The New Boston Garden Corporation (Garden) appeals pursuant to G. L. c. 58A, § 13, from a decision of the Appellate Tax Board (board) with respect to real estate tax assessments on the North Station Terminal Building complex at 80-120 Causeway Street, Boston (premises), for the 1974 six-month transitional municipal fiscal period and for fiscal years 1975,1976, and 1977. The Board of Assessors of the city of Boston (city) cross appeals.
The Boston Garden is a roughly 88,000 square foot building which consists of the North Station railway terminal concourse area with related commercial space on the first floor, and the public arena commonly known as the Boston Garden. The arena is the home of the Boston Bruins, a National Hockey League franchise owned by the Garden. The arena is also the home of the Boston Celtics basketball team and the site of numerous family events, including the Ice Capades, concerts, and public gatherings.
In its petition to the board, the Garden alleged that the premises were overvalued and disproportionately assessed. The taxes in question were assessed on a property valuation of $3,848,000 and levied at an annual rate of $196.70 per thousand dollars of value for each relevant period with the *458exception of the 1977 fiscal year in which the tax rate was $252.90 per thousand. Taxes were thus assessed in the amount of $378,721.92 for the 1974 transitional period, $757,058.96 in each of 1975 and 1976, and $994,096.521 in 1977.
After a formal hearing pursuant to G. L. c. 58A, § 8, the board found that the fair cash value1 2 of the premises was $6,000,000 on each relevant date, and that the taxes should be assessed on a disproportionality ratio3 of 26.8% of the fair cash value, the ratio of assessment it found applicable to single-family dwellings (Class R-l). The board ordered abatements accordingly.
The Garden challenges the board’s findings of fair cash value and the disproportionality ratio as not supported by substantial evidence. The city challenges the board’s ruling that single family residences comprised the “lowest substantial class” of real property for purposes of determining the disproportionality ratio, as lacking subsidiary findings of fact, unsupported by the evidence, and contrary to law.
As we agree with the Garden’s contention that the issue raised by the city is not properly before the court for review, we dismiss the city’s cross appeal without considering the merits.4 The city has appealed only from the board’s *459April 3, 1980, denial of its November 28, 1979, motion to the board to alter or amend its July 6, 1979, decision in this case; and not from the July 6, 1979, decision itself. Even assuming that this appeal is from a “decision” of the board as permitted by G. L. c. 58A, § 13, an assumption not free from doubt, the city is precluded from raising issues on appeal that were not raised below. G. L. c. 58A, § 13. Beardsley v. Assessors of Foxborough, 369 Mass. 855, 856 n.3 (1976). The sole contention raised by the city at the hearing on its motion to alter or amend was that the board was required to apply the abatement procedure and classification system enacted by the Legislature in c. 797 of the Acts of 1979 (see G. L. c. 59, § 2A; G. L. c. 58A, § 14, inserted by St. 1979, c. 797, § 10), which limits the remedy available to a taxpayer whose property has been disproportionately assessed. To the extent that the city’s brief may be read as raising this issue now, we point to our recent decision in Keniston v. Assessors of Boston, 380 Mass. 888 (1980), that c. 797 may not constitutionally apply to taxes assessed for the years prior to fiscal 1980. We now turn to consider the issues raised by the Garden.
A. Fair Cash Value.
The Garden challenges the board’s finding of $6,000,000 as the fair cash value of the premises as not supported by substantial evidence. The Garden contends that by “sheer weight, comprehensiveness,” and “inherent reasonableness,” the record, including the city’s own evidence, cannot support a finding of fair cash value of $6,000,000. The Garden further contends that upon consideration of the record as a whole the overwhelming evidence requires a finding of fair cash value between $2,000,000 and $4,000,000. Thus, the Garden implicitly challenges the testimony of the city’s only witness, John Riley, which placed the fair cash value in excess of $5,000,000, as lacking in substantial probative force. In addition, the Garden contends that there was no substantial evidence supporting the board’s findings with regard to expenses attributable to the real estate, and its economic life. The Garden argues further that the board applied the wrong effective tax factor for fiscal year 1977.
*460We summarize the evidence and the findings of the board. The Garden presented its evidence through five witnesses. The first, Dale Braddock, is a civil engineer and consultant specializing in the design and construction of arenas and sports facilities. He was employed by the National Hockey League’s consulting engineer for arena design at the time of his testimony. He conducted a three-day “top to bottom” inspection of the Boston Garden. He concluded that the design of the arena did not meet modern design criteria and standards for a major league indoor sporting arena, including those criteria set by the National Hockey League. He characterized the arena as functionally obsolete.
