TUNKS, Chief Justice.1
Appellee Union Tower Corp. (plaintiff) filed suit against appellants City of Dallas, the Dallas Independent School District, and others (defendants) attacking the validity of the 1981 tax assessments made by defendants concerning real property owned by the plaintiff within their boundaries.2
The trial court submitted the case to the jury in seven special issues, to which the jury responded: (1) that the plaintiff rendered its realty in 1981 at an excessive value due to an accident or mistake; (2) that in making this rendition, plaintiff’s agent did not fail to exercise good faith; (3) that the actual ratio of assessment used by both the city and the school district in 1981 was sixty-four percent; (4) that the Board of Equalization erroneously set the value of plaintiff’s property higher than that at which it was rendered by plaintiff; (5) that the assessed value of plaintiff’s property was grossly excessive when compared to assessed values of other properties in the city and school district; (6) that the assessments of the 1981 Board resulted in sub[277]*277stantial injury to the plaintiff; and (7) that the market value of plaintiff’s property other than real estate was $35,000. Because of the stipulation, no issue was submitted concerning the value of the real estate.
The trial court, by its judgment, determined that the defendants’ 1981 assessments on plaintiff’s property were excessive and that plaintiff was entitled to relief under former article 7345f.3 The judgment awarded plaintiff recovery from the city in the sum of $71,144.90 with interest, and recovery against the school district in the sum of $88,945.05. Both awards were for the excess taxes paid by the plaintiff in 1981. The court determined that the properly assessed value of plaintiff’s property taxes by the city and the school district for the year 1981 was $26,582,400 and that such value was binding on both defendants for the 1982 tax year. The court decreed that the total amount of plaintiff’s tax liability to the City of Dallas for the year of 1982 was $136,394.29 and that the plaintiff, to the extent that it had paid more, was entitled to a refund of the excess. The court decreed that the total amount of plaintiff’s tax liability to the defendant school district for the year of 1982 was $160,026.04 and to the extent that plaintiff had paid more, it was entitled to a refund of the excess.
The plaintiff moved for judgment on the verdict, and the defendants moved for judgment notwithstanding the verdict. The trial court granted the plaintiff’s motion and overruled the defendants’ motion. Thereafter, defendants filed a motion for new trial, which was also overruled.
The defendants present twenty-three points of error on appeal. Ten points contend that the evidence is legally insufficient to sustain the jury findings or to prevent the granting of defendants’ motion for judgment notwithstanding the verdict. Six contend that evidence is factually insufficient to sustain the jury findings or that the jury findings are against the great weight of the evidence. Seven raise various other law points. We overrule all points of error and affirm the judgment of the trial court.
We have examined the evidentiary points of error and have considered the defendants’ arguments under them, as well as the authorities cited in support of them. On the authority of Garza v. Alviar, 395 S.W.2d 821 (Tex.1965) and R. Calvert, “No Evidence” and “Insufficient Evidence” Points of Error, 38 Texas L.Rev. 361 (1960), and our consideration of the evidence in this case, as discussed below, we overrule all of defendants’ evidentiary points of error.
The property, which is the subject of this suit, is a downtown office complex in Dallas known as the Fidelity Union Life Tower and Building. It was stipulated that on January 1, 1981, the building had a market value of $41,500,000. In addition to the parties’ stipulation as to the value of the property, the parties also stipulated “that plaintiff may pay in full all property taxes assessed by defendants during the penden-cy of this cause and without being deemed to have acquiesced in the propriety of the tax assessments at issue in this cause.” There was also a stipulation as to the tax rates of the defendants for the years 1981 and 1982.
The property was assessed by the defendants on a value of $37,738,396. Plaintiff’s contention is that it should be assessed on a value of $26,560,000. (Plaintiff rendered its building for taxes for 1981 on a valuation of $31,530,405, but it alleged that such rendition was the result of a mistake on its part, and the jury so found). The gist of plaintiff’s contentions is that its property was assessed at a higher percentage of its value than other property assessed by the defendants. The plaintiff’s pleading sought relief provided by former ai’ticle 7345f and to set aside the assess[278]*278ment on its property for violation of article VIII, section one of the Texas Constitution.
