policy existed. Members of the control group who were called as witnesses all testified to the nonexistence of such policy or practice. Appellant himself denied that he engaged in such practice during the training sessions, yet his level of enforcement activity while under supervision closely approximated that of the officers in the Anaheim area. That fact negated the existence of a general departmental policy of encouraging unwarranted and overzealous traffic law enforcement.
*783 (5) From the marked differential between appellant's level of enforcement activity and that of other officers as revealed by the data compiled by the CHP, coupled with the absence of such differential while appellant was under training supervision, it could be reasonably inferred that he was failing to take appropriate enforcement action while unsupervised.
Furthermore, in addition to the statistical data, the Board had before it other evidence bearing on appellant's efficiency. There was evidence that appellant's superiors had discussed with him his poor enforcement activity record on numerous occasions dating back as far as 1961 and that repeated efforts were made to improve appellant's performance through training programs. Appellant was placed on informal training status during the last half of 1965 and on formal training status in January 1966. On one occasion while discussing his performance with his superior, appellant admitted he showed "a poor day's work for the period covered, said that he would review his tolerance regarding law enforcement, and that he would get on the ball."
There was substantial evidence to support the Board's decision that the level of appellant's enforcement activity was so far below that of those officers performing like duties under like conditions as to justify a finding of inefficiency.

III
Appellant's final argument is that the low level of his traffic law enforcement activity does not support the fact that he was "inefficient" both because his job as traffic officer included performance of duties other than traffic law enforcement and because any attempt to measure his performance strictly in terms of the level of his enforcement activities failed to take into account the qualitative standard of his performance.
A public employer such as the CHP, like any private employer, has a legitimate interest in hiring and retaining employees who capably discharge their assigned duties efficiently. This interest is reflected by the fact that Government Code, section 19572, subdivision (c), makes inefficiency a ground for dismissing an employee.
General Policy Order 100.68 declares that while qualitative considerations cannot be ignored, "quality of enforcement without quantity is likewise not the best answer." The Commissioner of the CHP has determined that in order to maximize the CHP's potential for promoting highway safety, traffic law enforcement must be the overriding function of the highway patrolman and that any officer who fails in this important aspect of his job is not doing his duty in any meaningful sense. (6) Thus, under *784 departmental policy, if an officer's quantitative performance falls below minimum acceptable levels, his failing in this regard cannot be offset by the claim that the quality of such work as he does is superior. The departmental policy is not inherently unreasonable, particularly as applied to the facts of the present case.
Judgment affirmed.
Gardner, P.J., and Kaufman, J., concurred.
Appellant's petition for a hearing by the Supreme Court was denied April 14, 1971.

HEARING GRANTED
NOTES
[1]  Section 19572 of the Government Code provides in relevant part: "Each of the following constitutes cause for discipline of an employee, or person whose name appears on any employment list:...

"(c) Inefficiency."