Braddock further testified as follows. The fifty-year old building was in substantial disrepair due to age and extensive deferred maintenance. Although the basic structure of the arena was sound, there were several continuous maintenance problems requiring costly expenditures of the time of Garden personnel and of money. Due to design defects the roof leaked extensively. Also, due to design defects, ice removal from the hockey rink resulted in accumulation of water in cracks in the bottom structural slab and leakage into the North Station area. The heating system was inadequate, leaked continuously, and lacked available replacement parts. The electrical distribution system was inadequate and required extensive maintenance and use of personnel to keep it running. The arena seating was in poor condition and poorly designed. The ventilation system had not been properly maintained and lacked available replacement parts. Braddock predicted that the roof, the seating, and the heating, electrical, and ventilation systems would need replacement, requiring substantial capital expenditures. He also testified that storage, staging, and office space essential to the operation of the arena did not exist on the premises. Such facilities were leased in a neighboring building connected by a ramp. Later testimony revealed that this lease was to expire in 1986. Braddock’s testimony was unrebutted. Moreover, it was substantially corroborated by other witnesses. A written report of Braddock’s inspection was introduced in evidence.
*461The Garden also presented evidence through two witnesses of the circumstances surrounding three prior sales of the subject property. The witnesses, Charles Mulcahy, the executive vice president, clerk, and director of the Boston Garden Arena Corporation, and Mr. Richard Heath, a tax and corporation attorney, were participants in these sales.
The first transfer was a May 25, 1973, sale of the premises by its lessor to its lessee for $4,000,000. The lessee, the Boston Garden Arena Corporation (corporation), through a subsidiary corporation, then owned the Boston Bruins National Hockey League franchise as well as all the Bruins players’ contracts and the television rights to Bruins games. At the time of the sale there had been serious discussions among the Boston Redevelopment Authority (BRA) and the city of Boston, and certain private parties, including the owner of the Whalers, a new World Hockey Association franchise, with regard to building a new arena in Boston. Under the terms of its lease the corporation was prohibited from participating in any discussions or plans involving the construction of a new sports arena in Boston. Moreover, the Bruins were bound under the lease, which did not expire until 1986, to play all home games in the Boston Garden. The corporation feared that if a new arena were built, all the other teams and events would leave the Boston Garden, isolating the Bruins. Eager to participate in the development of the arena, the corporation was designated by the BRA in 1972 as a developer of the new arena subject to the condition that it obtain a release from the lease restrictions. These factors motivated the corporation’s 1973 purchase of the subject property.
The second transaction, which took place in August, 1973, was a stock transfer for approximately $7,000,000 of the subject property, as well as the Boston Bruins, which included the National Hockey League franchise, television rights and player contracts. The purchaser, then a subsidiary of the Storer Broadcasting Company (Storer), is the appellant in this action. In September, 1975, Storer, in a stock transfer including the same assets, sold the New *462Boston Garden Corporation to the LMJ Corporation, also for $7,000,000.
Mr. Heath testified that the 1975 sale was originally negotiated and agreed upon as an asset sale. The sale was renegotiated as a stock transfer only for Federal tax purposes. Under the asset agreement which was executed on August 27, 1975, but never carried out, $5,000,000 was assigned as the value of the Boston Bruins. The land under Boston Garden was assigned a value of $500,000, and the value of the building was to be computed by a formula based upon the 1974 and 1975 balance sheets of the Garden. Mr. Heath testified that his computations under the contract formula resulted in a value of the building as of September 30, 1975, of $2,220,000, and that a final value under the contract of the premises, including the land and the building, would range between $2,500,000 and $2,800,000. A copy of the executed purchase and sale agreement and written documentation of the other transfers were made part of the record below.
Finally, the Garden presented evidence through two independent real estate appraisers, David Carey and Richard Dennis. Each appraiser independently examined the subject property and the Garden’s financial records of ownership and consulted with the Garden’s financial and operational personnel. They also reviewed literature published within the arena management industry and examined the facilities and interviewed the owners and operators of arenas in Chicago, Cleveland, Detroit, Montreal, and St. Louis — facilities comparable to the Boston Garden in terms of age, design, urban location, private ownership, rental use by similar professional indoor athletic teams, circuses, ice shows, rock concerts, and other like entertainments. Each appraiser used and relied in part on both the “market data” and “capitalization of income” methods to determine the value of the premises. Each appraiser submitted a detailed written report which was made part of the record below. Both appraisers substantially corroborated Braddock’s testimony regarding the physical condition of the Boston Garden.
*463Dennis relied primarily on the market data approach. He considered the 1973 sale and the 1973 and 1975 stock transfers as persuasive market data from which the price set by willing buyers and sellers could be ascertained. In addition, he considered a 1977 sale of the St. Louis Arena, the only sale of a comparable property within the relevant time frame in what Dennis characterized as a national or international market for old urban arenas housing National Hockey League teams.
