The evaluation of accuracy and uniformity in the mass valuation of properties in the city of Johannesburg, South Africa

Property taxation is one of the many sources governments use to raise revenue (De Visser, 2024). The money accruable from the source of revenue is used to provide municipal services that make life meaningful for the people (Ndevu and Muller, 2017). According to the Department of Corporate Government and Traditional Affairs (2009) these services include roads, housing, health facilities, water, educational facilities, refuse removal, recreational facilities, and public lighting. Over the years, the South African local government has imposed property rates on all properties with each municipal jurisdiction (De Visser, 2024).

Like many other countries, especially in the developed world, the South African property valuation offices have been utilising the ad valorem assessment to estimate the worth of properties for taxation purposes. Since several properties are involved in the value-based assessment, the manual valuation of properties cannot accommodate the process without limitations (McCluskey and Franzsen, 2018).

Arguably, inaccurate value estimates are generally caused by the difficulties inherent in manual assessment (Venter et al., 2025). Such an estimate would attract higher property taxation if a property is overvalued. Where a property is undervalued, such properties would enjoy lower taxation, suggesting under-taxation (Atilola et al., 2019; Uy, 2021; Singh, 2024). The issue of undervaluation caused disagreements between the City of Johannesburg (CoJ) and various stakeholders, including the South African Property Owners Association (SAPOA) (Ngubeni, 2022). According to the courts, municipalities occasionally purposefully undervalue residential properties, which lowers the quantum of their municipal rates and tax income (Ignatova, 2019). Municipalities are also accused of overvaluing the commercial assets to offset the loss that results from undervaluing residential homes. The courts ordered the municipalities to always aim for increased valuation accuracy and uniformity when assessing property values (Rammala, 2022; Emsley, 2024).

On account of valuation inaccuracies and inequities, valuers have always been accused of subjectivity and unreliability (Adair and McGreal, 1988). The inaccuracies and inequities are also attributed to employing traditional manual valuation procedures in assessing properties, which have been practised for over 3 decades. However, although the conventional approaches are usually considered sufficient for evaluating a single or a few properties, they become troublesome when the scope is expanded (Yacim and Boshoff, 2020). Therefore, a large discrepancy between the estimated values and the market price in the local real estate market is said to be caused by the incapacity to assess a group of properties using manual assessments, on the part of the municipal valuers. Once more, before arguing for full use of the computer-assisted mass appraisal (CAMA), a method that uses statistical models and computer software to value large numbers of properties, it is necessary to carefully examine the example data in this study because a property's assessed value serves as the tax base for calculating the amount of tax paid to local authorities in South Africa (Rammala, 2022).

Thus, there is a growing debate on how best to tackle the problems of inconsistencies and inaccuracies in valuation, and this has been the case at least for the past 3 decades (Cheloti and Mooya, 2021). In the past, especially in the early days of discourse on valuation accuracy and inequity, the studies on valuation accuracy were mainly focused on and limited to individual valuations (Crosby, 2000). Yacim and Boshoff (2018a, b, 2019, 2020) and Boshoff et al. (2019) studied mass valuation of properties using differing computer-assisted techniques and example data from Cape Town. No studies have been conducted on accuracy and uniformity in municipal valuations in South Africa. The pursued gap relates to the observation that the municipalities do not subject their General Valuation Rolls (GVRs) and Supplementary Valuation Rolls (SVRs) to post-valuation date ratio analysis. Accordingly, the study was focused on the municipal GVR of the City of Johannesburg's 2022 GV, owing to the convenience of data availability.

This study is structured in six sections. Section 1 is the introduction, Section 2 reviews the literature on mass valuation accuracy and uniformity, and Section 3 presents the study area's locality. Section 4 outlines the research methodology, Section 5 presents the results and discussion, and Section 6 presents the conclusion and recommendations.

Damodaran (2012) and Pinto et al. (2021) assert that valuation is the foundation for financial transactions, investment decisions, mergers and acquisitions, taxation, and regulatory compliance. This may be a single property valuation or a mass valuation. Mass valuation is often required for various purposes, including statutory property rating, mortgage securities and company annual financial statements (AFS). Therefore, the accuracy and uniformity of valuation methodologies are essential for establishing fair values, determining market prices, and maintaining the efficiency of financial markets. Studying valuation accuracy and uniformity is motivated by the high stakes involved in the value estimates. It also enables the investors and authorities to make informed decisions. Accurate valuations provide a solid foundation for investment decisions, risk management strategies, and fair pricing of financial instruments. Uniform valuation practices enhance market efficiency by facilitating price discovery, enabling efficient allocation of resources, and reducing information asymmetry (Damodaran, 2012).