The witnesses called by the plaintiff were experts in certain fields of real estate, including tax assessments of real property, appraisal of realty, and the science of statistics. Their qualifications as experts have not been challenged. The witnesses procured records of 1196 real estate sales within the defendants’ tax boundaries during the period between June and December of 1980. The records are used by brokers in the real estate business to determine the value of real estate in that area. Based upon these records, the experts assessed the valuations to be sixty-one percent of the sales prices by calculating the ratio of the amounts for which the properties were assessed by the defendants for 1981 to their sales prices in the last half of 1980.
The plaintiff also called Dr. A.W. Hunt, an expert in the science of statistics, as a witness. He confirmed the procedure followed by the plaintiff’s experts in assessing valuations as being consistent with practices recognized as valid within the science of statistics. Dr. Hunt testified that he randomly selected two hundred fifteen of the sales records to confirm by interviewing the parties involved. Of the two hundred fifteen sales, one hundred thirty seven were confirmed, nine were found to be inaccurate, and sixty nine were not confirmed because he was unable to interview the persons involved. He testified that he considered the conclusion reached as to the defendants’ assessment ratio to be accurate within two to three percent.
Kenneth Graeber, executive director of the State Property Tax Board, testified that he is in charge of conducting a biannual study of the market value of taxable property in each of the State’s 1,070 school districts. The studies are used to provide the State Legislature with information in distributing funds for public education. The State Property Tax Board conducted a study of the Dallas Independent School District’s tax assessments for the year 1981. It concluded that the district assessed residential realty at sixty percent of its market value. This conclusion strongly supports the testimony of plaintiff’s witnesses.
Plaintiff called Charles McIntyre, its vice president, and Jerry Hubbard, a tax consultant it employed to prepare and file its 1981 rendition, to support the allegation that the property rendition had been too high. McIntyre testified that the plaintiff bought the property from Fidelity Union Life Insurance Company in November of 1980. Although he did not actively participate in the negotiations leading up to the sale, he was aware of them. He said that the seller and the buyer agreed on a cash price of $40,000,000. The plaintiff, buyer, chose to pay $20,000,000 in cash and the rest of the purchase price over a period of years. The seller required the $20,000,000 cash payment and payments of $25,000,000 over a period of years. McIntyre further testified that the additional $5,000,000 was “the time value” of the amount of the purchase of which was to be spread over a period of years.
Hubbard testified that at the time he prepared plaintiff’s rendition, he believed that the defendants used sixty percent of market value as a value of real property for tax assessment and that he incorrectly believed that the plaintiff had paid $45,000,-000 for its property. Based upon these beliefs, Hubbard rendered the property at approximately seventy percent of $45,000,-000. Moreover, Hubbard testified that he was working under the pressure of a deadline when preparing the rendition and did not discover the error in the purchase price in time to correct his rendition before filing it.
Plaintiff called two officials of the City of Dallas to the witness stand: Seymour, the manager of assessment in the Department of Revenue and Taxation, and David Black, director of the Department of Revenue and Taxation. The two officials testified that during 1978 and 1979, a revaluation of taxable property occurred within the boundaries of the defendants, resulting in an increase of values at which the property was to be taxed. The increased values [279]*279were the basis of the assessments of 1980 taxes.
Black testified that the Department of Revenue and Taxation is responsible for about 380,000 separate tax accounts, so that it was not feasible to make an independent, on-site appraisal of the property in each account. To value property, the City of Dallas uses a “mass appraisal system”— characteristics of property that have something to do with its value are put into a computer file along with facts as to recent comparable sales, information as to improvements or additions, etc. The value of the property is calculated by computer from time to time. Black admitted that the mass appraisal system was not “designed to pinpoint value,” but that it was an “appropriate appraisal methodolgy” for a taxing district such as the City of Dallas. Specifically, Black testified that the mass appraisal system was accurate within fifteen percent. He testified that the City of Dallas did not have an assessment ratio in effect for the year of 1981. For that reason, he informed the Board of Equalization that the “target assessment” in the 1981 assessment program “was designed to place properties on the roll at eighty-five percent of the January 1, 1980, values.” This would result in half of the properties on the tax roll falling below eighty-five percent and half above eighty-five percent, but none would be assessed at more than the January 1, 1981, market value. He reasoned that values had increased fifteen percent or more since the evaluations on which the 1980 assessments were based.