Dennis made a detailed inspection of the St. Louis Arena. Like the Boston Garden, it was built in 1928. The latter arena is located in the downtown section of St. Louis which has a metropolitan population comparable to that of Boston. An interstate route immediately passes the arena with interchanges within a thousand feet. It also fronts on a public way with access from the downtown area. It has 18,000 seats to the Boston Garden’s 15,500. It houses a National Hockey League team and other identical events housed by the Boston Garden.
Included in the St. Louis sale was an adjacent 86,000 square foot exhibition building and 2,500 on-site parking spaces. In the four years prior to the sale more than $8,000,000 was spent to refurbish the arena. Refurbishments included modern escalators, seating, new concession booths, new public toilets, sky-boxes, and modern scoreboard facilities. The mechanical and electrical systems were completely refurbished. Unlike the Boston Garden, the arena meets modern design standards in many respects. The St. Louis property was sold for $4,150,000. Dennis testified that his analysis of the St. Louis property, which he characterized as “far superior” to the subject property, resulted in a market indicator of $2,150,000 as the value of the subject property. He concluded over-all, based upon the four considered transactions, that the value of the subject property was $2,500,000 on each of the relevant dates.
Carey, in contrast to Dennis, did not rely primarily on the market data approach. It was his opinion that he could not derive a precise value from the prior sales because of the *464multiplicity of interests involved in those sales. Nevertheless, he testified that his analysis of the same four sales considered by Dennis resulted in a market value indicator in the range from $2,000,000 to $3,000,000. His valuation based upon the comparable sale of the St. Louis Arena was $2,500,000, although he indicated during cross-examination that this was probably a high figure.
Because he could derive no precise value figure from the market data, Carey relied primarily on the capitalization of income method. He analyzed the income and expenses of the Garden allocable to ownership of the real estate to derive net income figures for each of the relevant time periods. He used a total capitalization rate of approximately 26%, consisting of the sum of a 10.85% return of investment rate, a 2% risk factor, a 7.5% recapture of investment rate based upon an economic life of ten years, and a tax factor of 6.04% which was derived as the product of a tax rate of $196.70 per thousand and an assessment ratio of 30.72%. Application of the capitalization rate to the net income figures resulted in fair cash values which declined from $3,250,000 for fiscal years 1974-1975 to $2,800,000 for fiscal year 1977. Using a similar methodology, Dennis applied a total capitalization rate of 23% to slightly higher net income figures resulting in a declining value from $4,028,000 to $3,416,000.5
The city presented its evidence through the testimony of a single witness, John Riley, a career real estate assessor employed in the city’s assessing department. Riley, relying solely on the capitalization of income method, found a value ascending from $5,200,000 for fiscal years 1974-1975 and 1976, to $5,300,000 for fiscal year 1977.6
In finding a fair cash value of $6,000,000, the board “did not give much weight” to the prior sales of the subject property*4657 or to the sale of the St. Louis Arena.8 Rather, it relied primarily on the capitalization of income approach. In applying the capitalization of income method, the board adopted Carey’s analysis for fiscal 1974-1975 with certain adjustments. The board accepted Carey’s gross income of $2,396,000 as being “fair and reasonable.” However, the board thought his expense figure of $1,548,000 was “somewhat high,” especially its salary component. The board allowed $1,136,000 for expenses, yielding a net income of $1,260,000. The board also thought Carey’s capitalization rate of 26% was somewhat high. The board allowed Carey’s return of investment rate of 10.85 %. The board reduced the recapture rate to 5 % based upon an economic life of twenty years, and did not allow the 2% risk factor. Finally, the board used a tax factor of 5.27 % arrived at by multiplying the tax rate of $196.70 per thousand by an assessment ratio of 26.8%, resulting in a total capitalization rate of 21 % .9