The terms “valuation” and “accuracy” combine to form the idea of valuation accuracy. Estimating a valued property's actual sale price is known as valuation. Conversely, accuracy, a key component, describes the quality of being exact. As a result, valuation accuracy is likely the reverse of valuation inaccuracy. It shows how close the actual sales price is to the projected value. To put it another way, the question of valuation accuracy is: How closely does the anticipated value match the real price? Inaccurate valuations can have far-reaching implications. They can misrepresent the actual value of assets, leading to overvaluation or undervaluation. Overvaluation can result in inflated asset prices, leading to speculative bubbles and financial crises, as witnessed in the housing market bubble of the late 2000s. Conversely, undervaluation can hinder investment opportunities, discourage economic growth, and erode market confidence (Penman, 2013; Venter et al., 2025).

Valuation uniformity can be seen as an antithesis of valuation inconsistency (Ayedun et al., 2012). This concept is buttressed by promoting fairness and valuation transparency amongst various properties. Consequently, it ensures a level playing field for market participants by increasing public trust in real estate valuation and lowering the likelihood of conflicts. Smith and Johnson (2018) define value homogeneity as the standardised valuation across neighbourhoods and properties. Inconsistencies in valuation pose challenges in comparing and evaluating assets across different contexts. Inconsistency can arise due to variations in valuation methods, assumptions, and data sources. This lack of uniformity can hinder the accurate assessment of asset values, impair market transparency, and introduce arbitrage opportunities. Inconsistency also undermines investor confidence, raising doubts about the reliability and credibility of valuation results (Smith and Johnson, 2018).

There are numerous studies on valuation accuracy (or inaccuracy) and uniformity (or inconsistency) in various countries, including Nigeria, Asia, the United Kingdom, Australia, China, Japan, and South Africa (Crosby, 2000; Ogunba, 2004; Rossini and Kershaw, 2008; Ayedun et al., 2012; Pi-Ying, 2011; Babawale and Omirin, 2012; Bogin and Shui, 2020). Most of these studies are comparative studies focusing on single property valuation. Historically, the studies compare the use of valuation models on the same data set or establish the degree of valuation uniformity across various samples. According to Ogunba (2004), in the developed world, especially in the US and the UK, the debate on valuation accuracy and uniformity dates to the later decades of the 20th century. Initially, the discussion was focused on commercial properties. Bogin and Shui (2020) studied the accuracy of the Automated Valuation Models (AVMs) in the rural areas of the United States (US), especially for credit risk management. They found that valuations conducted for the underlying collateral value were mainly inaccurate. Since the inception of studies on valuation accuracy (or inaccuracy) in the UK, researchers have improved the sample size from units to thousands, to affirm the validity and reliability of the results (Hutchison et al., 1995).

In the case of developing countries, such as Nigeria, the valuation accuracy and inconsistency studies were conducted by Ogunba (2004), Ajibola (2010), Ayedun et al. (2012) and Effiong (2015). Valuation challenges were traced to inconsistencies in the valuation ingredients, such as input data, valuation methods and deficiencies in education and practices (Ogunba, 2004; Babawale and Omirin, 2012). The studies also revealed that, amongst others, the causes of valuation inaccuracy include a dearth of market data, poor property sales, data banks, market assumptions, and inadequate experience and training of the valuers (Ajibola, 2010; Ayedun et al., 2012; Effiong, 2015).

Mass appraisal (valuation) is defined as a process of valuing a group of properties at a given date using standardised approaches and statistical testing (Kauko and D'Amato, 2008; International Association for Assessing Officers (IAAO), 2013; Yacim and Boshoff, 2016). The standardised approaches have evolved to embrace the hedonic price models (HPMs), which use the ordinary least squares (OLS) estimator, Spatial Models, and, lately, the Machine learning (ML)/Artificial intelligence (AI) models (Yacim and Boshoff, 2014; Wang and Li, 2019).

