This is an appeal from an order of the district court made in a proceeding to review, by writ of certiorari, an order of the compensation insurance board (hereinafter referred to as the board) fixing rates for compensation insurance premiums in Minnesota for the year beginning January 1, 1951. The district court affirmed the order of the board and discharged the writ of certiorari. Ap*470pellants represent Minnesota employers who are paying workmen’s compensation insurance premiums to companies writing this insurance in the state of Minnesota.
Appellants attack the order of the board directing an increase of 8.2 percent in the premium rate over the rate in effect in 1950 as arbitrary, oppressive, unreasonable, and without evidence in the record to support it.
To aid in understanding the problems presented by this case, we set out herewith a brief explanation of the rate-making process as it is carried out under the statutes. The board, created by M. S. A. 79.02, consists of the commissioner of insurance, one member of the industrial commission to be chosen by the commission, and a third person, versed in the subject of workmen’s compensation insurance and in the making of rates therefor, to be appointed by the governor. The board is authorized to approve a minimum and adequate and reasonable rate to provide for the solvency of insurers writing workmen’s compensation insurance and to secure reasonable rates. .§ 79.07. Every insurer transacting the business of workmen’s compensation insurance in the state is designated a member of the Minnesota compensation rating bureau organized under §§ 79.01 to 79.23. | 79.11. Among other things, it is the duty of the bureau to assist the board in the rate-making process. § 79.11. The National Council on Compensation Insurance is an organization of workmen’s compensation insurance carriers which acts as a central statistical and actuarial body making compilations of statistical data, performing computations, and evolving rating methods for use by rating organizations such as the bureau, which cooperates with it.
The workmen’s compensation rate must be high enough to provide the revenue necessary to cover the amount needed for the payment of workers’ claims and also to cover the expenses and provide a profit to the insurance carrier. The part of the rate to be used for the payment of claims is called the pure premium. The other part is called the expense loading. The board establishes a permissible loss ratio, which is expressed as the percentage of the total rate intended to provide the required pure premium. For many years, *471the permissible loss ratio has been set at 61 percent. This allowed 39 percent of the total premium to cover the expenses of the insurance companies. By using the insurance experience of premiums collected and losses incurred over the two most recently completed policy years,2 adjusted by certain factors to bring the experience up to date, the board reaches an expected loss ratio. If the expected loss ratio on the basis of the adjusted past experience differs from the permissible loss ratio established by the board, the rate schedule is revised upward or downward to eliminate the difference.
On September 29, 1950, the bureau filed a proposal with the board for the revision of rates providing for a 10.6 percent increase in the then existing rate. This was the substance of the recommendations made to the bureau by the National Council. The board held a public hearing on October 25, 1950, in which all interested persons, including appellants, were allowed to participate. Appellant Minnesota Employers’ Association submitted a proposal for a reduction of 6.9 percent in rates. The Insurance Buyers Association submitted exhibits supporting a recommendation of 2.9 percent reduction. On November 22, 1950, the board issued the order authorizing an increase of 8.2 percent.
Since 1933, the permissible loss ratio has been set by the board at 61 percent. The figures, showing the loss ratio actually developed on the basis of the standard earned premium, indicate that the method of predicting the anticipated losses and premiums produces serious errors. In the calendar years 1915 to 1919, the loss ratio on the basis of the standard earned premium ranged from 55 percent to 50.5 percent and averaged 53.1 percent for that period. Had the prediction process been more accurate, the results would more closely approximate 61 percent. Appellants contend that according *472to their method of computation an excess premium of $9,676,451 has been paid in the years 1945 to 1949, because the board underestimated the expected premiums and overestimated the expected losses. To obtain this figure, appellants use the losses actually incurred to compute what standard earned premium would have produced a loss ratio of 61 percent. They then allow 39 percent of the standard earned premium thus computed as expenses. Appellants contend that premiums have been overpaid in this amount, even though the board in the past five years has consistently modified downward the rate proposal of the National Council and the bureau, as shown below.
The bureau’s proposal made prior to the order under review here was for a 10.6 percent increase, and the board granted an increase of 8.2 percent.
It will thus be seen that, although the board has consistently ordered a rate substantially lower than that proposed by the bureau, the actual loss ratio on the basis of standard earned premium has turned out lower than the permissible loss ratio.