1. The Substantial Evidence Test.
Although it is well established that decisions of the board must be supported by substantial evidence, Pequot Assocs. v. Assessors of Salem, 376 Mass. 270, 274-277 (1978), New Bedford Gas & Edison Light Co. v. Assessors of Dartmouth, *466368 Mass. 745, 749 (1975), and cases cited, this standard is not susceptible of a simple definition. We have frequently stated that substantial evidence is “such evidence as a reasonable mind might accept as adequate to support a conclusion.” See, e.g., Boston Edison Co. v. Selectmen of Concord, 355 Mass. 79, 92 (1968), quoting from G. L. c. 30A, § 1. Under this standard we are required to decide “whether experience permits the reasoning mind to make the finding; [i.e.,] whether the finding could have been made by reference to the logic of experience.” Id., quoting from L.L. Jaffe, Judicial Control of Administrative Action 598 (1965). A finding of the board must be set aside if “the evidence points to no felt or appreciable probability of the conclusion or points to an overwhelming probability of the contrary.” Id. Significantly, we are not required to affirm the board merely on a finding that the record contains evidence from which a rational mind might draw the desired inference. Our determination must be made “upon consideration of the entire record.” Cohen v. Board of Registration in Pharmacy, 350 Mass. 246, 253 (1966), quoting from G. L. c. 30A, § 14 (8) (State Administrative Procedure Act). L.L. Jaffe, supra at 600-602. 4 K.C. Davis, Administrative Law 127 (1958). “The substantiality of evidence must take into account whatever in the record fairly detracts from its weight.” Cohen, supra, quoting from Universal Camera Corp. v. NLRB, 340 U.S. 474, 488 (1951). L.L. Jaffe, supra at 602. W.B. Leach & P.J. Liacos, Massachusetts Evidence 330 (4th ed. 1967). See also Arthurs v. Board of Registration in Medicine, ante 299, 304 (1981).
The Garden contends that the city’s own evidence placed the fair cash value of the subject property at no more than $5,300,000, and thus concludes that the board’s finding of a value beyond the range of the expert testimony is therefore not supported by substantial evidence. See 6 Nichols, Eminent Domain § 26.731, at [26-557]-[26-579] (rev. 3d ed. 1980); Commonwealth v. Milby-Farmer, Inc., 494 S.W.2d 88 (Ky. 1973); Montana v. Emery, 156 Mont. 507, 509 *467(1971); Camp Bel-Aire, Inc. v. State of N.Y., 34 App. Div. 2d 867 (N.Y. 1970). However, the cited authorities stand for the proposition that “[a] total award and its various components must be within the range of expert testimony or supported by other evidence and sufficiently explained by the court” (emphasis added), Camp Bel-Aire, Inc. v. State of N.Y., supra, citing In re City of N.Y. [A & W Realty Corp.], 1 N.Y. 2d 428 (1956), and Spyros v. State of N.Y., 25 App. Div. 2d 696 (N.Y. 1966). Thus, the board is not strictly confined to the range of the testimony with regard to total value. By selecting higher range components of value from the testimony, the board could find a total value supported by the evidence that is outside the range of the testimony. This is consistent with the requirement that the board must base its findings and conclusions on the substantial evidence as supported by the record. The board must “find supporting subsidiary facts and must set forth reasons for its conclusion.” Assessors of Lynnfield v. New England Oyster House, Inc., 362 Mass. 696, 700 (1972). We have not in the past required the board to specify the precise manner in which it determined the fair cash value of the subject property. See id.; Jordan Marsh Co. v. Assessors of Malden, 359 Mass. 106, 110 (1971). Even assuming that greater specificity is required in a case such as this where the board’s determination of value is outside the range of the testimony, we believe that in this case the board has been adequately specific in this regard for us to meaningfully perform our appellate function.
2. Substantiality of the City’s Evidence.
Under the substantial evidence test, a reviewing court may undertake a strictly limited review of the credibility of witnesses. Although we must meticulously avoid weighing the evidence, testimony that cannot reasonably form the basis of impartial, reasoned judgment may be discredited; e.g., testimony that “carries its own death wound,” NLRB v. Pittsburgh S.S. Co., 337 U.S. 656, 660 (1949), or supporting testimony that is robbed of persuasive substance by other testimony, not itself directly contradicted, which *468logically impairs the supporting testimony. L.L. Jaffe, supra at 605-607.
In this regard we conclude that Riley’s testimony, which places the fair cash value of the subject property in excess of $5,000,000, is substantially lacking in probative force. Riley computed net income from a gross income figure of less than $700,000 and an expense figure of $130,000. These figures reflect the income and expense experience of the Boston Garden for years prior to the tax years in question at a time when the Boston Garden was under different ownership and was, according to the unrebutted testimony of other witnesses, run under an entirely different system. Riley made no adjustments of these figures for inflation or for any other purpose. These figures attribute no expenses whatever to the arena area. He conceded that he had no familiarity with the income or expense experience of comparable arenas and that he did not consult arena management industry literature. He used separate capitalization rates for the concourse area (30%) and the arena area (10%) of the subject property. He was unable to identify any considerations upon which the rates were based. He used no tax factor in computing the value of the arena area. He gave no consideration to mortgage financing rates or rates of return on equity investment. He did not know at what level mortgage lending rates were in Boston during the period in question. Unrebutted testimony placed them at an all-time high in 1974. His 10% capitalization rate for the arena, based in part upon an economic life of thirty years, assumed that a reasonable investor would seek only a 6.6% return on investment, despite the evidence placing mortgage lending rates at an all-time high. In choosing an economic life of thirty years, he apparently disregarded the condition of the premises and the prospect that a new arena would be built in Boston. He was unaware that the Boston Garden Arena Corporation had been designated as a joint developer for the proposed new arena. The board thought Riley’s income and expense figures and his capitalization rate of 10% were low and therefore disregarded them.