The study by Pi-Ying (2011) compares the OLS and the Artificial Neural Networks (ANNs) regarding their ability to produce accurate valuations in Kaohsiung City in Taiwan. In the case of the OLS, results show the R² of 69.4% and the MAPE of 24.71%. In the case of the ANNs, results show the R² of 75.84% and the MAPE of 19.02%. The results also show Hit Ratios (HR) favourable to using the ANNs. This indicates that the ANNs achieved a better accuracy level than the OLS. In a comparative study between the ANN models and other approaches, including the OLS, conducted on 2,694 properties, McCluskey et al. (2013) test the predictive capabilities of each model to attain valuation accuracy. The study's results are consistent with various other studies that test the performance of ANNs, in that it was confirmed that the ANNs produce more accurate value estimates. Like other studies, the study also reveals that the only problem with the ANNs relates to the limitation on the explicability of the black box.

Yacim and Boshoff (2016) compared five mass valuation methods, including the ANNs, on 3,494 properties with recorded sales in Cape Town, South Africa. With the aid of the RMSE, the MAPE, and the U-statistic, the study sought to compare the mass valuation methods in terms of their performance and predictive accuracy. The results of this study show that, amongst the five models considered, the Back Propagation ANNs and the M5P trees proved to be the best in terms of performance and accuracy.

Abidoye and Chan (2016) reviewed numerous studies that evaluated the use of ANNs in valuations, ranging from 1997 to 2013. These studies cut across countries such as Australia, the United States, and the United Kingdom. It was found that the ANNs were performing better than the other models. Despite the superior predictive capabilities of the ANNs, all studies agreed on the black box limitations. Interestingly, Abidoye and Chan (2016) indicated that other researchers (Cortez, 2010; Ticono et al., 2011) suggest that there may be techniques, such as sensitivity analysis, that can assist in resolving the ANNs' limitations.

Valuation accuracy is measured by comparing the estimated values to the actual sale prices (Crosby, 2000) using the “margin of error” principle used in courts (Crosby et al., 1998. According to Ayedun et al. (2012), most studies assessing valuation accuracy or inaccuracy relating to the valuation of single properties suggest a margin of error between 5 and 25%. Crosby et al. (2003) emphasised reconciling the difference between the valuation and sale date when measuring valuation accuracy.

The testing of mass valuation outcomes for accuracy and uniformity has been evolving for decades. This was sparked by the risk of horizontal and vertical inequity, which could lead to users losing confidence in the valuations. Measurement and testing of the outcomes became necessary to ascertain fairness and equity. Thus, statistical measures such as the ASR, PRD, PRB, COD, COV, RMSE, and MAPE, which are used in mass valuations, are employed (Quintos, 2014; Carter, 2016).

According to Quintos (2014) and Carter (2016), in the computation of the ASR, vertical inequity exists when the ratio (ASR) is either less than or greater than 1. In these instances, vertical inequity is regarded as either regressive or progressive. Vertical equity exists only when the ratio (ASR) equals one on the dot. The PRD refers to the mean of all the ASR ratios. Horizontal inequity involves directly comparing two similar properties in the same neighbourhood or even across neighbourhoods (Carter, 2016). This is ensuring fairness and equality in the imposition of rates and taxes. There is horizontal inequity if the assessment values are unequal (Denne, 2011). Rossini and Kershaw (2008) studied the accuracy of various AVMs used in mass valuation in the Marion LGA, Adelaide Metropolitan Area, South Australia. The study area consisted of 41,000 assessable properties and 1,294 actual sales. The models were tested with RMSE, MAPE, COV, COD, and PRD. The results showed that the introduced AVMs were not much different in accuracy from the traditionally used methods.

In all the studies reviewed, there is general agreement that inaccuracy remains the biggest concern in real estate valuation. Although various methods and measures were used to measure valuation accuracy and uniformity, the IAAO (2013) standard on ratio studies is adopted in many countries and provides the preferred statistical measures of accuracy and uniformity.

Owing to the numerical nature of the municipal valuation data, the study adopted a quantitative approach, underpinned by the statistical measures used to measure accuracy and uniformity in accordance with the IAAO.