The city auditor for the City of Dallas recommended to its tax department that a study be made of its 1981 assessments for the purpose of determining if any “inequities” had resulted therefrom. Black testified that because such a study could not have been completed before the tax notices were sent out, the study was not done. The City did, however, employ Dr. Gary Cadenhead, a professor at the University of Texas, to study the assessments of commercial personal property. Dr. Cadenhead testified that the fixed assets of such property were assessed at sixty-four percent of their market value; the inventory was assessed at eighty-four percent.
Hubbard was recalled to the stand to testify to the ratio of the assessments to the market value of the property assessed. His mathematic calculations were based on the testimony of the other witnesses. For example, he made mathematical calculations, based on the testimony of Dr. Hunt, indicating that residential real property was assessed at sixty-one percent of its market value, and he used the city’s records, containing the total assessed value of residential real property, to compute the total market value of such property. By using the State Property Tax Board’s report of the ratio of assessment as to commercial real property and the testimony of Dr. Cadenhead as to business personal property, Hubbard was able to calculate the total market value of all property on the tax rolls of the defendants, and by reference to the tax rolls, he was able to calculate that the total value of the property assessed was sixty-four percent of the total market value. Hubbard further testified that if plaintiff’s property had been assessed at sixty-four percent of its stipulated market value of $41,500,000, it would have been assessed at $26,560,000 and that plaintiff would have been taxed $160,411.66 less than it had been taxed.
Defendants vigorously argue that the plaintiff’s proof that they assessed property in their boundaries at less than its market value does not mean that they used a “ratio of assessment” in their plan for assessment. Defendants contend that a “ratio of assessment” means a preconceived and adopted plan to assess property at a percentage less than its full market value and that plaintiff only proved the “level of assessments” resulting from their action. Defendants introduced into evidence copies of resolutions adopted in January of 1980, in which they directed the director of the tax department to assess taxable property at 100% of market value commencing with the calendar year 1980.
[280]*280As to the defendants’ argument based on a distinction between the terms “ratio of assessment” and “level of assessment,” such a distinction is but an exercise in semantics — the terms mean the same thing when expressed in percentage of market value. Article VIII, section one of the Texas Constitution makes unequal assessments illegal without references to whether it is done pursuant to an adopted plan. Consequently, we hold that plaintiff’s proof that the defendants assessed its property at ninety percent of its value and assessed the other property in their boundaries at an average of sixty-four percent of its value, whether by proof of a “level of assessment” or a “ratio of assessment,” established the illegality of the assessment of plaintiff’s property.
Despite the city’s declaration in its resolutions that its intention was to assess property at one-hundred percent of its value, on July 1, 1981, Black wrote a memorandum to the Board of Equalization in which he stated, referring to the basis for the 1981 assessments, that they “were placed on the 1980 Roll at a conservative 100% of market value. In essence, the target assessment was designed to place properties on the roll at 85% of the January 1, 1980, values (widely regarded as December, 1978) ...” (emphasis added). Assuming the Board followed Mr. Black’s suggestion, it resulted in the assessment of plaintiff’s property at ninety percent of its market value and the assessment of the other owners’ properties at sixty-four percent of their value. This evidence shows the fraud and illegality of the plan. State v. Whittenburg, 153 Tex. 205, 265 S.W.2d 569 (1954). The inevitable conclusion — the “conservative 100% of market value,” at which the property was assessed in 1980, was in fact, much less than its true market value.