*4693. Substantiality of the Garden’s Evidence.
The Garden places much reliance for its position on the disregarded evidence of the prior sales of the subject property. We have observed in the past that “[ajctual sales are . . . very strong evidence of fair market value, for they represent what a buyer has been willing to pay to a seller for a particular property.” First Nat’l Stores, Inc. v. Assessors of Somerville, 358 Mass. 554, 560 (1971). However, the city correctly argues that the evidentiary value of such sales in less than arm’s-length transactions is diminished. Jordan Marsh Co. v. Assessors of Malden, 359 Mass. 106,108 (1971). We conclude that the board could properly find that the three prior transactions were not at arm’s length and hence had limited relevance to establishing fair market value.
The city correctly argues that the board is “not required to believe the testimony of any particular witness,” Assessors of Quincy v. Boston Consol. Gas Co., 309 Mass. 60, 72 (1941), and is not required to adopt any particular method of valuation that may have been urged by appellant’s expert witnesses, see Assessors of Lynnfield v. New England Oyster House, Inc., 362 Mass. 696, 701-702 (1972). Assessors of Nahant v. Costin, 356 Mass. 726, 726 (1969). Thus, the rejection by the board of the evidence of prior sales does not, by itself, constitute error. Similarly, the board properly could decline to use evidence of comparable sales, albeit relevant, as a basis of determining fair market value. The board did so in this case, choosing instead to use the “income capitalization method.” Nevertheless, since we must, for other reasons, remand this case for further findings, we consider briefly the board’s rejection of the St. Louis sale as not being “comparable.”
The board’s conclusion, that the premises and the St. Louis arena are not comparable, is not supported in the record. The unrebutted testimony of both appraisers was that the St. Louis Arena, although far superior to the Boston Garden in many respects, was nevertheless sufficiently comparable to establish an indicator of market value of the premises.
*470The city argues that Dennis’s appraisal report, which showed substantial differences between the two arenas, supports the board’s conclusion that the arenas are not comparable, i.e., out of sixteen factors compared, only three were substantially the same in both facilities. However, Dennis testified that these were not the factors that established the comparability of the two arenas. The comparability depends on “fundamental similarities”; in this case: identical age, urban location, housing National Hockey League franchise, approximately similar capacity, similar concourses and general seating arrangement, having concession stands, and being the principal place for other similar entertainment events. That is, basic comparability is established upon considering the general character of the properties. Once basic comparability is established, it is then necessary to make adjustments for the differences, looking primarily to the relative quality of the properties, to develop a market indicator of value.
Of the sixteen factors considered by Dennis, the Boston Garden was superior only with regard to access by public transportation due to proximity with North Station. Private vehicle access was one of the three similar factors. The St. Louis Arena was superior with regard to the remaining twelve factors.10
Unrebutted testimony also established that the appropriate market to consider in looking for comparable sales of National Hockey League arenas is a national, rather than local, market. There is thus no basis for the board’s conclusion that the properties are not comparable due to the distance between them.
In sum, unrebutted and corroborated testimony establishes that the two arenas are comparable for the purpose of valuating the subject property. The board may not reject this testimony without a basis for such rejection in the record. “[Ejvidence of a party having the burden of proof may not be disbelieved without an explicit and objectively ade*471quate reason.” L.L. Jaffe, supra at 607. “If the proponent has presented the best available evidence, which is logically adequate, and is neither contradicted nor improbable, it must be credited . . . .” Id. at 608.
Although the board is not required to rely primarily on the particular testimony or to adopt this particular method of valuation to arrive at a precise value figure, the evidence of this sale, as well as the other market data evidence, precludes a reasoned finding, in the absence of affirmative evidence to the contrary, that it was not relevant to the value of the premises.
We turn now to consider the Garden’s contentions that there was no credible evidence to support the board’s determination of fair market value based solely on expenses and capitalization rate.
Expenses. The Garden’s experts provided expense figures for the' years in question, ranging from $1,503,700 to $1,787,000. The board’s finding that expenses were $1,136,000 was outside the range of this testimony. We agree with the Garden’s contention that there was no substantial evidence to support the board’s finding that the experts’ expense figures were “somewhat high especially the expenses for salaries.” The Garden’s appraisers testified to the actual expenses incurred by the Garden during the years in question. Both experts testified that the expenses they allocated to the premises were consistent in character and magnitude with the expenses incurred by owners of comparable arenas and with the expenses incurred by the lessee of the premises under the lease in effect prior to the 1973 sale of the property. We note that although the total expense figures provided by the two appraisers differ due to a difference in methodology — Dennis’s expense figures are consistently about $50,000 lower than Carey’s — their figures for the salary components of expenses are identical. The “high” expense figure is further corroborated by the testimony of Braddock, as well as the two appraisers, that physical deficiencies in the premises cause continuing extraordinary maintenance and operating costs, both as to equipment and personnel.