The CoJ is the largest metropolitan municipality, with the most extensive rateable property portfolio in South Africa. The CoJ property portfolio is diverse, amounting to above 750,000 properties, largely including non-income and income-producing categories. It is a perfect anecdotal representation of all property typologies in the country. The study area is composed of 17 neighbourhoods. The City of Tshwane Metropolitan Municipality defines the CoJ to the northern border, Sedibeng District Municipality to the southern border, City of Ekurhuleni Metropolitan Municipality to the eastern border and the West Rand District to the western border. Figure 1 depicts the locality map of the study area in relation to the entire Gauteng Province and the other municipalities within the province.

At the time of valuation for the 2018 GV, the area was home to 758,998 rateable properties, with a variety of land uses including residential, agricultural, commercial, sectional titles, agriculture and vacant land. Figures 2 and 3 are maps of the CoJ. While Figure 2 shows the map within the broader Gauteng Province, Figure 3 shows the map of Johannesburg depicting all the neighbourhoods and suburbs that are within.

The data used in the study was obtained from the CoJ's valuation division on a disc in Excel format. The disc contained two data sets, including 758,998 properties in the 2018 GV and the 32,102 sales recorded against the properties, post valuation date. The data sets were merged and subjected to data cleansing and selection.

The study employed a combination of probability and non-probability sampling methods, including the convenience and purposive sampling methods (Teddlie and Yu, 2007). Random sampling is a probability sampling technique where each unit in the population has an equal and independent chance of being selected. This method minimises selection bias, ensures that the sample is representative of the population, and renders findings more reliable and generalisable. Convenience sampling involves selecting participants who are easily accessible to the researcher, often due to time or resource constraints (Golzar et al., 2022). Purposive sampling is sometimes referred to as judgmental or selective sampling. It is a non-probability sampling technique, where the researcher deliberately selects or excludes data based on expert judgment, predefined criteria, or study objectives. In this method, not all population members have an equal chance of selection. It focuses on including the most relevant, reliable, or representative cases. (Makwana et al., 2023).

Convenience sampling was only used in selecting CoJ as a case study because it was the only metropolitan municipality willing to share its municipal valuation data, albeit from the past valuation roll- 2018 GV (Makwana et al., 2023). Purposive sampling was employed to select all the sales that occurred 12 months post the municipal valuation date (Makwana et al., 2023). The sampled sales data constituted a list properties located in 10 of the 17 neighbourhoods of the City. These 10 neighbourhoods include Soweto, Lenasia, Lenasia South, Alexander, Ivory Park, Diepsloot, Orange Farm, and Midrand. Roodepoort, and Ennerdale. In order to align with the valuation date, all the sampled sales were subjected to the Residential Property Price Index (RPPI) and the All-Risk Yield (ARY) of 7.5%.

Accordingly, the following few paragraphs provide a step-by-step approach to arriving at the final sample used in this study. Thus, the flow chart in Figure 3 gives a simplified procedure.

Figure 4 outlines the stepwise sampling procedure. The population of 758,998 properties on the general valuation roll was carefully restricted to 32,102 recorded sales between July 2017 and June 2018. Outlier transactions (1,684) were purposefully removed to ensure minimal distortions. This was followed by randomly excluding 9,562 residential sales in strict compliance with IAAO standards. Therefore, the final sample comprised 20,856 valid sales used for analysis (see also Table 1), a testament to the thoroughness of our process.

The ratio between the residential properties and income-producing properties was initially 3.8:1, representing the total sample size of 32,102 comprising 1,684 outliers, 24,098 residential properties and 6,320 income-producing (non-residential rental property) properties. Following the infusion of the specifications in IAAO (2013), which effected to improve on the sample's representativeness, the residential component of the sample was reduced by randomly selecting 9,562 sales. After the reduction, the new sample size became 20,856, consisting of 14,536 residential and 6,320 income-producing properties, yielding a 2.3:1 ratio, which also reflects the ratio in the population.

Whilst it is true that if used separately, convenience sampling and purposive sampling as non-probability methods, may compromise the reliability and generalisability of the findings, it worth noting that in this study, they were only used to select CoJ as a study area and the post valuation sales as the only sales against which the valuation could be judged. Random sampling dominated the sampling exercise by randomly selecting the sales to be excluded in compliance with the IAAO standards, and the exclusion of the outliers. This renders the ultimate selected sample of 20,856, adequately random to eliminate bias and guarantees validity and generalisability of the results.