Respondents criticize appellants’ computation of $9,676,451 as the amount of excess premium paid, by pointing out that appellants have used a combination of policy-year and calendar-year figures and that appellants have allowed, as expenses, 39 percent of a theoretical earned premium. Respondents maintain that the 39 percent for expenses should be figured on the standard earned premium, as developed by the rates actually in effect, in order to make the computation of excess premium realistic.
Respondents maintain that appellants’ figures do not present a realistic picture of the operation of the workmen’s compensation *473rating system. A large amount of money is returned to policyholders by way of refunds because of premium discounts and retrospective rating, as well as by dividends paid or credited to policyholders. They present figures to show that the loss ratios figured on the premiums actually retained by the insurance companies varied from 63.7 percent in 1945 to 64.4 percent in 1949 and averaged 61.7 percent for the five years. Their figures show an excess of standard earned premium of $5,080,436 over the expenses allowed by the expense ratio; but they also show that $2,539,763 was returned by way of “refunds due to premium discounts and retrospective rating” and that $6,428,994.85 was returned or credited to policyholders as dividends. With this background, we turn to the contentions of the parties.
Appellants contend that the board improperly used certain factors which are used in the rate-making formula to adjust the past experience. As mentioned above, the formula used attempts to predict the insurance experience for the following year by using the experience of previous years, adjusted by factors known to have changed since the experience was acquired. The change in wage levels was one of the changing conditions considered in the board’s computation. Since the premium rate is figured on each $100 of payroll, it will be seen that the increasing wage level will have the effect of increasing collectible premiums. The board used 1947 and 1948 as its basic experience policy years. It developed figures to show an average weekly wage of $53.13 for the policy year 1948 and $55.08 for the policy year 1949. It decided to add 3% percent to the 1949 weekly wage of $54.17, resulting in an average weekly wage of $56.07 for 1950.
The figures thus indicated that the 1950 wages would be 5.5 percent above 1948 and 1.8 percent above 1949. These figures were used to adjust the premium experience in the following manner:
*474
The hoard adjusted the premium experience for the policy year 1947 by the percentage of increase of 1950 wages over 1948, and the premium experience for policy year 1948 by the percentage of increase of 1950 wages over 1949. Appellants contend that the board should use wage factors corresponding to the year’s experience being adjusted and that use in the manner of the board is arbitrary and unreasonable. They argue that, had the wage factor been applied properly, all other considerations unchanged, the formula would have produced an increase in rate of 2.1 percent rather than the 8.2 percent increase ordered by the board. In answer to this contention, respondents, argue that the board applied the factor in the manner it did after careful deliberation and without mistake. They say that the application of the factor was an exercise of judgment and that the court cannot substitute its judgment for .that of the board.
Appellants contend that the medical cost factor used by the board to allow for changes in the cost of medical services is not supported by the evidence and is unreasonable. In computing the medical cost adjustment factor for the experience of policy year 1947, the board first looked to the medical factor used in the 1949 determination to adjust the experience of policy year 1946. The board then compared the percentage by which the 1950 wages exceeded the 1947 wages with the percentage by which the 1949 wages exceeded 1946 wages. This ratio was applied to the medical adjustment factor previously used, and the result was designated the new factor. The same method was used to determine the adjustment factor for the experience of 1948.
*475
Appellants argue that the application of the formula involves a determination by the board that medical expenses can be expected to bear a constant relation to wage levels and that this determination is without evidence to support it. Respondents answer that the record contains evidence to establish that expected medical costs have increased even beyond the increase allowed in the board’s computation.
Appellants also attack the method of application of the accident factor by the board. The purpose of the accident factor is to adjust the rates so as to reflect the trend, upward or downward, in the frequency and severity of accidents per hour of exposure. This trend has been steadily downward in recent years. The board adjusted the loss experience as follows:
The accident factor is computed by using statistics supplied by the National Safety Council. These figures indicate that in 1948 acci*476dent frequency on the average of all industries was 11.49 disabling injuries per 1,000,000 man hours. The 1948 accident severity figure shows the loss of 1.12 days per 1,000 man hours. To get its figure of .874, the board first added the frequency and severity figures, which produced a total of 12.61. This sum was then subtracted from 100 to get the figure 87.89, which divided by 100 gives the factor .874. The same process was used with the 1947 figures, which were 13.26 for frequency and 1.23 for severity. Appellants first question the propriety of adding the frequency and severity figures, and it is indeed difficult to understand the reasoning underlying the addition, unless it is thought that a crude adjustment will produce satisfactory results. Appellants contend that the proper way to apply the accident factor is to establish a ratio between the frequency and severity factors for the base experience years and frequency and severity factors for 1949, which are the most recent figures available. Adding the frequency figure of 10.14 and the severity figure of 1.02 for 1949, the result is 11.16. The total of these figures for 1947 is, 14.49, and for 1948 the total is 12.61. Using the ratio 11.16, the factor for 1947 is .770 and the ratio 11.16 14.49 12.61 produces a factor of .885 for 1948.