*472The city argues that the board is not required to itemize each expense it disallows or the specific elements of the numerical capitalization rate found. See Assessors of Lynnfield v. New England Oyster House, Inc., 362 Mass. 696, 700 (1972). We agree. Nevertheless, such findings must be supported by the record. Noting in Assessors of Lynnfield that “the quality of the board’s decision could have been improved by more specific findings on the various elements which it accepted in arriving at its conclusion,” id., we nevertheless upheld the board where, unlike here, its determination of value was supported by the evidence of record. In that case the board rejected as too high the repair and maintenance allowance selected by the assessors’ expert. We upheld the finding because it was “not, when considered with all the evidence, inconsistent with the general finding of value reached by the board” (emphasis added). Id. at 700-701.
Contrary to the city’s contention, we find no affirmative evidence on which the board could base its subsidiary finding of annual expenses of $1,136,000. The city relies upon the fact that the Garden’s ownership of the Bruins and related interests required an allocation of expenses to the ownership of the subject property, and the appraisers accepted as fair and reasonable the Garden’s own allocations as found on its books. However, these factors do not make that evidence inherently untrustworthy. Indeed, by accepting Carey’s similarly derived income figure, the board, contrary to the city’s contention, has apparently accepted the appraiser’s methodology as sound. In any event, disbelief of any particular evidence does not constitute substantial evidence to the contrary. Salisbury Water Supply Co. v. Department of Pub. Utils., 344 Mass. 716, 721 (1962). W.B. Leach & P.J. Liacos, supra at 330.
The city argues further that in the face of conflicting testimony about the amount of expenses incurred, the board acted properly within its discretion to make an independent factual determination; that where the expenses attributable to the subject property were based upon estimates and al*473lowances, the board is not required to accept the opinions or the calculations of any expert witness, but could apply its experience and judgment to determine the amount of expenses. Assessors of Nahant v. Costin, 356 Mass. 726, 727 (1969). Assessors of Lynnfield v. New England Oyster House, Inc., supra at 700. However, in Assessors of Nahant and Assessors of Lynnfield “[t]he board’s conclusion was based upon adequate subsidiary findings which in turn were supported by substantial evidence.” 356 Mass, at 727. In Assessors of Quincy v. Boston Consol. Gas Co., 309 Mass. 60, 72 (1941), we declared: “[T]he conclusion reached by the board . . . did not coincide with the figure given by any witness, but it does not follow . . . that this conclusion was, therefore, unsupported by the evidence. The board was not required to believe the testimony of any particular witness but it could accept such portions of the evidence as appeared to have the more convincing weight. The market value of the property could not be proved with mathematical certainty and must ultimately rest in the realm of opinion, estimate and judgment. . . . The board could select the various elements of value as shown by the record and from them form, as it properly did, its own independent judgment.” (Emphasis added, citations omitted.) The essential requirement is that the board exercise judgment. The Garden has presented logically adequate and uncontradicted evidence of expense. The board must have a rational articulable basis in the evidence for finding expenses to be substantially less than the evidence has shown them to be. Cf. Assessors of Lynn v. Shop-Lease Co., 364 Mass. 569, 574 (1974); L.L. Jaffe, supra at 608. We find no such basis in the evidence to support the board’s conclusion.
Capitalization rate. The Garden contends that the board’s selection of a recapture of investment rate of 5% based upon an economic life of twenty years is not supported by substantial evidence. We agree.