The Median ASR, MAPE, and RMSE were used to evaluate accuracy. The COD, PRD, and PRB were applied to assess vertical and horizontal uniformity (Yacim and Boshoff, 2016; Gnat, 2020; Przekop, 2022; Rossini and Kershaw, 2008). The appropriateness of these measures is confirmed practice in countries that have adopted the IAAO standards (Denne, 2011).

The Assessed Value, Sales Price Ratio (ASR) compares the assessed value of a property to its actual sale price. The formula for calculating the ASR is in equation (1):

According to Parker et al. (2011), the ASR evaluates the accuracy and fairness of property assessments. A low ASR indicates that the assessed values are generally lower than the actual sale prices, while a high ASR suggests overvaluation. Ideally, the ASR should be close to 1 (or 100%) to indicate that the assessed values align closely with market prices. The ASR monitors the performance of the assessment method and ensures that properties are assessed fairly and uniformly. If the ASR deviates significantly from the desired range, it may prompt a reassessment of property values or adjustments to the assessment methodology. By identifying discrepancies between assessed values and actual sale prices, the ASR helps maintain equity and consistency in property taxation. It provides a quantitative measure to determine the accuracy of the assessment process and supports the goal of fair and equitable property taxation.

Carter (2016) states that the total of all appraised values (AV) must be divided by the sum of all sales prices (SP) after the weighted mean of the sample is divided by the mean of the sales ratio of all properties.

The IAAO guidelines state that a score of 0.98–1.03 is acceptable and represents negligible vertical inequality. Values greater than 1.03 indicate regressive vertical inequality and values less than 0.98 indicate progressive inequality.

According to Carter (2016) and Denne (2011), PRB is another measure of vertical equity (or inequity). It indicates whether the assessed values are equitable across the high-valued and low-valued properties. A positive PRB denotes a progressive assessment in that it suggests that the high-value properties are over-valued, compared to the low-value properties (Carter, 2016). A negative PRB implies a regressive regime. As guided by Carter (2016), the PRB is calculated with the aid of a linear regression analysis equation, mathematically represented as in equation 3:

A few steps may be necessary to calculate the PRB. First, the ASR of all properties must be calculated by dividing the Assessed Value (AV) by the Sales Price (SP). The second step is dividing each Assessed Value (AV) by the median ASR. The third step is calculating the independent variables (x-range) by adding half of the sales price (SP) to half of the quotient of the assessed value, divided by the median ASR and then dividing the logarithm of the sum, divided by the logarithm of 2. As a fourth step, the dependent variable (y-y-range) is calculated by dividing the difference between the ASR and the median ASR by the median ASR. Once these steps are completed, a regression analysis is applied to the independent and dependent variables to determine the PRB. Therefore, (⁠$x1)$ represents the PRB. It is the coefficient of x in the regression equation, which is the independent variable.

The Coefficient of Dispersion (COD) measures the spread of variables around a central value derived from a measure of central tendency, such as the mean, the median, and the mode. In real estate, it is used to attempt to understand valuation consistency in mass appraisal. As such, the assessment sales ratio (ASR) is fundamental to determining COD. The following formula, equation 4, is used to determine the COD.

In calculating the COD, the ASR for each property is first calculated as a second step, subtracting the median of all the ASRs from each ASR. Thirdly, divide the sum of the absolute values of the differences by the number of data points. Lastly, the resulting quotient is divided by the median. The outcome represents the COD, which can be expressed as a percentage of the median. A lower COD outcome suggests stability and homogeneity or consistency.

The COV can be explained as a relative measure of dispersion, mathematically represented as the ratio of the standard deviation to the mean. It seeks to show the degree of variability of the data points from the mean. In mass appraisals, this measure concerns the standard deviation of the assessments (estimates) from the sales price (actuals). A lower value of the COV suggests more accurate assessment values (estimates). Thus, equation (5) is used for calculating the COV:

The symbols (⁠$xi$⁠), (⁠$μ$ ), and (N) represent the sample mean and sample size in the data set, respectively. First, it is best to determine the standard deviation using the formula in the numerator. The numerator represents the standard deviation of a sample. It is important to note that the above formula assumes the employment of a sample instead of the population. It is suitable for evaluating mass appraisals because the data points included in the study are a sample selected based on convenience.

