In this appeal we must review the valuation of the real property of a golf course country club for the purpose of municipal taxation. The owner of the real property (club or club facilities) is Black Rock Golf Club, LLC (Black Rock). The board of assessors of the town of Hingham (assessors) valued the club at $20 million for fiscal year 2006 and at $18.6 million for fiscal year 2007.1 Those values resulted in tax bills of $186,760 and $169,911, respectively. In both years Black Rock filed an application for abatement. The assessors denied both applications. Black Rock appealed to the Appellate Tax Board (board). See G. L. c. 58A, § 7; G. L. c. 59, §§ 64, 65. The *409board concluded that the assessors had overvalued the club, and granted abatements to Black Rock for both years. The assessors have timely appealed to this court. For the following reasons, we vacate the final decision of the board and remand the case for further proceedings.

Background. 1. Description of the club. The parties do not dispute the size and nature of the club’s property or its membership arrangements. The real estate of the club encompasses approximately 175 acres allocated to an eighteen-hole golf course and practice areas, a four-level clubhouse, a recreation center, an outdoor pool, and five outdoor tennis courts, walkways, and parking lots. Developers completed the course during 2002 and the main buildings by close of 2003. A large-scale residential development adjoins the club. It employs the name Black Rock Condominiums but operates under separate ownership.2

The club is a private for-profit enterprise. Only members may use its facilities. It offers three categories of membership: full membership, single golf membership, and recreational membership. A full membership provides a family with access to all of the club’s resources. A single golf membership furnishes access to the golf course for one person. A recreational membership entitles the holder to use all of the nongolf facilities. The club’s by-laws authorize a maximum of 325 full golf memberships and twenty-five single golf memberships.

An incoming member must pay a one-time initiation fee. The fee is partially refundable. If a member resigns, the club will pay the resignee the refundable portion of the initiation fee after three new members join the club. No interest accrues on members’ and resignees’ refundable amounts because the club uses those amounts to support operations. During the two tax years in question, the initiation fee for a full membership was $125,000, of which $90,000 was refundable. Of the club’s more than 300 members, only eighty-six had paid the $125,000 figure. Other members had paid initiation fees ranging from $65,000 to $115,000. Some *410members had not paid any initiation fee but instead had received their memberships as an incentive to purchase a condominium in the residential development.

The operation of the club generated four categories of income: (1) golf revenue comprised of membership dues,3 guest fees, cart rentals, tournament fees, and initiation fees; (2) clubhouse food and beverage sales; (3) merchandise sales; and (4) miscellaneous amenities and services.4

2. Proceedings before the board. In the board proceedings, both the assessors and Black Rock submitted detailed written appraisal reports and testimony by their respective experts: for the assessors, general certified real estate appraiser Emmet T. Logue; for Black Rock, general certified real estate appraiser Jeffrey R. Dugas. The assessors submitted a valuation based on a capitalization of income methodology. Black Rock submitted its valuation on a variation of a capitalization of income analysis and on a supplemental market study of the sale prices of five golf course country clubs.5

*411a. Assessors’ valuation. The assessors’ expert employed a direct approach to income capitalization; he estimated the income earned by Black Rock as owner and operator of the club for the tax years in question and applied a capitalization rate to it. He estimated the club’s gross revenue at $8,396,220 for 2006 and $8,940,489 for 2007. He further estimated the club’s operating expenses at $5,781,571 for 2006 and $6,198,741 for 2007. He subtracted the operating expenses from the gross revenue and took a three percent deduction for reserves for replacements and a four percent deduction for “entrepreneurship return.” He concluded that the club produced net income to be capitalized of $2,077,740 in 2006 and $2,171,780 in 2007. He then applied a capitalization rate of 10.42 percent to the 2006 net income and a rate of 10.40 percent to the 2007 net income. That computation (division of the percentage into the net income) produced a valuation of $19.9 million (rounded slightly downward) for 2006 and $20.9 million for 2007.