There was unrebutted evidence that the subject property is fifty years old, badly deteriorated, and functionally obsolete in its principal use. Proposals for development of a new *474arena had been made by private investors and backed by local government agencies. Indeed the city concedes as much in its brief. In arguing that the evidence of the 1973 sale of the Garden was irrelevant to fair cash value the city states: “[There] was the risk in continuing ownership of the Garden complex at a time when there were active negotiations by its tenant, the Boston Celtic basketball team, and others, to develop a new indoor sports arena. ... In the event that [such] a development . . . were successful, the sellers could anticipate many of its tenants, such as the Celtics, the circus, the Ice Follies and others not subject to the same restrictive lease provisions as the Bruins, would almost certainly stage their entertainment events in the new facility. . . . Such an eventuality would severely reduce its income, and presented a current business risk of some magnitude. Indeed, ‘these prospects were a looming catastrophe for these owners.’”11
The storage, staging, and office facilities lease for the adjacent property was to expire in 1986. Unrebutted testimony indicated that purchasers and potential purchasers looked upon the premises not as a long-term investment in income-producing property but as an asset which had to be bought in order to acquire a successful ice hockey team or a profitable concession operation. Indeed, the property was characterized by the various witnesses as a candy box you *475must pay for in order to buy some candy. Alluding to these factors, the Garden’s two appraisers assigned a maximum period of ten years for the economic life of the subject property. Riley, in contrast, used an economic life of thirty years. This figure was neither explained by Riley, nor corroborated by other evidence. A finding “must be set aside ‘when the record . . . clearly precludes the Board’s decision from being justified by a fair estimate of the worth of the testimony of witnesses.’” L.L. Jaffe, supra at 607, quoting from Universal Camera Corp. v. NLRB, 340 U.S. 474, 490 (1951). We have already discussed the improbable character of much of Riley’s testimony in this case relevant to his selection of capitalization rate. In the light of that testimony and the testimony of the other witnesses on this point, we do not believe that a reasoning decisionmaker could rely on Riley’s unexplained and uncorroborated testimony to broaden the range of the expert testimony as to economic life and rate of recapture of investment.
Tax factor. The board’s tax factor of 5.27% was arrived at by multiplying the tax rate of $196.70 per thousand by the assessment ratio of 26.8%. However, the board found for fiscal year 1977 that the real estate taxes were assessed at a rate of $252.90, not $196.70. Thus, the correct effective tax rate is reached by multiplying $252.90 by 26.8%. See Assessors of Lynn v. Shop-Lease Co., 364 Mass. 569, 572-573 (1974). The finding of value for fiscal 1977 must therefore be adjusted accordingly.
B. Disproportionality Ratio.
The Garden contends that there is no affirmative evidence to support the board’s finding of 26.8 % as the ratio of assessed value to fair cash value for the lowest substantial class of real estate (single-family residences). We disagree.
The city entered in evidence a study written by its expert statistician which criticized the methodology relied upon by the Garden to establish a disproportionality ratio of 23%, and which concluded that this ratio was too low. The report *476observed that the State “1976 Equalization Study” indicates a disproportionality ratio of 26.8%. Although the report also criticizes this figure as too low, and although the report itself did not stand up well on cross-examination, we observe that none of the figures urged by the parties went unscathed on the record. The “1976 Equalization Study” is a Statewide study of disproportionality ratios for each city and town prepared by the State Tax Commission (now the Commissioner of Revenue) pursuant to G. L. c. 58, § 10C. In view of the experience and expertise of the commission, and the fact that the study was prepared by the commission in the performance of its official duties, the board could properly give weight to this evidence. We are unpersuaded by the Garden’s contention that it was deprived an adequate opportunity to dispute the accuracy of the State report.
Conclusion. The decision of the board is reversed, and the case is remanded for further proceedings in accordance with this opinion. The city’s appeal is dismissed. The taxpayer is to have the costs of both appeals.
So ordered.
Justice Kaplan participated in the deliberations on this case, but retired before the opinion was issued.
*477APPENDIX A
EXPERT DATA: CAPITALIZATION OF INCOME
I. INCOME and EXPENSES
Carey
Fiscal Fiscal Fiscal
1974-1975 1976 1977
Effective Gross Income $2,396,000. $2,587,000. $2,550,000.
Expenses 1,548,000. 1,787,000. 1,782,000.
Net Operating Income 848,000. 800,000. 768,000.
Dennis
Effective Gross Income $2,492,300. $2,687,200. $2,643,800.
Expenses 1,503,700. 1,730,700. 1,709,700.
Net Operating Income 988,600. 956,500. 934,100.
Reserves 66,000. 78,000. 94,000.
Net Operating Income* 922,600. 878,500. 840,100.
Riley
Arena Concourse
Effective Gross Income $453,470. $336,487.
Expenses 0 130,000.
Net Operating Income* 453,470. + 206,487.
$659,957
Board
Effective Gross Income .$2,396,000.
Expenses 1,136,000.
Net Operating Income* 1,260,000.