The RMSE gives the total measure of model accuracy, claim Bogin and Shui (2020). The RMSE measures the model's prediction errors and residuals. Additionally, it can show how well models perform in forecasting and prediction (Chai and Draxler, 2014). According to Pi-Ying (2011), the RMSE is the residuals' (trendlines') standard deviation. The residuals indicate how far the sales data points deviate from the trendline. A model's performance indicates how well it can anticipate outcomes. The OLS model utilised in the CoJ was tested using RMSE within the study's parameters. A model produces more accurate valuation estimations if its RMSE is lower. Numerous formulae are used to represent the RMSE. However, for the assessment under consideration, the following equation (6) was used:

After finding the residuals, they are squared and totalled. The next step is to calculate the square root of the sum of the squared residuals, divided by either the sample or the total number of residuals (n). The response to this represents the RMSE. The RMSE formula resembles the standard deviation formula, a concept you may already know.

De Mytenaere et al. (2016) emphasise the practical application of MAPE, a forecasting accuracy metric frequently employed when the number to be predicted is known to stay well above zero. When presented as a percentage, the MAPE becomes a powerful tool, gauging the forecast system's or model's accuracy. It is calculated by dividing the real value by the absolute rate of each data point less than the actual value. A lower MAPE indicates that the model is less inaccurate. Equation 7 defines it as follows, providing a clear and practical understanding of its application:

The calculation process, which involves deducting the estimated values (yi) from the real sales prices (xi), dividing by the actual sales price (xi), and then multiplying by 100 (100%), serves a key role in our method. It helps determine the percentage of errors. The absolute values of the same are then calculated, put together, and divided by the sample size (n). The matrix proposed by Lewis (1982) for evaluating data performance in terms of MAPE is shown in Table 2.

The statistics in Table 3 depict the statistics on the universe of the CoJ rateable properties. It also summarises all the statistical measures relating to the sample data used in the study.

Tables 4 and 5 depict the statistical measures used in assessing the accuracy and uniformity of mass valuation in the CoJ GV of 2018. These include the measures recognised by the IAAO, including the ASR, MAPE, and the RMSE regarding accuracy and PRD, PRB, and COD regarding uniformity.

The sample data were processed to determine the values of the accuracy (Median ASR, MAPE, and RMSE) and uniformity (COD, PRB, and PRD) measures. The tests revealed results within the acceptable parameters of the IAAO standard and otherwise good practice.

The tests' results, as depicted in Table 4, reveal that the overall valuations are accurate to a good degree. Assessed against the IAAO standards, this result suggests that the CoJ's GV was fairly accurate with a slight bias towards under-assessment. This result is not of major concern, especially because the residential class constitutes the largest and dominant class in the sample data pertaining to municipal valuation.

The Median Absolute Sales Ratio (ASR) is a critical measure of central tendency in property valuation accuracy, especially where the data distribution is skewed or contains outliers. For the City of Johannesburg's General Valuation Roll (GVR) of the year 2018, the obtained median ASR is 0.90, which aligns exactly with the lower boundary of the acceptable range per IAAO standards (0.90–1.10). This result indicates a generally accurate valuation level with a slight bias toward under-assessment. A median ASR 1.00 would represent perfect valuation parity between assessed values and market sales prices. A result of 0.90 suggests that, on average, assessed values are approximately 90% of actual sale prices. Given that the data includes diverse property classes, primarily residential, with some income-producing properties, this level of accuracy is considered acceptable and indicative of a consistent mass appraisal system. Significantly, the use of the median rather than the mean further strengthens confidence in the reliability of this finding, given its resistance to distortion from extreme values.

However, the slight under-assessment implied by a 0.90 median ASR should not be dismissed outright, especially given its implications for revenue and equity. While this bias may be acceptable within IAAO parameters, it could impact municipal budgeting if it systematically undervalues taxable property bases. Nevertheless, under-assessment is generally preferable to over-assessment from a policy standpoint, as it tends to avoid undue taxpayer burden. Moreover, this result reflects a strong central tendency given the scale and complexity of Johannesburg's property market. The residential classification, which comprises the majority of sampled data, most reflects this trend and suggests that the valuation system is functioning adequately in terms of fairness and compliance with global mass appraisal standards. Continuous monitoring and calibration, particularly in areas where ASR drops below 0.90, would help ensure sustained compliance and public trust in property taxation processes.