We also hold that the evidence supports the finding that the “actual ratio of assessment” used in 1981 was sixty-four percent and that this finding establishes the “assessment ratio” as that term was used in former article 7345f, section 4(b). That article provided:
(b) If the court or jury finds that the value as ascertained by the board of equalization is in error, meaning it is higher than the value set out by the property owner in a rendition filed prior to the board of equalization hearings as required by law, then the court or jury shall fix a value for the property in question as of January 1 of the tax year in controversy. In fixing the value of the property in question, the court or jury shall determine the cash market value and multiply that value by the assessment ratio, if any, in effect for the taxing authority involved.
In a proceeding under this article, the “cash market value” is multiplied by the “assessment ratio” found by the court or jury in fixing the value of the property to which the prevailing tax rate is applied to determine the proper amount of the tax. We hold that the term “assessment ratio” as used in this article is not limited to an assessment ratio established in advance by the taxing authority, but includes the actual “ratio of assessment” found by the court or jury, on “level of appraisal,” as defendants prefer to term it.
This interpretation of former article 7345f is confirmed by our examination of sections 42.21-42.26 of the current Property Tax Code (Vernon 1982 and Vernon Supp.1985), which bring forward the provisions of former article 7345f with some modifications. Section 42.26 authorizes the district court in such a proceeding to change the “appraised value” of the property in question to “the value calculated on the basis on the weighted average level of appraisal” of “other properties in the district.” We regard these provisions as providing substantially the same remedy as that provided by former article 7345f, but using the term “weighted average level of appraisal” in place of “assessment ratio” so as to exclude any implication that property may properly be assessed according to a predetermined assessment ratio forbidden by section 26.01 of the Code. We [281]*281conclude that “assessment ratio” as used in former article 7345f is equivalent to “average level of assessment," and thus affords relief to the taxpayer from unequal taxation, whether or not the taxing authorities have used a predetermined assessment ratio.
We do not hold that the “assessment ratio” so established is otherwise legally permissible. Former article 7174 provided:
Each separate parcel of real property shall be valued at its true and full value in money, excluding the value of crops growing or ungathered thereon.
In determining the true and full value of real and personal property the assessor shall not adopt a lower or different standard of value because the same is to serve as a basis of taxation_
TEX.REV.CIV.STAT.art. 7174 (1925) (repealed by Act of June 13, 1979, ch. 841, § 6(a)(1), 1979 Tex.Gen.Laws, Local & Spec. 2329). This statute has been interpreted as requiring assessment of all property at full market value. Crystal City Independent School District v. Johnson, 535 S.W.2d 730, 732 (Tex.Civ.App.—Tyler 1976, no writ); see Lively v. Missouri K. & T.R.R. Co., 102 Tex. 545, 120 S.W. 852, 856 (1909); cf. TEX.PROP.TAX CODE § 26.02 (Vernon Supp.1985). We hold only that the actual “assessment ratio” or “level of appraisal” as found by the jury establishes the taxable value for the purpose of the relief provided by former article 7345f, although defendants may have disregarded the statutory requirement that all property be assessed at “full value.”
The eleventh point of error asserts that “[T]he trial court had no jurisdiction to grant relief under former article 7345f because there is no evidence that the taxpayer filed a sworn affidavit with the Board of Equalization prior to invoking the provisions of said article.” Under the heading “Defense to appeal,” section 5 of former article 7345f provided that “a taxpayer shall be required to file with the board of equalization a sworn affidavit, in addition to the rendition, prior to invoking the provisions of this article but shall not be required to appear personally or by representative.” We do not interpret this provision of former article 7345f as imposing a limit on the jurisdiction of a court to hear an appeal, but rather as providing a defense to such an appeal.
If defendants pleaded this provision of article 7345f as a defense, it was not until they filed an amended pleading the day the case was called for trial. The appellate record does not show that they either asked for or were granted leave to file the amended pleading. The late filing of defendants’ amended pleading, without leave of court, violated both Texas Rule of Civil Procedure 63 and Dallas County Local Practice Rule 1.9(a). We hold that, under the circumstances, the trial court was justified in disregarding the amended pleading. Cf. Allright, Inc. v. O’Neal, 596 S.W.2d 208 (Tex.Civ.App.—Houston [14th Dist.] 1980, no writ). Furthermore, defendants’ amended answer did not specifically plead that plaintiff breached the statute by failing to file an affidavit. It pleaded only that “plaintiff has failed to comply with the prerequisites for relief under article 7345f, including without being limited to, the failure of plaintiff to exercise good faith in estimating the fair market value of its property.” We do not construe this pleading as giving fair notice that defendant would raise the defense of failure to file the affidavit.