Changing only this element in the board’s formula, according to appellants’ contention, produces a result indicating an increase in the rate of about 3.8 percent instead of an increase of 8.2 percent, as ordered by the board. Respondents maintain that appellants’ formula is inaccurate, in that it applies the accident and frequency figures which are calendar-year figures to policy-year losses. They *477claim that the use of appellants’ formula would raise the rates even higher than those ordered by the board if the accident and severity figures were used so as to reflect a policy year rather than a calendar year.
Under the statute, the board is directed to set a minimum, adequate, and reasonable rate for workmen’s compensation insurance. The rates to be charged must be fixed in advance in order to operate under future conditions, which may vary considerably. The widely adopted formula used by the board attempts to do this by using experience developed in the past, adjusted by factors known to have changed. This formula divides the premium into two components, the pure premium and the expense loading. Whether the rate developed is reasonable can be ascertained by determining the reasonableness of the components. Mississippi River Fuel Corp. v. Federal Power Comm. 82 App. D. C. 208, 225, 163 F. (2d) 433, 450. Thus, assuming that the expense-loading factor is set at a proper figure, it is not difficult to say that the rate is unreasonable if it provides for a pure premium greatly in excess of the amount required to pay the claims. The difficulty is that the experience to be developed under the pure premium part of the rate is not available either when the rate is set or later, when it is reviewed.
The reasonableness of the expense-loading factor, here set at 41.5 percent (formerly 39 percent) of the standard earned premium, depends on whether such a loading factor provides revenue unduly larger than that required to meet expenses and provide a fair profit to the carrier. An examination of the biennial reports of the compensation insurance board for the past several years indicates that the expenses of the insurance companies in terms of the percentages of the standard earned premium do not tend to vary greatly from year to year. It would seem, therefore, that the difficulty in setting the ratio between pure premium and expenses is not due to the inability to foresee the effect of the rate, but in determining what is a reasonable profit and how it is to be computed.
If the experience developed under the rate were available, it would be a simple matter to pass upon its reasonableness. How*478ever, the board must set, and courts must pass upon, the rate without the advantage of knowing what will be the experience under the rate. There are many contingencies, for example, wage levels, employment levels, and costs of medical service, which affect the experience to be developed, and many of these are subject to wide fluctuations between the time the board sets the rate and the time it is in effect. The board is thus faced with the very difficult task of predicting the future trends of the various factors affecting the insurance experience, and it could well be that the most carefully considered rate formula would produce inaccurate results because of some unforeseeable change in economic conditions.
It can be seen from the foregoing that neither the board, at the time the rate was set, nor this court, at the present time, is in a position to state that the rate set will produce reasonable results— that the actual loss ratio will not differ substantially from the permissible loss ratio. It thus becomes the function of the board to use all sources of information and experience in a reasonable manner to set a rate which will produce results as close as possible to what is desired. It is the function of the court to review the action of the board in order to insure that the board adheres to methods logically calculated to produce a reasonable rate. Where it appears, as it does here, that the rates have been consistently inaccurate over a period of years, it is especially necessary that the methods adopted by the board be carefully scrutinized.
We regard as significant the fact that the actual loss ratio on the basis of standard earned premium deviates sharply from the permissible loss ratio. The formula is devised on the basis of standard earned premium, and it is on that basis that the accuracy of the rate set must be determined.
The basic formula itself seems well adapted for the purpose of fixing the rate, and none of the parties hereto questions its use. Appellants attack the methods used by the board to adjust the past experience for changes in the wage level, medical costs, and accident frequency and severity. We are convinced that from a mathematical standpoint the contentions of appellants are sound.