The Mean Absolute Percentage Error (MAPE) evaluates the average absolute deviation between the assessed and actual sales prices, expressed as a percentage (Lewis, 1982). In the context of the CoJ's GV of the year 2018, the MAPE was found to be 19.05%, which falls within the acceptable threshold of up to 20% per IAAO and valuation industry practice for residential and mixed property classifications. MAPE is an intuitive and easily interpretable statistic; in this case, it suggests that, on average, property assessments deviate from actual market prices by roughly 19%. Given that the sample primarily consists of residential properties (with a minor representation of income-producing assets), this result is acceptable, albeit close to the upper tolerance boundary.

It is essential to note that MAPE does not differentiate the direction of error, over- or under-assessment, but focuses purely on the magnitude of deviation. While an MAPE under 10% is ideal and indicates an exact model, the IAAO recognises the practicality of achieving this only under stable market conditions or smaller jurisdictions. For large and diverse urban property markets such as Johannesburg, a 19.05% MAPE suggests commendable performance, especially in market volatility, socio-economic heterogeneity, and complex property types (Lewis, 1982). Importantly, this reinforces the finding from the ASR analysis: the fact valuation model is operating with reasonable precision. Nevertheless, future improvements could be pursued through stratified modelling approaches or localised calibrations to reduce MAPE further, thereby tightening valuation consistency and minimising taxpayer grievances.

The Root Mean Square Error (RMSE) for the CoJ valuation model is reported at R123,514.66, a currency-based measure that reflects the standard deviation of residuals or prediction errors. RMSE penalises larger errors more significantly than MAPE or ASR due to the squaring of residuals. Although the IAAO does not prescribe a definitive benchmark for RMSE, lower values generally indicate higher valuation accuracy. In this context, an RMSE in the R123,000.00 range is not trivial, especially when contrasted against the average sales price of R424,912.42, representing roughly 30% of the average transaction. This result affirms that while most predictions are reasonably close to actual sales values, there is still a substantial degree of deviation in individual property assessments. This variance may be due to a mix of unique property characteristics or modelling limitations.

The utility of RMSE lies in its ability to flag models that perform well on average but occasionally produce highly erroneous assessments, especially for atypical or high-value properties. Given that RMSE is sensitive to such outliers, the CoJ's result implies a need for further examination into the tail ends of the value distribution, especially in higher-end residential and income-producing classes. When RMSE is considered alongside MAPE and ASR, a coherent picture emerges: the valuation model demonstrates acceptable central accuracy (ASR) and reasonable average error (MAPE) but retains areas of high variability (RMSE). While acceptable, continued refinement of property groupings, model stratification, and outlier treatment methods would help reduce RMSE and enhance model robustness over time.

The test results are depicted in Table 5, which shows that the overall valuations are uniform to a good degree. Assessed against the IAAO (2017) standards, this result suggests that the CoJ's GV of 2018 was uniform horizontally and vertically.

Price-related bias (PRB) measures the degree and direction of vertical inequity in assessments, particularly whether high-value properties are systematically over- or under-assessed. For the CoJ's GV of 2018, the PRB was calculated at 0.01, comfortably within the IAAO's accepted range of 0.05 to +0.05. This result indicates an essentially neutral bias, with a slight progressive skew-meaning that higher-value properties tend to be assessed marginally above their actual market prices. While this degree of bias is minimal and statistically insignificant, it is nonetheless an important indicator of valuation equity, especially given growing concerns globally about equitable taxation.

The PRB's low absolute value reflects well on the uniformity of the CoJ's valuation process. A more negative PRB (e.g. <– 0.05) would have indicated potential overburdening of higher-value property owners, while a more positive value (>+0.05) would suggest regressivity. At 0.01, the system demonstrates a balanced property treatment across the value spectrum. This finding aligns with the acceptable PRD and COD results, reinforcing that horizontal and vertical uniformity are maintained. Significantly, PRB adds granularity beyond PRD, helping detect subtle biases that might go unnoticed. Its use in mass appraisal should be encouraged to complement more traditional measures.