Nor do we hold that failure to file such an affidavit, if properly pleaded and proved, would be fatal to plaintiff’s claim under former article 7345f. The apparent reason for the statutory requirement is to prevent the filing of spurious, unfounded protests, particularly when the taxpayer does not appear in person before the Board. Although the plaintiff presented no evidence that it had filed an affidavit, it presented evidence that its protest was not a spurious one. Furthermore, although the statute did not require the plaintiff to appear before the board, it did so through its representative, Hubbard, who had prepared its rendition. Hubbard and other witnesses [282]*282undoubtedly furnished the board more information under oath than would have been furnished in an affidavit.
In Watkins v. Douglass, 614 S.W.2d 892 (Tex.Civ.App.—Texarkana 1981, no writ), the court held that the taxpayer had substantially complied with and was entitled to an appeal under the terms of former article 7345f, although he failed to strictly comply with the statute as to the filing of his rendition. The court stated, “article 7345f was designed to provide relief to taxpayers from excessive valuations and it should not be strictly construed against them.” Id. at 895. See also Banquete Independent School District v. Tenneco, Inc.—Tennessee Gas Pipeline Division, 618 S.W.2d 824 (Tex.Civ.App.—Houston [1st Dist.] 1981, writ ref’d n.r.e.). Consequently, the eleventh point of error is overruled.
We recognize that in order to establish a right to relief under the constitution, the taxpayer must establish substantial injury. Conflicts between taxpayers and taxing authorities over the validity of tax assessments have led to much litigation in Texas. There are, as a result, a great many reported cases dealing with such litigation. Unfortunately, not all of those reported cases are entirely clear and consistent in stating the applicable rules of law. See M. Yudof, The Property Tax in Texas Under State and Federal Law, 51 Texas L.Rev. 885, 895 (1973). We have, therefore, selected the cases of State v. Whittenburg, 153 Tex. 205, 265 S.W.2d 569 (1954), and Whelan v. State, 155 Tex. 14, 282 S.W.2d 378 (1955), as having clearly and authoritatively stated the rules of law controlling the disposition of this case.
Whittenburg involved a suit by the State and local taxing authorities to recover delinquent taxes and penalties. The defendant taxpayers alleged that the assessments on which the State’s suit was based were illegal. The court ruled for the State, holding, among other things not relevant to this case, that the taxpayers did not show that they had sustained substantial injury resulting from the alleged illegal assessments.
In Whittenburg, 265 S.W.2d at 569, the court pronounced and authenticated some rules applicable to a ease in which a taxpayer seeks to establish the invalidity of an assessment of his property for taxes. Those rules are: The board of equaliza-tions’s assessment of property for taxes is a quasi-judicial function and it can successfully be attacked only by proof of fraud, want of jurisdiction, illegality, or the adoption of an arbitrary and fundamentally erroneous plan or scheme of valuation. Grossly excessive valuation may, in law, be sufficient to establish such fraud or illegality as to render a valuation void, but the fact that the trial court or jury differs with the valuation will not suffice as a basis for avoiding the board’s action. To prevail in his attack of the board’s valuation on the basis of unlawful discrimination, the taxpayer need not make a comparison with all other property in the taxing jurisdiction, but must make a reasonable showing in that respect. When the taxpayers’s attack is made on the basis that the board followed an arbitrary plan or scheme, to prevail he must not only show that the plan was arbitrary and illegal, but also that its use worked to his substantial injury.