*479To fully adjust the premium experience for the wage increases up to 1950, it would seem that the premium experience for a given year should he adjusted by the degree of increase in 1950 over that year. Thus, the 1947 experience should be adjusted by the ratio of 1950 wages to 1947 wages, rather than by the ratio of 1950 to 1948 wages, as referred to above. The medical factor, as used by the board, contains at least two assumptions that are unsupported by any evidence or findings. The board’s calculation assumes, first, that the medical factor used at the previous hearing in 1949 was correct, and, second, that medical costs fluctuate in proportion to changes in wage levels. The formula used by the board to compute the accident frequency and severity factor does not in any reasonable manner utilize the information presented on the decrease in accident frequency and severity between the experience years and 1949, the latest year for which figures are available. A logical application of that information would be to establish a trend using the figures for the experience years and the latest figures available, somewhat as suggested by appellants. The board’s method completely fails to reflect the degree of change actually occurring between the experience year and the latest year.
As mentioned above, there is no certainty that mathematically sound adjustments would produce results more accurate than those used by the board. Indeed, a trend well developed in past experience might reverse itself completely so that the factor developed from the trend would help produce an inaccurate result. This possibility emphasizes the difficulty inherent in prospective rate making for workmen’s compensation, but does not free the board from the obligation to apply the adjustment factors in a logical manner.
We do not mean by the above observations that the board is required to use a mathematically precise formula to make the various adjustments. The board, in its discretion, may consider facts and circumstances which are not incorporated in the formula for the computation of a given adjustment factor, but which affect the adjustment. For example, the board may have reason to believe that economic conditions did not justify a full adjustment for the *480increase in wages in 1950 over 1947. Of course, the board is free to consider elements not directly incorporated in the formula; but, when doing so, the board must be required to state its reasons and the underlying facts so as to establish a chain of reasoning between the facts and the conclusion reached. When the board deviates from what appears to be a mathematically sound method of reaching the answer sought, it must explain the considerations and reasoning behind the deviation. Whether or not the board had a basis in reason for what was done cannot be left to speculation. Mississippi River Fuel Corp. v. Federal Power Comm. 82 App. D. C. 208, 163 F. (2d) 433. Otherwise, this court would be unable to review intelligently the rate orders, and the board, for all practical purposes, would be subject to no judicial restraint.
We disagree with the suggestion of respondents that the board would have been acting reasonably if it had accepted the bureau’s proposal in its entirety. The statutes impose upon the board the duty to set the rate. The bureau’s function is merely advisory. The board’s experience with the bureau proposals in the past would not justify complete acceptance, without an inquiry into whether the bureau had made corrections designed to eliminate the sources of error.
As can be seen from the above discussion of the three adjustment factors, the board’s order does not meet the test, and it will therefore be necessary for the board to reconsider the rate question in the light of this opinion.
Appellants also attack the reasonableness of the board’s action in incorporating the profit and contingency factor of 2.5 percent. This reduced the permissible loss ratio to 58.5 percent and provided 41.5 percent for expense loading, profit, and contingencies. The inclusion of this factor had the effect of raising the rate 4.3 percent. The board evidently decided that 41.5 percent was required to cover expenses and provide a reasonable profit. The board made no findings as to what it found the expense experience to be, nor the method by which it proposed to compute a reasonable profit.
*481Respondents argue that the record contains evidence that the figures for 1949 show that the basis for expense in workmen’s compensation was 40.2 percent. The record contains no explanation of the source nor the method of calculation nor any indication that the board accepted that figure as correct. The highest figure for expenses for workmen’s compensation for 1949 that appears in the tabulation in the fourteenth biennial report of the board is 37.66 percent. There was testimony in the record that the convention of National Association of Insurance Commissioners had approved of the profit and contingency factor, but this information, as it appears in the record, is very misleading. It appears that the National Association had recognized the propriety of a profit-and-contingency factor, but had appointed a subcommittee to submit recommendations as to what that specific factor should be. This subcommittee submitted a report to the workmen’s compensation committee of the association recommending a factor of 1.5 percent. This report was adopted by the workmen’s compensation committee, but when the subject came before the full session the National Association voted to delete that part of the committee report relating to the profit and contingency factor and to discharge the subcommittee from further consideration of that subject. See, Annual Report of National Council on Compensation Insurance, March 6, 1952, p. 15.
It is obvious that in order to set a reasonable rate by the present basic formula it is essential that the ratio of pure premium to expense loading and profit-and-contingency be set at a reasonable figure. This ratio is not made reasonable merely because the board orders it or the bureau proposes it. Such a ratio can be established only after appropriate findings on expense requirements and what constitutes a reasonable profit. This defect in the board’s order must be corrected on remand.
The order of the district court affirming the order of the board is reversed with directions to remand to the board for further proceedings in conformity with this opinion.