As one element of estimated income, the assessors imputed and included interest on members’ initiation fees. Appraiser Logue characterized the fees as “non-interest bearing loan[s] to the [c]lub.” To place a value on the assumed benefit of the free use of the initiation amounts, he calculated and added interest income on those amounts at the rate of the ten-year United States Treasury bills as of January, 2005, and January, 2006.

b. Black Rock’s valuation. In contrast, Black Rock did not simply estimate the club’s net income and apply a capitalization rate. Instead, its expert estimated the fair market rental income which Black Rock could have achieved if it had chosen to lease the club to a third-party management company, a common practice in the golf club industry. To determine the rental potential of the club for the tax years 2006 and 2007, appraiser Dugas analyzed the lease terms employed by a set of eleven other club owners and third-party managers. From that survey he concluded that a fair market lease would have based rent on certain percentages of the club’s revenues from golf activity, food and *412beverage sales, merchandise sales, and miscellaneous receipts. From his sample he projected that Black Rock could have leased the club and received annual rent equal to the sum of twenty-two percent of golf revenue, ten percent of food and beverage sales, six percent of merchandise sales, and five percent of miscellaneous revenue. He applied those percentages to the revenue streams of the club and concluded that Black Rock could have achieved rent of $1,259,465 in 2005 and $1,330,356 in 2006, respectively, as determinants of the disputed assessments effective as of January 1, 2005, and January 1, 2006. He calculated a capitalization rate of 10.996 percent for the first year and 10.920 percent for the second year.6 The application of those rates to the estimated rental income figures resulted in rounded valuations of $11.5 million for the first year and $12.2 million for the second year.

Black Rock supplemented its capitalization method with a market study of proposed comparable sales. Its survey contained the data of the sales of five clubs. Four were in Massachusetts, and one in Pennsylvania.7 By this method, Black Rock’s expert proposed a valuation of “$10,000,000 to $11,000,000.”

c. Board’s decision. As its main reasoning, the board adopted Black Rock’s capitalization or market rental hypothesis. It referred glancingly to the comparable sales approach but did not employ it as an element of its decision. It made some slight adjustments. It increased the rental percentage for the golf revenue from twenty-two percent to twenty-five percent, and adopted the assessors’ capitalization rates instead of Black Rock’s. The higher rental rate for golf revenue and the reduced capitalization rate produced slightly higher valuations. After rounding, the board valued the club at $13.39 million as of January, 1, 2006, and at $14.09 million as of January 1, 2007.

*413The board rejected the assessors’ higher valuation for two main reasons. The board found the computation of imputed interest on initiation fees to be flawed because (1) that method assigned interest income to both refundable and nonrefundable portions of the fees; and (2) the assessors estimated the amount of received initiation fees on the faulty premise that all members had paid the maximum figure of $125,000, when in fact most members had paid considerably less and some none at all. The board concluded that the assessors’ “calculation of imputed interest income was likely overstated and so inflated [the] estimates of value as to render them unreliable.”

Analysis. 1. Standard of review. Municipal assessors carry “a statutory and constitutional obligation to assess all real property at full and fair cash value.” Coomey v. Assessors of Sandwich, 361 Mass. 836, 837 (1975), citing Part II, c. 1, § 1, art. 4, of the Constitution of the Commonwealth; art. 10 of the Declaration of Rights; and G. L. c. 59, §§ 38, 52. A taxpayer may challenge an assessment as excessive by petition to the municipal assessors for an abatement. G. L. c. 59, § 59. If the assessors deny the abatement, the aggrieved taxpayer may appeal to the Appellate Tax Board. G. L. c. 59, §§ 64-65. The taxpayer may appeal from a final decision of the board to this court. G. L. c. 58A, § 13.

While G. L. c. 58A, § 13, as appearing in St. 1998, c. 485, § 2, authorizes only an appeal “as to matters of law,” the accumulated decisions hold that the reviewing court will examine the board’s adjudication for “a correct application of the law” and for a basis in “substantial evidence.” Mount Auburn Hosp. v. Assessors of Watertown, 55 Mass. App. Ct. 611, 616 (2002). Massachusetts Bay Lines, Inc. v. Commissioner of Rev., 72 Mass. App. Ct. 321, 325-326 (2008). “Substantial evidence is ‘such evidence as a reasonable mind might accept as adequate to support a conclusion,’ taking ‘into account whatever in the record fairly detracts from its weight.’ ” Assessors of Brookline v. Buehler, 396 Mass. 520, 524 (1986), quoting from New Boston Garden Corp. v. Assessors of Boston, 383 Mass. 456, 466 (1981). The board’s expertise is entitled to “some deference.” McCarthy v. Commissioner of Rev., 391 Mass. 630, 632 (1984). Koch v. Commissioner of Rev., 416 Mass. 540, 555 (1993). As *414appropriate, that deference will extend to “the board’s judgment concerning the feasibility and fairness of alternate proposed methods of property valuation.” Massachusetts Inst. of Technology v. Assessors of Cambridge, 422 Mass. 447, 452 (1996).