*478II. CAPITALIZATION RATE
New Boston
Garden Corp. City Board
(Carey) (Dennis) Arena Concourse
Investment
Band Mortgage Lease
Method Method Method
Return of Investment 10.85% i- n 6.7%-10.85%
Risk 2.0% 17%
Recapture of Investment 7.5% - 3.3% 5.0%
Life Expectancy (yrs) (10) (10) (30) (20)
Tax Factor 6.04% 6.04% 5.27%
Capitalization Rate 26 % 23% 10% 30% 21 %
VALUE $3,250,000* $3,750,000) $5,200,000† $6,000,000)
*479APPENDIX B
Item Boston Garden St. Louis Arena Comparison
Capacity 14,700 18,000 (Z>
Obstructed Views 1,400 + 100 (Z>
Vertical Trans-No escalator & Two modern escaC/D
port two poor elevators lators reaching
the two upper
tiers
Clubs & Res-Garden Club — Dome Club — S
taurants 300 seats 750 seats
Goal Tender’s —
100 seats
Parking Owned & None 2,500 S
Controlled
Offices — Admin. Administration — 2 3-Story Towers S
& Admin. Club none (leased at of Offices; one for
150 Causeway) Admin, and one
Club — extremely for the Blues, fur-
limited nishings and fix-
tures all done in
Early ’70’s
Land Area 38,000 s.f./2 Acres 7 Acres + S
Staging & Ex-None — leased at 80,000 s.f. Builds
hibition Space 150 Causeway St. ing on same site
— remote immediately adja-
cent to Arena
Heating System Edison Steam, Oil Fired oil syss
Very Poor tem in good
Condition condition — low
utility bills
Air conditioning None None o
Ice Plant Modern and new Modern and New o
Ice Surface Suspended on Built on unexcas
Steel supported vated solid land
concrete slab over — no leak prob-
RR concourse lems — Meets NHL
with leakage size standards
problems and attendant maintenance cost and problems — Rink size is below NHL standards
*480Access/Egress
Public Trans.
Private Vehicle Access
Concession
Stations
Patron access is above street levels and first interior levels are below all seats
Good access to MBTA
Good
12 — Fair
condition
Patrons enter at concourse level with 2 seating tiers below and 2 above/consistent with modern arena design
Surface — buses
Good
15 — Good
condition
S
I
O
s
0 = No difference
S = St. Louis Arena Superior
1 = St. Louis Arena Inferior
The figure, found by the board, includes a water charge of approximately $20,000.
Fair cash value or fair market value is “the price an owner willing but not under compulsion to sell ought to receive from one willing but not under compulsion to buy.” Boston Gas Co. v. Assessors of Boston, 334 Mass. 549, 566 (1956).
“Under our decisions ‘a taxpayer has a right to have his assessment reduced so that it is “proportional to the assessments of the class of property valued at the lowest percentage of fair cash value.” ’ ” Tregor v. Assessors of Boston, 377 Mass. 602, 602, cert, denied, 444 U.S. 841 (1979), quoting from Assessors of Weymouth v. Curtis, 375 Mass. 493, 501 (1978), quoting from Shoppers’ World, Inc. v. Assessors of Framingham, 348 Mass. 366, 377-378 n.10 (1965).
The issue as to whether single-family residences comprise the “lowest substantial class” of real property was properly before us in French v. Assessors of Boston, post 481 (1981), decided this day. In that case we uphold the board’s finding that single-family residences comprise such a class.
See Appendix A.
See Appendix A.
With regard to the prior sales, the board found:
“The board did not give much weight to these sales. The first sale of the subject property was influenced by other motives including a buyer who wanted to get out of a restrictive lease and a seller with a long-term lease with only partial reimbursement for real estate taxes. There was some duress involved in this sale and it does not appear to be an arms-length transaction. The other two sales were stock transfers and business interests were intermingled with the sale of the real estate.”
With regard to the sale of the St. Louis Arena, the board found: “This arena was also built in 1928 like the subject property. Substantial improvements have been made to this arena. The access to public transportation of the subject property was superior to this arena, however. There were many other differences between the two structures including land area, seat capacity and so forth, and because of these many differences and the distance from the subject property, the board did not consider it very comparable and did not give it much weight.”
See Appendix A.
See chart reproduced as Appendix B.
Although the Garden raises no express objection to the board’s rejection of Carey’s addition of a 2 % risk factor to the capitalization rate, and although Dennis did not add such a factor, this rejection is, in light of the record, somewhat questionable. Indeed, “[t]he requirement of substantial evidence ... is an attempt to guarantee that the law rather than the will of the factfinder is the measure of judgment.” L.L. Jaffe, Judicial Control of Administrative Action 599 (1965). The purpose of our review is “to limit the opportunity for transmuting a preconception into judgment by picking and choosing what will support that preconception and willfully ignoring whatever weighs against it” (emphasis in original). Id. at 607. If the decisionmaker “ignores all the evidence [favorable to] one side in a controversy and with studied design gives credence to the testimony [favorable to] the other side, the findings would be arbitrary and not in accord with the legal requirement.” Id., quoting from NLRB v. A. Sartorius & Co., 140 F.2d 203, 205 (2d Cir. 1944).
Before taxes and debt service.
Derived from fiscal 1975 income, this appraiser’s highest valuation.
Value applicable to each year.