The case of Whelan, 282 S.W.2d at 378, also involved a suit by the State and local taxing authorities for delinquent taxes. The county admittedly used a ratio assessment of thirty-three and one third percent of market value. The evidence showed that the county arbitrarily valued a nonproductive oil and gas leasehold interest at one dollar per acre. Cattle were valued at ten and fifteen dollars per head. The defendant-taxpayers alleged that the assessments of their properties were discriminatory and invalid. The court held that as to the assessment of non-productive oila dn gas and cattle the defendants failed to show that any substantial injury resulted to them. Id. at 380-81.
The defendants in Whelan pleaded that the assessments of their property were discriminatory and invalid because there was, in the applicable years, approximately $18,-000,000 on deposit in banks that was not on [283]*283the tax rolls. During the trial, the defendants offered evidence to prove their allegation, but the trial court, on objection, excluded it. The supreme court held the trial court’s exclusion of such evidence was reversible error. Id. at 384. The defendants had filed a rendition of their taxable property which included an item, “cash on hand.” The court further determined that the “cash on hand” embodied in the rendition of their taxable property included money on deposit in banks. Id. at 383.
The particular importance of the Whelan case, as authority controlling the disposition of this case, is its holding that had the defendants been allowed to present their offered evidence, and if it had in fact proved their allegation as to the bank deposits and their omission from the tax rolls, that proof would have established not only that the county’s tax plan was illegal, but also that they had sustained substantial injury from the use of such plan. The court stated:
In the light of what we have said, it follows that the testimony was admissible. If the proffered testimony supported the pleadings it would have shown that by placing bank deposits on the tax rolls approximately $6,000,000 would have been added thereto. The total amount of petitioners’ taxes levied for state, county and school purposes, exclusive of penalties and interest, was $38,-878.68, and the total amount levied for county purposes alone was $13,562.04. Assuming, as we must, that the budgetary needs of the county and school district were met by the tax rate adopted and levied on the assessed valuation, the addition of $6,000,000 in assessed valuation should have resulted in a substantial reduction of petitioners’ taxes, either through reduced assessed valuation of the property on the tax rolls or through a reduced tax rate. A proportionate reduction of assessed valuation would have resulted in a reduction of petitioners’ taxes by one-sixth of their total taxes, or $6,479. A proportionate reduction of the tax rate for county purposes alone would have resulted in a reduction of petitioners’ taxes by approximately one-sixth of the taxes due the county, or $2,244. It can hardly be questioned or doubted that on the record before the court the proffered evidence, if undisputed, would have shown substantial injury as a matter of law in that petitioners’ taxes were excessive to the extent indicated. (Emphasis added).
Id. at 383-84. The same reasoning applies when, as here, the evidence shows that other property was assessed at a lower ratio of true value than the property in question. Lively v. Missouri K. & T.R.R., 102 Tex. 545, 120 S.W. 852, 856 (1909).
In view of these authorities, we conclude that even though plaintiff stipulated that its property was assessed at less than its full market value, the evidence and jury finding that other property in the city and school district were assessed at an actual ratio substantially lower than the ratio applied to plaintiff’s property establishes discrimination which entitles plaintiff to relief under the constitutional requirement that taxes be equal and uniform. These facts show substantial injury because if all property had been assessed at the same ratio as the property in question, the tax rate necessary to raise the same amount of revenue would have been lower on plaintiff’s property.
Moreover, regardless of the requirements for equitable relief from discriminatory taxation under the constitution, former article 7345f, which was enacted in 1977 and was in effect when the 1981 assessments was made, provides a specific remedy when a taxpayer’s property is assessed at a higher ratio or level of appraisal than the average ratio used for other property in the taxing district.
The taxable value established by this assessment ratio is binding on the taxing authorities for the year in question and for the succeeding tax year. Article 7345f, § 4(c); TEX.PROP. TAX CODE § 42.27(c) (Vernon 1982) (repealed, TEX. LAWS 1983, p. 5033, ch. 905, § 2, eff. Aug. 29, 1983. [284]*284Consequently, we hold that whether plaintiffs claim is based on former article 7345f or on article VIII, section 1, the trial court properly determined the proper amount of plaintiff's tax liability for both 1981 and 1982. We have considered all of defendants’ points of error, including those not specifically discussed herein. We conclude that they present no reversible error, therefore overruled.
Affirmed.