At the same time, “[a] reviewing court must set aside a finding of the board if ‘the evidence points to no felt or appreciable probability of the conclusion or points to an overwhelming probability of the contrary.’ ” Irving Saunders Trust v. Assessors of Boston, 26 Mass. App. Ct. 838, 841 (1989), quoting from New Boston Garden Corp. v. Assessors of Boston, 383 Mass, at 466. The determination of substantial evidence has the character of a “matter of law.” See Olympia & York State St. Co. v. Assessors of Boston, 428 Mass. 236, 240 (1998); Information Servs., Inc. v. Commissioner of Rev., 48 Mass. App. Ct. 197, 198 (1999).

2. Assessors’ valuation. On appeal, the assessors have not argued directly and specifically for the adoption of their methodology and resulting valuation by a detailed criticism of the board’s rejection of it. See part 2.C., supra. If they do so implicitly by their extended attack on the board’s general acceptance of Black Rock’s competing valuation rationale, then on the record and briefing we view the board’s identification of weaknesses in the assessor’s methodology as valid. The board’s rejection of the assessors’ methodology has the support of substantial evidence. We turn, then, to an examination of the board’s general acceptance (with adjustments) of Black Rock’s valuation.

3. Black Rock’s market rental valuation. The assessors attack Black Rock’s market rental capitalization method in two phases. First, they contend that its expert did not furnish sufficient evidence that a fair market management lease would rest on the differing percentages of multiple revenue streams for golf activity, food and beverage, merchandise, and miscellaneous sources. Second, they argue that, even if such leases were common for golf club management, Black Rock’s proposed application of the criteria to its club failed because its expert was relying on non-comparable golf course facilities for his rental percentages.8 For the following reasons, we agree.

*415First, the expert did not adequately establish that a fair market lease would calculate rent on the basis of different fixed percentages of a club’s four revenue streams. He offered that extrapolation. However, none of the eleven clubs considered by Black Rock’s appraiser followed the model of a management rental rate based on discrete percentages of revenues from golf, food and beverage, merchandise, and miscellaneous sales.9

*416Five of the clubs maintained rent at fixed annual amounts;10 three at annual base figures supplemented by percentages of revenues;11 two at annual base figures with alternate revenue percentage amounts;12 and one at a pure percentage of particular revenues.13

Further, if the surveyed leases did employ revenue percentages, that rental methodology would not likely apply to the Black Rock property. Of the eleven properties relied on by its appraiser, eight were public.14 They generated golf revenue through daily greens fees. Their objective would be to maximize the number of rounds played. By contrast, as a private club, Black Rock would generate its main revenue from initiation fees and membership dues.15 While Black Rock’s appraiser treated initiation and dues revenues as golf-generated, they dif*417fer in kind from the user fees on which public courses rely for revenue. The board applied the market rental survey process to the club, but it did not explain the comparability of the relatively fixed annual income from Black Rock’s system of prescribed initiation fees and dues, on the one side, and the public course facilities’ variable revenues from greens fees and user fees, on the other.

Although the law permits the board to choose between reasonable alternative valuation methods, Pepsi-Cola Bottling Co. v. Assessors of Boston, 397 Mass. 447, 449 (1986), it nonetheless requires the board to assure the reasonableness of its choice by adequate findings and reasoning intelligible to the parties and the reviewing court. That requirement inheres in the standard of review for correct application of the law to fact finding supported by substantial evidence. In this instance, the lack of comparability between the surveyed eleven properties and the club subtracts from the value of the data submitted by Black Rock so as to bring their net weight below the level of substantial evidence. New Boston Garden Corp. v. Assessors of Boston, 383 Mass, at 466, and cases cited. Accordingly, we must vacate the decision of the board.

Conclusion. While the assessors have effectively challenged the board’s adoption of Black Rock’s methodology, they have not demonstrated the incorrectness of the board’s rejection of their own income capitalization rationale. The case illustrates the difficulty of valuation of special purpose real estate. We remand it to the board for further proceedings in the nature of fact finding, reasoning, or both, in light of our analysis.16 We deny Black Rock’s request for the award of appellate attorney’s fees; the assessors’ appeal was not frivolous within the meaning of Mass.R.A.R 25, as appearing in 376 Mass. 949 (1979).

The decision of the Appellate Tax Board is vacated, and the case is remanded to the board for further proceedings not inconsistent with this opinion.

So ordered.