The Price Related Differential (PRD) for the CoJ valuation sample was 1.02, within the IAAO's acceptable range of 0.98–1.03. PRD assesses vertical equity by comparing the spread of assessment ratios across different property values. A PRD above 1.03 indicates regressivity (high-value properties are under-assessed), while a PRD below 0.98 indicates progressivity (high-value properties are over-assessed). The CoJ's result suggests a slight regressive tendency within the permissible band. This is consistent with the PRB score and the broader interpretation of the ASR data.

In practical terms, this score implies that assessments are relatively proportional across the value spectrum. It does not suggest systemic bias but does hint at some inconsistencies, particularly within the residential classification, which the findings note had a slightly higher PRD of 1.036. This class-specific deviation may reflect modelling limitations or challenges in estimating upper-value residential properties, where heterogeneity is higher. As such, while the overall PRD is acceptable, refinement efforts should consider property-type stratification. PRD is vital in ensuring taxpayer equity, as regressivity can lead to disproportionately low taxes for affluent property owners. Continued attention to this measure supports equitable municipal finance.

The coefficient of dispersion (COD) measures horizontal equity, the consistency of assessments among properties of similar type and value. The COD result for the CoJ's GV of 2018 was 18.87%, within the IAAO's acceptable threshold of ≤20% for residential and income-producing property. This indicates a generally uniform assessment model, where properties with similar characteristics are assessed consistently. COD is particularly relevant in assessing the fairness of local taxation and citizen perceptions of justice in property tax systems.

Despite being acceptable, the COD value approaches the upper limit of the IAAO threshold, suggesting that some submarkets or property types may be less uniformly assessed than others. This could result from data quality, model specification, or market heterogeneity variations. For example, older properties or those in informal housing sectors may introduce complexity that affects uniformity. This further underscores the importance of detailed submarket analysis. Nevertheless, achieving a COD under 20% in a large and diverse municipality like Johannesburg is commendable and reflects disciplined mass appraisal methods. Future improvements could focus on narrowing this dispersion, especially within high-volume and variability residential classifications.

This study set out to introduce and demonstrate the practical application of ratio studies within South African municipal valuations, intending to discourage practices that undermine valuation accuracy and equity. Specifically, it aimed to assess the CoJ's GV of 2018 against the International Association of Assessing Officers (IAAO, 2017) Standard on Ratio Studies, establishing a benchmark framework for evaluating valuation performance. Guided by a quantitative methodology and underpinned by statistical techniques aligned with the IAAO standard, the study subjected the CoJ roll to rigorous ratio analysis. The findings confirm the applicability and relevance of the IAAO Standard in the South African municipal valuations. It also reveals that the CoJ roll demonstrates a generally acceptable level of valuation accuracy and horizontal and vertical equity.

The study underscores the importance of conducting post-valuation date ratio evaluations in South African municipalities. Institutionalising this practice will enhance the transparency and defensibility of municipal valuations, especially in light of recurring legal disputes, and promote greater public trust in property assessments. More importantly, it will encourage valuation professionals to adhere more strictly to international best practices, thereby enhancing the quality and integrity of future valuation rolls. By offering a simplified application of the IAAO standards adapted to local conditions, this research advances the agenda of localising global valuation frameworks to suit South African mass valuation practices. The study also empowers ratepayers by equipping them with a clearer understanding of valuation accuracy and equity, thus fostering more informed and constructive engagement with municipal valuation reports.

Although the study has some limitations regarding municipalities' reluctance to provide the valuation data and a small sample of post-valuation-date sales, it is especially compared to the large population of rateable properties within CoJ. However, this was mitigated through the CoJ's availing of the data for the previous valuation roll. Further mitigation relates to employing the corrective measures recommended by the IAAO (2017), which improved the sample's representativeness. These limitations do not inhibit the study from making an impact relating to its practical implications, which is what the study seeks to achieve.

The study recommends future investigations of a similar nature in other municipalities across the country, ultimately contributing to developing a more robust and accountable municipal valuation system in South Africa. It is also recommended that all municipal valuations, including the GVRs and the Supplementary Valuation Rolls (SVRs), be subjected to a post-valuation date, compulsory, and independent validation assessment to ascertain valuation accuracy and uniformity and improve public confidence in municipal valuation.